ORIGINAL_ARTICLE
Transverse Vibration for Non-uniform Timoshenko Nano-beams
In this paper, Eringen’s nonlocal elasticity and Timoshenko beam theories are implemented to analyze the bending vibration for non-uniform nano-beams. The governing equations and the boundary conditions are derived using Hamilton’s principle. A Generalized Differential Quadrature Method (GDQM) is utilized for solving the governing equations of non-uniform Timoshenko nano-beam for pinned-pinned, clamped–clamped, clamped–pinned, clamped–free, clamped–slide, and pinned-slide boundary conditions. The non-dimensional natural frequencies and the normalized mode shapes are obtained for short and stubby nano-beams where influences varying cross-section area, small scale, shear deformation, rotational moment of inertia, acceleration gravity and the self-weight of the non-uniform Timoshenko nano-beam are discussed. The present study illus-trates that the small scale effects are more significant for smaller size of nano-beam, larger nonlocal parameter and higher vibration modes. Further, the compression forces due to gravity and the self-weight of the nano-beam also like the small scale effect are reduced the magnitude of the fre-quencies of the nano-beam.
http://macs.journals.semnan.ac.ir/article_327_e19b0feb33c053f63c0ced02b44f9f4c.pdf
2015-04-01T11:23:20
2018-10-18T11:23:20
1
16
10.22075/macs.2015.327
Nonlocal elasticity
Gravity
Timoshenko
Non-uniform nano-beam
Generalized differential quadrature method
Keivan
Torabi
kvntrb@kashanu.ac.ir
true
1
Department of Solid Mechanics, Faculty of Mechanical Engineering, University of Kashan, Kashan, Iran
Department of Solid Mechanics, Faculty of Mechanical Engineering, University of Kashan, Kashan, Iran
Department of Solid Mechanics, Faculty of Mechanical Engineering, University of Kashan, Kashan, Iran
LEAD_AUTHOR
Majid
Rahi
rahimajid@gmail.com
true
2
Department of Solid Mechanics, Faculty of Mechanical Engineering, University of Kashan, Kashan, Iran
Department of Solid Mechanics, Faculty of Mechanical Engineering, University of Kashan, Kashan, Iran
Department of Solid Mechanics, Faculty of Mechanical Engineering, University of Kashan, Kashan, Iran
AUTHOR
Hassan
Afshari
afshari_hasan@yahoo.com
true
3
Department of Solid Mechanics, Faculty of Mechanical Engineering, University of Kashan, Kashan, Iran
Department of Solid Mechanics, Faculty of Mechanical Engineering, University of Kashan, Kashan, Iran
Department of Solid Mechanics, Faculty of Mechanical Engineering, University of Kashan, Kashan, Iran
AUTHOR
[1] Wang LF, Hu HY. Flexural Wave Propagation in Single-walled Carbon Nanotubes. Phys Rev B 2005; 71: 1–7.
1
[2] Eringen AC. Nonlocal Polar Elastic Continua. Int J Eng Sci 1972; 10: 1–16.
2
[3] Eringen AC, Edelen DGB. On Nonlocal Elasticity. Int J Eng Sci 1972; 10: 233–248.
3
[4] Eringen AC. On Differential Equations of Nonlocal Elasticity and Solutions of Screw Dislocation and Surface Waves. J Appl Phys 1983; 54: 4703–4710.
4
[5] Eringen AC. Nonlocal Continuum Field Theories. Springer-Verlag; 2002.
5
[6] Lu P, Lee HP, Lu C, Zhang PQ. Dynamic Properties of Flexural Beams using a Nonlocal Elasticity Model. J Appl Phys 2006; 99: 073510.
6
[7] Peddieson J, Buchanan GG, McNitt RP. Application of Nonlocal Continuum Models to Nanotechnology. Int J Eng Sci 2003; 41: 305–312.
7
[8] Reddy JN, Wang CM. Deflection Relationships between Classical and Third-order Plate Theories. Acta Mech 1998; 130(3–4): 199–208.
8
[9] Wang Q. Wave Propagation in Carbon Nanotubes via Nonlocal Continuum Mechanics. J Appl Phys 2005; 98: 124301.
9
[10] Wang Q, Varadan VK. Vibration of Carbon Nanotubes Studied using Nonlocal Continuum Mechanics. Smart Mater Struct 2006; 15: 659–666.
10
[11] Wang CM, Zhang YY, Ramesh SS, Kitipornchai S. Buckling Analysis of Micro- and Nano-rods/tubes based on Nonlocal Timoshenko Beam Theory. J Phys D Appl Phys 2006; 39: 3904–3909.
11
[12] Reddy JN. Nonlocal Theories for Bending, Buckling and Vibration of Beams. Int J Eng Sci 2007; 45: 288–307.
12
[13] Wang CM, Zhang YY, He XQ. Vibration of Nonlocal Timoshenko Beams. Nanotechnology 2007; 18: 1–9.
13
[14] Murmu T, Pradhan SC. Buckling Analysis of a Single-walled Carbon Nanotube Embedded in an Elastic Medium based on Nonlocal Elasticity and Timoshenko Beam Theory and using DQM. Physica E 2009; 41: 1232–1239.
14
[15] Şimşek M. Nonlocal Effects in The Forced Vibration of an Elastically Connected Double-carbon Nanotube System under a Moving Nanoparticle. Comput Mater Sci 2011; 50: 2112–2123.
15
[16] Lu P, Lee HP, Lu C, Zhang PQ. Application of Nonlocal Beam Models for Carbon Nanotubes. Int J Solids Struct 2007; 44: 5289–5300.
16
[17] Reddy JN. Energy Principles and Variational Methods in Applied Mechanics. John Wiley & Sons; 2002.
17
[18] Reddy JN. Theory and Analysis of Elastic Plates and Shells. Taylor & Francis; 2007.
18
[19] Reddy JN, Pang SD. Nonlocal Continuum Theories of Beams for The Analysis of Carbon Nanotubes. J Appl Phys 2008; 103: 023511.
19
[20] Hutchinson JR. Shear Coefficients for Timoshenko Beam Theory. J Appl Mech 2001; 68: 1–6.
20
[21] Meirovitch L. Fundamentals of Vibrations. McGraw-Hill; 2001.
21
[22] Ke LL, Xiang Y, Yang J, Kitipornchai S. Nonlinear Free Vibration of Embedded Double-walled Carbon Nanotubes based on Nonlocal Timoshenko Beam Theory. Comp Mater Sci 2009; 47: 409–417.
22
[23] Hijmissen JW, Horssen WTV. On Transverse Vibrations of a Vertical Timoshenko Beam. J Sound Vib 2008; 314: 161–179.
23
[24] Bellman R, Casti J. Differential Quadrature and Long-term Integration. J Math Anal Appl 1971; 34: 235–238.
24
[25] Bellman R, Kashef BG, Casti J. Differential Quadrature a Technique for The Rapid Solution of Nonlinear Partial Differential Equations. J Comput Phys 1972; 10: 40–52.
25
[26] Zong Z, Zhang Y. Advanced Differential Quadrature Methods. Chapman & Hall/CRC; 2009.
26
[27] Shu C. Differential Quadrature and Its Application in Engineering. Sprimger; 2000.
27
[28] Mestrovic M. Generalized Differential Quadrature Method for Timoshenko Beam. MIT Conf Comput Fluid Solid Mech 2003.
28
[29] Du H, Lim MK, Lin NR. Application of Generalized Differential Quadrature Method to Structural Problems. J Num Meth Engrg 1994; 37: 1881–1896.
29
[30] Du H, Lim MK, Lin NR. Application of Generalized Differential Quadrature to Vibration Analysis. J Sound Vib 1995; 181: 279–293.
30
[31] Mahmoud AA, Esmaeel RA, Nassar MM. Application of The Generalized Differential Quadrature Method to The Free Vibrations of Delaminated Beam Plates. J Eng Mech 2007; 14: 431–441.
31
[32] Wu T Y, Liu GR. A Differential Quadrature as a Numerical Method to Solve Differential Equations. Comput Mech 1999; 24: 197–205.
32
[33] Farchaly SH, Shebl MG. Exact Frequency and Mode Shape Formulae for Studying Vibration and Stability of Timoshenko Beam System. J Sound Vib 1995; 180: 205–227.
33
[34] Chen WR. Bending Vibration of Axially Loaded Timoshenko Beams with Locally Distributed Kelvin-Voigt Damping. J Sound Vib 2011; 330: 3040–3056.
34
[35] Arash B, Wang Q. A Review on The Application of Nonlocal Elastic Models in Modeling of Carbon Nanotubes and Graphenes. Comput Mater Sci 2012; 51: 303–313.
35
[36] Yang J, Ke LL, Kitipornchai S. Nonlinear Free Vibration of Single-walled Carbon Nanotubes using Nonlocal Timoshenko Beam Theory. Physica E 2010; 42: 1727–1735.
36
[1] Wang LF, Hu HY. Flexural Wave Propagation in Single-walled Carbon Nanotubes. Phys Rev B 2005; 71: 1–7.
37
[2] Eringen AC. Nonlocal Polar Elastic Continua. Int J Eng Sci 1972; 10: 1–16.
38
[3] Eringen AC, Edelen DGB. On Nonlocal Elasticity. Int J Eng Sci 1972; 10: 233–248.
39
[4] Eringen AC. On Differential Equations of Nonlocal Elasticity and Solutions of Screw Dislocation and Surface Waves. J Appl Phys 1983; 54: 4703–4710.
40
[5] Eringen AC. Nonlocal Continuum Field Theories. Springer-Verlag; 2002.
41
[6] Lu P, Lee HP, Lu C, Zhang PQ. Dynamic Properties of Flexural Beams using a Nonlocal Elasticity Model. J Appl Phys 2006; 99: 073510.
42
[7] Peddieson J, Buchanan GG, McNitt RP. Application of Nonlocal Continuum Models to Nanotechnology. Int J Eng Sci 2003; 41: 305–312.
43
[8] Reddy JN, Wang CM. Deflection Relationships between Classical and Third-order Plate Theories. Acta Mech 1998; 130(3–4): 199–208.
44
[9] Wang Q. Wave Propagation in Carbon Nanotubes via Nonlocal Continuum Mechanics. J Appl Phys 2005; 98: 124301.
45
[10] Wang Q, Varadan VK. Vibration of Carbon Nanotubes Studied using Nonlocal Continuum Mechanics. Smart Mater Struct 2006; 15: 659–666.
46
[11] Wang CM, Zhang YY, Ramesh SS, Kitipornchai S. Buckling Analysis of Micro- and Nano-rods/tubes based on Nonlocal Timoshenko Beam Theory. J Phys D Appl Phys 2006; 39: 3904–3909.
47
[12] Reddy JN. Nonlocal Theories for Bending, Buckling and Vibration of Beams. Int J Eng Sci 2007; 45: 288–307.
48
[13] Wang CM, Zhang YY, He XQ. Vibration of Nonlocal Timoshenko Beams. Nanotechnology 2007; 18: 1–9.
49
[14] Murmu T, Pradhan SC. Buckling Analysis of a Single-walled Carbon Nanotube Embedded in an Elastic Medium based on Nonlocal Elasticity and Timoshenko Beam Theory and using DQM. Physica E 2009; 41: 1232–1239.
50
[15] Şimşek M. Nonlocal Effects in The Forced Vibration of an Elastically Connected Double-carbon Nanotube System under a Moving Nanoparticle. Comput Mater Sci 2011; 50: 2112–2123.
51
[16] Lu P, Lee HP, Lu C, Zhang PQ. Application of Nonlocal Beam Models for Carbon Nanotubes. Int J Solids Struct 2007; 44: 5289–5300.
52
[17] Reddy JN. Energy Principles and Variational Methods in Applied Mechanics. John Wiley & Sons; 2002.
53
[18] Reddy JN. Theory and Analysis of Elastic Plates and Shells. Taylor & Francis; 2007.
54
[19] Reddy JN, Pang SD. Nonlocal Continuum Theories of Beams for The Analysis of Carbon Nanotubes. J Appl Phys 2008; 103: 023511.
55
[20] Hutchinson JR. Shear Coefficients for Timoshenko Beam Theory. J Appl Mech 2001; 68: 1–6.
56
[21] Meirovitch L. Fundamentals of Vibrations. McGraw-Hill; 2001.
57
[22] Ke LL, Xiang Y, Yang J, Kitipornchai S. Nonlinear Free Vibration of Embedded Double-walled Carbon Nanotubes based on Nonlocal Timoshenko Beam Theory. Comp Mater Sci 2009; 47: 409–417.
58
[23] Hijmissen JW, Horssen WTV. On Transverse Vibrations of a Vertical Timoshenko Beam. J Sound Vib 2008; 314: 161–179.
59
[24] Bellman R, Casti J. Differential Quadrature and Long-term Integration. J Math Anal Appl 1971; 34: 235–238.
60
[25] Bellman R, Kashef BG, Casti J. Differential Quadrature a Technique for The Rapid Solution of Nonlinear Partial Differential Equations. J Comput Phys 1972; 10: 40–52.
61
[26] Zong Z, Zhang Y. Advanced Differential Quadrature Methods. Chapman & Hall/CRC; 2009.
62
[27] Shu C. Differential Quadrature and Its Application in Engineering. Sprimger; 2000.
63
[28] Mestrovic M. Generalized Differential Quadrature Method for Timoshenko Beam. MIT Conf Comput Fluid Solid Mech 2003.
64
[29] Du H, Lim MK, Lin NR. Application of Generalized Differential Quadrature Method to Structural Problems. J Num Meth Engrg 1994; 37: 1881–1896.
65
[30] Du H, Lim MK, Lin NR. Application of Generalized Differential Quadrature to Vibration Analysis. J Sound Vib 1995; 181: 279–293.
66
[31] Mahmoud AA, Esmaeel RA, Nassar MM. Application of The Generalized Differential Quadrature Method to The Free Vibrations of Delaminated Beam Plates. J Eng Mech 2007; 14: 431–441.
67
[32] Wu T Y, Liu GR. A Differential Quadrature as a Numerical Method to Solve Differential Equations. Comput Mech 1999; 24: 197–205.
68
[33] Farchaly SH, Shebl MG. Exact Frequency and Mode Shape Formulae for Studying Vibration and Stability of Timoshenko Beam System. J Sound Vib 1995; 180: 205–227.
69
[34] Chen WR. Bending Vibration of Axially Loaded Timoshenko Beams with Locally Distributed Kelvin-Voigt Damping. J Sound Vib 2011; 330: 3040–3056.
70
[35] Arash B, Wang Q. A Review on The Application of Nonlocal Elastic Models in Modeling of Carbon Nanotubes and Graphenes. Comput Mater Sci 2012; 51: 303–313.
71
[36] Yang J, Ke LL, Kitipornchai S. Nonlinear Free Vibration of Single-walled Carbon Nanotubes using Nonlocal Timoshenko Beam Theory. Physica E 2010; 42: 1727–1735.
72
ORIGINAL_ARTICLE
The Effects of the Moving Load and the Attached Mass-Spring-Damper System Interactions on the Dynamic Responses of the Composite Plates: An Analytical Approach
In the current study, the effects of interactions of the moving loads and the attached mass-spring-damper systems of the composite plates on the resulting dynamic responses are investigated comprehensively, for the first time, using the classical plate theory. The solution of the coupled governing system of equations is accomplished through tracing the spatial variations using a Navier-type solution and the time variations by means of a Laplace transform. Therefore, the results are exact. The effects of various material, stiffness, and kinematic parameters of the system on the responses are investigated comprehensively and the results are illustrated graphically. Apart from the novelties presented in the modeling and solution stages, some practical conclusions have been drawn such as the fact that the amplitude of vibration increases for both the free and forced vibrations of the plate and the suspended mass, when the magnitude of suspended mass increases.
http://macs.journals.semnan.ac.ir/article_328_9f386968487e91a858c16b0fcbe44a52.pdf
2015-04-01T11:23:20
2018-10-18T11:23:20
17
30
10.22075/macs.2015.328
Composite plate
Dynamic response
Laplace transform
Attached mass-spring system Moving load
Sina
Fallahzadeh Rastehkenar
true
1
Faculty of Mechanical Engineering, K.N. Toosi University of Technology, Tehran, Iran
Faculty of Mechanical Engineering, K.N. Toosi University of Technology, Tehran, Iran
Faculty of Mechanical Engineering, K.N. Toosi University of Technology, Tehran, Iran
AUTHOR
Mohammad
Shariyat
shariyat@kntu.ac.ir
true
2
Faculty of Mechanical Engineering, K.N. Toosi University of Technology, Tehran, Iran
Faculty of Mechanical Engineering, K.N. Toosi University of Technology, Tehran, Iran
Faculty of Mechanical Engineering, K.N. Toosi University of Technology, Tehran, Iran
LEAD_AUTHOR
[1] Wong JY. Theory of Ground Vehicles. 3rd edition, John Wiley & Sons Inc.; 2001.
1
[2] Jazar RN. Vehicle Dynamics: Theory and Applications. Springer; 2008.
2
[3] Ellis BR, Ji T. Human-Structure Interaction in Vertical Vibrations. Proc Inst Civ Eng, Struct Build, 1997; 122: 1–9.
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[5] Ranjan V, Ghosh MK. Forced Vibration Response of Thin Plate with Attached Discrete Dynamic Absorbers. Thin-Wall Struct 2005; 43: 1513–1533.
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[6] Turhan O. On the Fundamental Frequency of Beams Carrying a Point Mass: Rayleigh Approximation Versus Exact Solutions. J Sound Vib 2000; 230(2): 449–459.
6
[7] Kompaz O, Telli S. Free Vibration of a Rectangular Plate Carrying Distributed Mass. J Sound Vib 2002; 251: 39–57.
7
[8] Wong WO. The Effect of Distributed Mass Loading on Plate Vibration Behavior. J Sound Vib 2002; 252: 577–583.
8
[9] Chiba M, Sugimoto T. Vibration Characteristics of a Cantilever Plate with Attached Spring-Mass System. J Sound Vib 2003; 260: 237–263.
9
[10] Li QS. An Exact Approach for Free Vibration Analysis of Rectangular Plates with Line-concentrated Mass and Elastic Line-Support. Int J Mech Sci 2003; 45: 669–685.
10
[11] Zhou D, Ji T. Free Vibration of Rectangular Plates with Continuously Distributed Spring-Mass. Int J Solids Struct 2006; 43: 6502–6520.
11
[12] Éshmatov BK, Khodzhaev DA. Dynamic Stability of a Viscoelastic Plate with Concentrated Masses. Int Appl Mech 2008; 44(2): 208–216.
12
[13] Khodzhaev DA, Éshmatov BK. Nonlinear Vibrations of a Viscoelastic Plate with Concentrated Masses. J Appl Mech Tech Phys 2007; 48(6): 905–914.
13
[14] Ciancio PM, Rossit CA, Laura PAA. Approximate Study of the free Vibrations of a Cantilever Anisotropic Plate Carrying a Concentrated Mass. J Sound Vib 2997; 302: 621–628.
14
[15] Alibeigloo A, Shakeri M, Kari MR. Free Vibration Analysis of Antisymmetric Laminated Rectangular Plates with Distributed Patch Mass Using Third-Order Shear Deformation Theory. Ocean Eng 2007; 35: 183–190.
15
[16] Watkins RJ, Santillan S, Radice J, Barton Jr O. Vibration Response of an Elastically Point-Supported Plate with Attached Masses. Thin-Wall Struct 2010; 48: 519–527.
16
[17] Malekzadeh K, Tafazoli S, Khalili SMR. Free Vibrations of Thick Rectangular Composite Plate with Uniformly Distributed Attached Mass Including Stiffness Effect. J Compos Mater 2010; 44: 2897–2918.
17
[18] Amabili M, Carra S. Experiments and Simulations for Large-Amplitude Vibrations of Rectangular Plates Carrying Concentrated Masses. J Sound Vib 2012; 331: 155–166.
18
[19] Agrawal OP, Stanisic MM, Saigal S. Dynamic Responses of Orthotropic Plates Under Moving Masses. Eng Arch 1988; 58: 9–14.
19
[20] Taheri MR, Ting EC. Dynamic Response of Plates to Moving Loads Finite Element Method. Comput Struct 1990; 34: 509–521.
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[21] Zaman MM, Taheri R., Alavappillaix A. Dynamic Response of a Thick Plate on Viscoelastic Foundation to Moving Loads. Int J Numer Ana Meth Geomech 1991; 15: 627–647.
21
[22] de Faria AR, Oguamanam DCD. Finite Element Analysis of the Dynamic Response of Plates Under Traversing Loads Using Adaptive Meshes. Thin-Wall Struct 2004; 42: 1481–1493.
22
[23] Wu JJ. Dynamic analysis of a rectangular plate under a moving line load using scale beams and scaling laws. Comput Struct 2005; 83: 1646–1658.
23
[24] Sun L. Dynamics of plate generated by moving harmonic loads. J Appl Mech 2005; 72: 772–777.
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[25] Malekzadeh P, Fiouz AR, Razi H. Three-Dimensional Dynamic Analysis of Laminated Composite Plates Subjected to Moving Load. Compos Struct 2009; 90: 105–114.
25
[26] Reddy JN. Mechanics of Laminated Composite Plate: Theory and Analysis. CRC Press; 1997.
26
[27] Spiegel MR. Advanced Mathematics for Engineers and Scientists. McGraw-Hill; 1971.
27
ORIGINAL_ARTICLE
Atomic Simulation of Temperature Effect on the Mechanical Properties of Thin Films
The molecular dynamic technique was used to simulate the nano-indentation test on the thin films of silver, titanium, aluminum and copper which were coated on the silicone substrate. The mechanical properties of the selected thin films were studied in terms of the temperature. The temperature was changed from 193 K to 793 K with an increment of 100 K. To investigate the effect of temperature on the mechanical properties, two different ways including step by step and continuous ways, were used. The temperature in the indentation region was controlled and the effect of temperature increase due to the friction between the indenter and the film was taken into account. The temperature effects on the material structure, piling-up and sinking-in phenomena were also considered. The results show that the elasticity modulus and hardness of thin films decrease by increasing temperature. These mechanical properties also decreased due to the increase in temperature, in the indentation region, which in turn was due to the interaction between the indenter and the thin film.
http://macs.journals.semnan.ac.ir/article_329_a96542613abc853af54a7424edde5d29.pdf
2015-04-01T11:23:20
2018-10-18T11:23:20
31
38
10.22075/macs.2015.329
Thin film coatings
Molecular dynamic simulation
Nano-indentation test
Film temperature
Mechanical Properties
M.R.
Ayatollahi
m.ayat@iust.ac.ir
true
1
School of Mechanical Engineering, Iran University of Science and Technology, Tehran, Iran
School of Mechanical Engineering, Iran University of Science and Technology, Tehran, Iran
School of Mechanical Engineering, Iran University of Science and Technology, Tehran, Iran
LEAD_AUTHOR
A.S.
Rahimi
saleh_rahimi@mecheng.iust.ac.ir
true
2
School of Mechanical Engineering, Iran University of Science and Technology, Tehran, Iran
School of Mechanical Engineering, Iran University of Science and Technology, Tehran, Iran
School of Mechanical Engineering, Iran University of Science and Technology, Tehran, Iran
AUTHOR
A.
Karimzadeh
true
3
School of Mechanical Engineering, Iran University of Science and Technology, Tehran, Iran
School of Mechanical Engineering, Iran University of Science and Technology, Tehran, Iran
School of Mechanical Engineering, Iran University of Science and Technology, Tehran, Iran
AUTHOR
[1] Ashurst WR, Carraro C, Maboudian R, Frey W. Wafer Level Anti-Stiction Coatings for MEMS. Sens Actuators A 2003; 104: 213–221.
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[2] Bourhis ELE. Indentation Mechanics and
2
its Application to Thin Film Characterization. Vacuum 2011; 82: 1353–1359.
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[3] Radhakrishnan G, Robertson RE, Adams PM, Cole RC. Integrated TiC Coatings for Moving MEMS. Thin Solid Films 2002; 420: 553–564.
4
[4] Cao Y, Allameh SM, Nankivil D, Sethiaraj S, Otiti T, Soboyejo W. Nanoindentation Measurements of the Mechanical Properties of Polycrystalline Au and Ag Thin Films on Silicon Substrates: Effects of Grain Size and Film Thickness. Mater Sci Eng A 2006; 427: 232–240.
5
[5] Hong SH, Kim KS, Kim YM, Hahn JH, Lee CS, Park JH. Characterization of Elastic Moduli of Cu Thin Films using Nano-indentation Technique. Compos Sci Technol 2005; 65: 1401–1402.
6
[6] Sharpe WN, Yuan B, Edwards RL. A New Technique for Measuring the Mechanical Properties of Thin Films. J Micro-Electro-Mechanical Syst 1997; 6 (3): 193–198.
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[7] Minfray C, Martin JM, Esnouf C, Mogne T Le, Kersting R, Hagenhoff. A Multi-technique Approach of Tribo-film Characterization. Thin Solid Films 2004; 447: 272–277.
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[8] Oliver WC, Pharr GM. An Improved Technique for Determining Hardness and Elastic Modulus using Load and Displacement Sensing Indentation Experiments. J Mater Res 1992; 7(6): 1564–1583.
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[9] Burnett PJ, Rickerby DS. The Mechanical Properties of Wear Resistant Coatings: Modeling of Hardness Behavior. Thin Solid Films 1987; 148: 51.
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[10] Hay JL, Oliver WC, Bolshakov A, Pharr GM. Using the Ratio of Loading Slope and Elastic Stiffness to Predict Pile-up and Constraint Factor during Indentation. MRS Symp Proc, Fundamentals of Nano-indentation and Nano-tribiloy 1998.
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[11] Hay JC, Pharr GM. Critical Issues in Measuring the Mechanical Properties of Hard Films on Soft Substrates by Nano-indentation Techniques. Mater Res Symp Proc 1998; 505: 65–70.
12
[12] Tang KC, Arnell RD. Determination of Coating Mechanical Properties using Spherical Indenters. Thin Solid Films 1999; 356: 263–269.
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[13] Saha R, Xue ZY, Huang Y, Nix WD. Indentation of a Soft Metal Film on a Hard Substrate: Strain Gradient Hardening Effects. J Mech Phys Solids 2001; 49: 1997–2014.
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[14] Saha R, Nix WD. Effects of The Substrate on The Determination of Thin Film Mechanical Properties by Nano-indentation. Acta Mater 2002; 50: 23–38.
15
[15] Seung Min Han , Ranjana Saha, William D. Nix. Determining Hardness of Thin Films in Elastically Mismatched Film-on-substrate Systems using Nano-indentation. Acta Mater 2006; 54: 1571–1581.
16
[16] Szlufarska I, Kalia R, Nakano A, Vashishta P. Atomistic Mechanisms of Amorphization during Nano-indentation of SiC: A Molecular Dynamics Study. Phys Rev B 2005; 71: 1–11.
17
[17] Chen HP, Kalia RK, Nakano A, Vashishta P, Szlufarska I. Multi-milion-atom Nano-indentation Simulation of Crystalline Sillicon Carbide: Orientation Dependence and Anisotropic Pileup. J Appl Phys 2007; 102(6): 063514.
18
[18] Zaminpayma E. Computer Simulation on TiO2 Nanostructure Films and Experimental Study Using Sol–Gel Method. J Clust Sci 2009; 20: 641–649.
19
[19] Shi YF, Falk ML. Structural Transformation and Localization during Simulated Nano-indentation of A Non-crystalline Metal Film. Phys Rev Let 2005; 95: 1–5.
20
[20] Peng P, Liao G, Shi T, Tang Z, Gao Y. Molecular Dynamic Simulations of Nano-indentation in Aluminum Thin Film on Silicon Substrate. Appl Surf Sci 2010; 256: 6284–6290.
21
[21] Hwang SF, Li YH, Hong ZH. Molecular Dynamic Simulation for Cu Cluster Deposition on Si Substrate. Comput Mater Sci 2012; 56: 85–94.
22
[22] Gerolf Z, Alexander H, Herbert H. Pair vs Many-body Potentials: Influence on Elastic and Plastic Behavior in Nano-indentation of FCC Metals. J Mech Phys Solids 2009; 57: 1514–1526.
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[23] Yan Y, Sun T, Dong S, Liang Y. Study on Effects of The Feed on AFM-based Nano-lithography Process using MD Simulation. Comput Mater Sci 2007; 40: 1–5.
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[24] Fang T, Wu J. Molecular Dynamics Simulations on Nano-indentation Mechanisms of Multilayered Films. Comput Mater Sci 2008; 43: 785–790.
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[26] Ayatollahi MR, Rahimi A,Karimzadeh A. Study on Effect of Thickness of Thin Films on Mechanical Properties Measured by Nano-indentation and Comparison by The Molecular Dynamics (MD) Simulation. The Bi-Annual International Conference on Experimental Solid Mechanics and Dynamics (X-Mech) Tehran, Iran; 2014.
27
[27] Dasilva J, Rino P. Atomistic Simulation of The Deformation Mechanism during Nano-indentation of Gamma Titanium Aluminide. Comput Mater Sci 2012; 62: 1–5.
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[28] Wymyslowski A, Dowhan L. Application of Nano-indentation Technique for Investigation of Elasto-plastic Properties of The Selected Thin Film Materials. Micro-Electronics Reliab 2013; 53: 443–451.
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[29] Bolshakov A, Pharr GM. Influences of Pileup on the Measurement of Mechanical Properties by Load and Depth Sensing Indentation Techniques. J Mater Res 1998; 13: 1049–1058.
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[30] Liang L, Li M, Qin F, Wei Y. Temperature Effect on Elastic Modulus of Thin Films and Nano-crystals, Philos Mag 2013; 93(6): 574–583.
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[32] Hung Z, Gu LY, Weertman JR. Temperature Dependence of Hardness of Nano-crystalleve Copper in Low-temperature Range. Scripta Materialia 1997; 37: 1071–1075.
33
[1] Ashurst WR, Carraro C, Maboudian R, Frey W. Wafer Level Anti-Stiction Coatings for MEMS. Sens Actuators A 2003; 104: 213–221.
34
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[4] Cao Y, Allameh SM, Nankivil D, Sethiaraj S, Otiti T, Soboyejo W. Nanoindentation Measurements of the Mechanical Properties of Polycrystalline Au and Ag Thin Films on Silicon Substrates: Effects of Grain Size and Film Thickness. Mater Sci Eng A 2006; 427: 232–240.
38
[5] Hong SH, Kim KS, Kim YM, Hahn JH, Lee CS, Park JH. Characterization of Elastic Moduli of Cu Thin Films using Nano-indentation Technique. Compos Sci Technol 2005; 65: 1401–1402.
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[6] Sharpe WN, Yuan B, Edwards RL. A New Technique for Measuring the Mechanical Properties of Thin Films. J Micro-Electro-Mechanical Syst 1997; 6 (3): 193–198.
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[7] Minfray C, Martin JM, Esnouf C, Mogne T Le, Kersting R, Hagenhoff. A Multi-technique Approach of Tribo-film Characterization. Thin Solid Films 2004; 447: 272–277.
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[8] Oliver WC, Pharr GM. An Improved Technique for Determining Hardness and Elastic Modulus using Load and Displacement Sensing Indentation Experiments. J Mater Res 1992; 7(6): 1564–1583.
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[9] Burnett PJ, Rickerby DS. The Mechanical Properties of Wear Resistant Coatings: Modeling of Hardness Behavior. Thin Solid Films 1987; 148: 51.
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[10] Hay JL, Oliver WC, Bolshakov A, Pharr GM. Using the Ratio of Loading Slope and Elastic Stiffness to Predict Pile-up and Constraint Factor during Indentation. MRS Symp Proc, Fundamentals of Nano-indentation and Nano-tribiloy 1998.
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[11] Hay JC, Pharr GM. Critical Issues in Measuring the Mechanical Properties of Hard Films on Soft Substrates by Nano-indentation Techniques. Mater Res Symp Proc 1998; 505: 65–70.
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[12] Tang KC, Arnell RD. Determination of Coating Mechanical Properties using Spherical Indenters. Thin Solid Films 1999; 356: 263–269.
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[13] Saha R, Xue ZY, Huang Y, Nix WD. Indentation of a Soft Metal Film on a Hard Substrate: Strain Gradient Hardening Effects. J Mech Phys Solids 2001; 49: 1997–2014.
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[14] Saha R, Nix WD. Effects of The Substrate on The Determination of Thin Film Mechanical Properties by Nano-indentation. Acta Mater 2002; 50: 23–38.
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[15] Seung Min Han , Ranjana Saha, William D. Nix. Determining Hardness of Thin Films in Elastically Mismatched Film-on-substrate Systems using Nano-indentation. Acta Mater 2006; 54: 1571–1581.
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[16] Szlufarska I, Kalia R, Nakano A, Vashishta P. Atomistic Mechanisms of Amorphization during Nano-indentation of SiC: A Molecular Dynamics Study. Phys Rev B 2005; 71: 1–11.
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[17] Chen HP, Kalia RK, Nakano A, Vashishta P, Szlufarska I. Multi-milion-atom Nano-indentation Simulation of Crystalline Sillicon Carbide: Orientation Dependence and Anisotropic Pileup. J Appl Phys 2007; 102(6): 063514.
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[18] Zaminpayma E. Computer Simulation on TiO2 Nanostructure Films and Experimental Study Using Sol–Gel Method. J Clust Sci 2009; 20: 641–649.
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[19] Shi YF, Falk ML. Structural Transformation and Localization during Simulated Nano-indentation of A Non-crystalline Metal Film. Phys Rev Let 2005; 95: 1–5.
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[20] Peng P, Liao G, Shi T, Tang Z, Gao Y. Molecular Dynamic Simulations of Nano-indentation in Aluminum Thin Film on Silicon Substrate. Appl Surf Sci 2010; 256: 6284–6290.
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[21] Hwang SF, Li YH, Hong ZH. Molecular Dynamic Simulation for Cu Cluster Deposition on Si Substrate. Comput Mater Sci 2012; 56: 85–94.
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[22] Gerolf Z, Alexander H, Herbert H. Pair vs Many-body Potentials: Influence on Elastic and Plastic Behavior in Nano-indentation of FCC Metals. J Mech Phys Solids 2009; 57: 1514–1526.
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[23] Yan Y, Sun T, Dong S, Liang Y. Study on Effects of The Feed on AFM-based Nano-lithography Process using MD Simulation. Comput Mater Sci 2007; 40: 1–5.
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[24] Fang T, Wu J. Molecular Dynamics Simulations on Nano-indentation Mechanisms of Multilayered Films. Comput Mater Sci 2008; 43: 785–790.
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[25] Tersoff J. Modeling Solid-State Chemistry: Interatomic Potentials for Multi-component Systems. Phys Rev 1989; 39: 5566.
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[26] Ayatollahi MR, Rahimi A,Karimzadeh A. Study on Effect of Thickness of Thin Films on Mechanical Properties Measured by Nano-indentation and Comparison by The Molecular Dynamics (MD) Simulation. The Bi-Annual International Conference on Experimental Solid Mechanics and Dynamics (X-Mech) Tehran, Iran; 2014.
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[27] Dasilva J, Rino P. Atomistic Simulation of The Deformation Mechanism during Nano-indentation of Gamma Titanium Aluminide. Comput Mater Sci 2012; 62: 1–5.
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[28] Wymyslowski A, Dowhan L. Application of Nano-indentation Technique for Investigation of Elasto-plastic Properties of The Selected Thin Film Materials. Micro-Electronics Reliab 2013; 53: 443–451.
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[29] Bolshakov A, Pharr GM. Influences of Pileup on the Measurement of Mechanical Properties by Load and Depth Sensing Indentation Techniques. J Mater Res 1998; 13: 1049–1058.
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[30] Liang L, Li M, Qin F, Wei Y. Temperature Effect on Elastic Modulus of Thin Films and Nano-crystals, Philos Mag 2013; 93(6): 574–583.
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[31] Lebedev AB, Burenkov YA, Romanov AE, Kopylov VI, Filonenko VP, Gryaznov VG.Softening of The Elastic Modulus in Sub-microcrystalline copper. Mater Sci Eng A 1995; 203: 165–170.
65
[32]Hung Z, Gu LY, Weertman JR. Temperature Dependence of Hardness of Nano-crystalleve Copper in Low-temperature Range. Scripta Materialia 1997; 37: 1071–1075.
66
ORIGINAL_ARTICLE
The Structural and Mechanical Properties of Al-2.5%wt. B4C Met-al Matrix Nano-composite Fabricated by the Mechanical Alloying
In this study, aluminum (Al) matrix reinforced with micro-particles (30 µm) and nano-particles (50 nm) boron carbide (B4C) were used to prepare Al-2.5%wt., B4C nano-composite and micro-composite, respectively, using mechanical alloying method. The mixed powders were mechanically milled at 5, 10, 15 and 20 hrs. The XRD results indicated that the crystallite sizes of both the micro-composite and nano-composite matrix decreased with increasing milling time, showing 55 nm and 40 nm, respectively. Mechanical testing results showed an increase in the flexural strength from 98 to 164 and 115 to 180 MPa, and an increase in the hardness from 60 to 118 and 75 to 130 HV for micro-composite and nano-composite, respectively. The results indicate that the strength and hardness of the nano-composite are higher than those of the micro-composite due to the presence of the fine particles.
http://macs.journals.semnan.ac.ir/article_330_86c2f96d56faff2ec824d263b8d71a33.pdf
2015-04-01T11:23:20
2018-10-18T11:23:20
39
44
10.22075/macs.2015.330
Mechanical Properties
Al/B4C nano-composite
Mechanical alloying
S.
Alalhessabi
true
1
Department of Materials Engineering, Islamic Azad University, Shahrood Branch, Shahrood, Iran
Department of Materials Engineering, Islamic Azad University, Shahrood Branch, Shahrood, Iran
Department of Materials Engineering, Islamic Azad University, Shahrood Branch, Shahrood, Iran
AUTHOR
S.A.
Manafi
true
2
Department of Materials Engineering, Islamic Azad University, Shahrood Branch, Shahrood, Iran
Department of Materials Engineering, Islamic Azad University, Shahrood Branch, Shahrood, Iran
Department of Materials Engineering, Islamic Azad University, Shahrood Branch, Shahrood, Iran
AUTHOR
E.
Borhani
true
3
Department of Nano-Technology, Semnan University, Semnan, Iran
Department of Nano-Technology, Semnan University, Semnan, Iran
Department of Nano-Technology, Semnan University, Semnan, Iran
LEAD_AUTHOR
[1] Fogagnolo JB, Robert MH, Ruiz-Navas EM, Torralba JM. 6061 Al Reinforced with Zirconium Diboride Particles Processed by Conventional Powder Metallurgy and Mechanical Alloying. J Mater Sci 2004; 39: 127–132.
1
[2] Canakci A, Varol T. Production and Microstructure of AA2024-B4C Metal Matrix Composites by Mechanical Alloying Method. Usak University J Mater Sci 2012; 1: 15–22.
2
[3] Fogagnolo JB, Velasco F, Robert MH, Torralba JM. Effect of Mechanical Alloying on The Morphology, Microstructure and Properties of Aluminium Matrix Composite Powders. Mater Sci Eng A 2003; 342: 131–143.
3
[4] Abdoli H, Salehi E, Faranoush H, Pourazarang K. Evolutions during Synthesis of Al-AlN Nanostructured Composite Powder by Mechanical Alloying. J Alloy Compd 2008; 461: 166–172.
4
[5] Kaczmar JW, Pietrzak K, Wlosinsik W. The Production and Application of Metal Matrix Composite Materials. J Mater Process Technol 2000; 106: 58–67.
5
[6] Toptan F, Kilicarslan A, Karaaslan A, Cigdem M, Kreti I. Processing and Microstructural Characterisation of AA 1070 and AA 6063 Matrix B4Cp Reinforced Composites. Mater Des 2010; 31: 87–91.
6
[7] Mohanty RM, Balasubramanian K, Seshadri SK. Boron Carbide-Reinforced Alumnium 1100 Matrix Composites: Fabrication and Properties. Mater Sci Eng A 2008; 498: 42–52.
7
[8] Topcu I, Gulsov HO, Kadioglu N, Gulluoglu AN. Processing and Mechanical Properties of B4C Reinforced Al Matrix Composites. J Alloy Compd 2009; 482: 516–521.
8
[9] Shorowordi KM, Haseeb ASMA, Celis JP. Tribo-surface Characteristics of Al-B4C and Al-SiC Composites Worn under Different Contact Pressures. Wear 2006; 261: 634–641.
9
[10] Lee KB, Sim HS, Cho SY, Kwon H. Tensile Properties of 5052 Al Matrix Composites Reinforced with B4C. Metall Mater Trans A 2001; 32: 2142–2147.
10
[11] Thevenot F. Boron Carbide: A Comprehensive Review. J Eur Ceram Soc 1990; 6: 205–225.
11
[12] Kleiner S, Bertocco F, Khalid FA, Beffort O. Decomposition of Process Control Agent during Mechanical Milling and Its Influence on Displacement Reactions in The Al-TiO2 System. J Mater Chem Phys 2005; 89: 362–366.
12
[13] Fathy A, Wagih A, Abd El-Hamid M, Hassan AA. Effect of Mechanical Milling on the Morphology and Strutural Evaluation of Al-Al2O3 Nano-composite Powders. Int J Eng Trans A 2014, 27: 625–632.
13
[14] Sajjadi SA, Zebarjad SM. Influence of Nano-Size Al2O3 Weight Percent on The Microstructure and Mechanical Properties of Al-Matrix Nanocomposite. Powder Metall 2010; 471: 88–94.
14
[15] Khakbiz M, Akhlaghi F. Synthesis and Structural Characterization of Al-B4C Nano-composite Powders by Mechanical Alloying. J Alloy Compd 2009; 479: 334–341.
15
[16] Sharifi EM, Karimzadeh F, Enayati MH. Fabrication and Evaluation of Mechanical and Tribological Properties of Boron Carbide Re-inforced Aluminum Matrix Nanocomposites. Mater Des 2011; 32: 3263–3271.
16
[17] Cvijovic I, Vilotijevic M, Milan TJ. Characterization of Prealloyed Copper Powders Treated in High Energy Ball Mill. Mater Charact 2006; 57: 94–99.
17
[18] Mahboob H, Sajjadi SA, Zebarjad SM. Nanocomposite by Mechanical Alloying and Evaluation of the Effect of Ball Milling Time on the Microstructure and Mechanical Properties. In: Proceedings of International Conference on MEMS and Nanotechnology; 2008.
18
[19] Hull D, Bacon DJ. Introduction to Dislocations, Butterworth Heinemann Ltd.; 2001.
19
[20] Alizadeh A, Taheri-Nassaj E,Baharvandi HR. Preparation and Investigation of Al-4wt% B4C Nanocomposite Powders using Mechanical Milling. J Mater Sci 2011; 34: 1039–1048.
20
[21] Casati R, Vedani M. Metal Matrix Composites Reinforced by Nano-Particles. J Metals 2014; 4: 65–83.
21
[22] Borhani E, Jafarian HR, Adachi H, Terada D, Tsuji N. Annealing Behaviour of Solution Treated and Aged Al-0.2wt% Sc Deformed by ARB. Mater Sci Forum 2011; 667–669: 211–216.
22
[23] Moona M, Kim S, Jang J, Lee J. Orowan Strengthening Effect on The Nanoindentation Hardness of The Ferrite Matrix in Microalloyed Steels. Mater Sci Eng A 2008; 487(1–2): 552–557.
23
[1] Fogagnolo JB, Robert MH, Ruiz-Navas EM, Torralba JM. 6061 Al Reinforced with Zirconium Diboride Particles Processed by Conventional Powder Metallurgy and Mechanical Alloying. J Mater Sci 2004; 39: 127–132.
24
[2] Canakci A, Varol T. Production and Microstructure of AA2024-B4C Metal Matrix Composites by Mechanical Alloying Method. Usak University J Mater Sci 2012; 1: 15–22.
25
[3] Fogagnolo JB, Velasco F, Robert MH, Torralba JM. Effect of Mechanical Alloying on The Morphology, Microstructure and Properties of Aluminium Matrix Composite Powders. Mater Sci Eng A 2003; 342: 131–143.
26
[4] Abdoli H, Salehi E, Faranoush H, Pourazarang K. Evolutions during Synthesis of Al-AlN Nanostructured Composite Powder by Mechanical Alloying. J Alloy Compd 2008; 461: 166–172.
27
[5] Kaczmar JW, Pietrzak K, Wlosinsik W. The Production and Application of Metal Matrix Composite Materials. J Mater Process Technol 2000; 106: 58–67.
28
[6] Toptan F, Kilicarslan A, Karaaslan A, Cigdem M, Kreti I. Processing and Microstructural Characterisation of AA 1070 and AA 6063 Matrix B4Cp Reinforced Composites. Mater Des 2010; 31: 87–91.
29
[7] Mohanty RM, Balasubramanian K, Seshadri SK. Boron Carbide-Reinforced Alumnium 1100 Matrix Composites: Fabrication and Properties. Mater Sci Eng A 2008; 498: 42–52.
30
[8] Topcu I, Gulsov HO, Kadioglu N, Gulluoglu AN. Processing and Mechanical Properties of B4C Reinforced Al Matrix Composites. J Alloy Compd 2009; 482: 516–521.
31
[9] Shorowordi KM, Haseeb ASMA, Celis JP. Tribo-surface Characteristics of Al-B4C and Al-SiC Composites Worn under Different Contact Pressures. Wear 2006; 261: 634–641.
32
[10] Lee KB, Sim HS, Cho SY, Kwon H. Tensile Properties of 5052 Al Matrix Composites Reinforced with B4C. Metall Mater Trans A 2001; 32: 2142–2147.
33
[11] Thevenot F. Boron Carbide: A Comprehensive Review. J Eur Ceram Soc 1990; 6: 205–225.
34
[12] Kleiner S, Bertocco F, Khalid FA, Beffort O. Decomposition of Process Control Agent during Mechanical Milling and Its Influence on Displacement Reactions in The Al-TiO2 System. J Mater Chem Phys 2005; 89: 362–366.
35
[13] Fathy A, Wagih A, Abd El-Hamid M, Hassan AA. Effect of Mechanical Milling on the Morphology and Strutural Evaluation of Al-Al2O3 Nano-composite Powders. Int J Eng Trans A 2014, 27: 625–632.
36
[14] Sajjadi SA, Zebarjad SM. Influence of Nano-Size Al2O3 Weight Percent on The Microstructure and Mechanical Properties of Al-Matrix Nanocomposite. Powder Metall 2010; 471: 88–94.
37
[15] Khakbiz M, Akhlaghi F. Synthesis and Structural Characterization of Al-B4C Nano-composite Powders by Mechanical Alloying. J Alloy Compd 2009; 479: 334–341.
38
[16] Sharifi EM, Karimzadeh F, Enayati MH. Fabrication and Evaluation of Mechanical and Tribological Properties of Boron Carbide Re-inforced Aluminum Matrix Nanocomposites. Mater Des 2011; 32: 3263–3271.
39
[17] Cvijovic I, Vilotijevic M, Milan TJ. Characterization of Prealloyed Copper Powders Treated in High Energy Ball Mill. Mater Charact 2006; 57: 94–99.
40
[18] Mahboob H, Sajjadi SA, Zebarjad SM. Nanocomposite by Mechanical Alloying and Evaluation of the Effect of Ball Milling Time on the Microstructure and Mechanical Properties. In: Proceedings of International Conference on MEMS and Nanotechnology; 2008.
41
[19] Hull D, Bacon DJ. Introduction to Dislocations, Butterworth Heinemann Ltd.; 2001.
42
[20] Alizadeh A, Taheri-Nassaj E,Baharvandi HR. Preparation and Investigation of Al-4wt% B4C Nanocomposite Powders using Mechanical Milling. J Mater Sci 2011; 34: 1039–1048.
43
[21] Casati R, Vedani M. Metal Matrix Composites Reinforced by Nano-Particles. J Metals 2014; 4: 65–83.
44
[22] Borhani E, Jafarian HR, Adachi H, Terada D, Tsuji N. Annealing Behaviour of Solution Treated and Aged Al-0.2wt% Sc Deformed by ARB. Mater Sci Forum 2011; 667–669: 211–216.
45
Moona M, Kim S, Jang J, Lee J. Orowan Strengthening Effect on The Nanoindentation Hardness of The Ferrite Matrix in Microalloyed Steels. Mater Sci Eng A 2008; 487(1–2): 552–557.
46
ORIGINAL_ARTICLE
Static Flexure of Soft Core Sandwich Beams using Trigonometric Shear Deformation Theory
This study deals with the applications of a trigonometric shear deformation theory considering the effect of the transverse shear deformation on the static flexural analysis of the soft core sandwich beams. The theory gives realistic variation of the transverse shear stress through the thickness, and satisfies the transverse shear stress free conditions at the top and bottom surfaces of the beam. The theory does not require a problem-dependent shear correction factor. The governing differential equations and the associated boundary conditions of the present theory are obtained using the principle of the virtual work. The closed-form solutions for the beams with simply supported boundary conditions are obtained using Navier solution technique. Several types of sandwich beams are considered for the detailed numerical study. The axial displacement, transverse displacement, normal and transverse shear stresses are presented in a non-dimensional form and are compared with the previously published results. The transverse shear stress continuity is maintained at the layer interface, using the equilibrium equations of elasticity theory.
http://macs.journals.semnan.ac.ir/article_331_b17ff7d54460e69a4422a27ee81b81ab.pdf
2015-04-01T11:23:20
2018-10-18T11:23:20
45
53
10.22075/macs.2015.331
Laminated beam
Soft core
Sandwich beam
Flexure
Trigonometric shear deformation theory
Atteshamuddin S.
Sayyad
attu_sayyad@yahoo.co.in
true
1
Department of Civil Engineering, SRES’s College of Engineering, Savitribai Phule Pune University, Kopargaon, Maharashtra, India
Department of Civil Engineering, SRES’s College of Engineering, Savitribai Phule Pune University, Kopargaon, Maharashtra, India
Department of Civil Engineering, SRES’s College of Engineering, Savitribai Phule Pune University, Kopargaon, Maharashtra, India
LEAD_AUTHOR
Y.M.
Ghugal
ghugal@rediffmail.com
true
2
Department of Applied Mechanics, Government College of Engineering, Karad, Maharashtra, India
Department of Applied Mechanics, Government College of Engineering, Karad, Maharashtra, India
Department of Applied Mechanics, Government College of Engineering, Karad, Maharashtra, India
AUTHOR
[1] Timoshenko SP. On the Correction for Shear of the Differential Equation for Transverse Vibrations of Prismatic Bars. Philos Mag 1921; 41(6): 742–746.
1
[2] Lo KH, Christensen RM, Wu EM. A High-order Theory of Plate Deformation, Part-1: Homogeneous Plates, ASME J Appl Mech 1977; 44: 663–668.
2
[3] Lo KH, Christensen RM, Wu EM. A High-order Theory of Plate Deformation, Part-2: Laminated Plates, ASME J Appl Mech 1977; 44: 669–676.
3
[4] Levinson M. A New Rectangular Beam Theory. J Sound Vib 1981; 74: 81–87.
4
[5] Reddy JN. A Simple Higher Order Theory for Laminated Composite Plates. ASME J Appl Mech 1984; 51: 745–752.
5
[6] Touratier M. An Efficient Standard Plate Theory. Int J Eng Sci 1991; 29(8): 901–916.
6
[7] Soldatos KP. A Transverse Shear Deformation Theory for Homogeneous Monoclinic Plates. Acta Mech 1992; 94: 195–200.
7
[8] Karama M, Afaq KS, Mistou S. A Refinement of Ambartsumian Multi-layer Beam Theory. Comput Struct 2008; 86: 839–849.
8
[9] Sayyad AS. Comparison of Various Refined Beam Theories for the Bending and Free Vibration Analysis of Thick Beams. Appl Comput Mech 2011; 5: 217–230.
9
[10] Sayyad AS., Ghugal YM, Borkar RR. Flexural Analysis of Fibrous Composite Beams under Various Mechanical Loadings using Refined Shear Deformation Theories. Compos Mech Comput Appl 2014; 5(1): 1–19.
10
[11] Sayyad AS. Static Flexure and Free Vibration Analysis of Thick Isotropic Beams using Different Higher Order Shear Deformation Theories. Int J Appl Math Mech 2012; 8(14): 71–87.
11
[12] Mechab I, Tounsi A, Benatta MA, Bedia EAA. Deformation of Short Composite Beam using Refined Theories. J Math Anal Appl 2008; 346: 468–479.
12
[13] Carrera E, Giunta G. Refined Beam Theories based on A Unified Formulation, Int J Appl Mech 2010; 2(1): 117–143.
13
[14] Carrera E, Filippi M, Zappino E. Laminated Beam Analysis by Polynomial, Trigonometric, Exponential and Zig-zag Theories. Eur J Mech A Solids 2013; 41: 58–69.
14
[15] Carrera E, Filippi M, Zappino E. Free Vibration Analysis of Laminated Beam by Polynomial, Trigonometric, Exponential and Zig-zag Theories. J Compos Mater 2014; 48(19): 2299–2316.
15
[16] Giunta G, Metla N, Belouettar S, Ferreira AJM, Carrera E. A Thermo-Mechanical Analysis of Isotropic and Composite Beams via Collocation with Radial Basis Functions. J Therm Stresses 2013; 36: 1169–1199.
16
[17] Chakrabarti A, Chalak HD, Iqbal MA, Sheikh AH. A New FE Model based on Higher Order Zigzag Theory for the Analysis of Laminated Sandwich Beam with Soft Core. Compos Struct 2011; 93: 271–279.
17
[18] Chalak HD, Chakrabarti A, Iqbal MA, Sheikh AH. Vibration of Laminated Sandwich Beams Having Soft Core, J Vib Control 2011; 18(10): 1422–1435.
18
[19] Gherlone M, Tessler A, Sciuva MD. A C0 Beam Elements based on the Refined Zig-zag Theory for Multi-layered Composite and Sandwich Laminates. Compos Struct 2011; 93: 2882–2894.
19
[20] Shimpi RP, Ghugal YM. A New Layerwise Trigonometric Shear Deformation Theory for Two-layered Cross-ply Beams. Compos Sci Technol 2001; 61: 1271–1283.
20
[21] Ghugal YM, Shinde SB. Flexural Analysis of Cross-ply Laminated Beams using Layerwise Trigonometric Shear Deformation Theory. Latin Am J Solids Struct 2013; 10(4): 675–705.
21
[22] Arya H. A New Zig-zag Model for Laminated Composite Beams: Free Vibration Analysis. J Sound Vib 2003; 264: 485–490.
22
[23] Sayyad AS, Ghugal YM. Effect of Transverse Shear and Transverse Normal Strain on Bending Analysis of Cross-ply Laminated Beams. Int J Appl Math Mech 2011; 7(12): 85–118.
23
[24] Mantari JL, Oktem AS, Soares CG. A New Trigonometric Shear Deformation Theory for Isotropic, Laminated Composite and Sandwich Plates. Int J Solids Struct 2012; 49(1): 43–53.
24
[25] Ferreira AJM, Roque CMC, Jorge RMN. Analysis of Composite Plates by Trigonometric Shear Deformation Theory and Multi-quadrics. Comput Struct 2005; 83(27): 2225–2237.
25
[26] Zenkour AM. Benchmark Trigonometric and 3-D Elasticity Solutions for an Exponentially Graded Thick Rectangular Plate. Arch Appl Mech 2007; 77: 197–214.
26
[27] Sayyad AS, Ghugal YM, Naik NS. Bending Analysis of Laminated Composite and Sandwich Beams according to Refined Trigonometric Beam Theory. Curved and Layered Struct 2015; 2: 279–289.
27
[28] Dahake AG, Ghugal YM. A Trigonometric Shear Deformation Theory for Flexure of Thick Beams. Procedia Eng 2013; 51: 1–7.
28
[29] Dahake AG, Ghugal YM. A Trigonometric Shear Deformation Theory for Flexure of Thick Beams. Int J Sci Res Publ 2012; 2(11): 1–7.
29
[30] Ghugal YM, Dahake AG. Flexure of Cantilever Thick Beams using Trigonometric Shear Deformation Theory. Int J Mech Aerosp Ind Mechatronic Manuf Eng 2013; 7(5): 380–389.
30
[31] Pagano NJ. Exact Solutions for Composite Laminates in Cylindrical Bending. Compos Mater 1969; 3: 398–411.
31
[1] Timoshenko SP. On the Correction for Shear of the Differential Equation for Transverse Vibrations of Prismatic Bars. Philos Mag 1921; 41(6): 742–746.
32
[2] Lo KH, Christensen RM, Wu EM. A High-order Theory of Plate Deformation, Part-1: Homogeneous Plates, ASME J Appl Mech 1977; 44: 663–668.
33
[3] Lo KH, Christensen RM, Wu EM. A High-order Theory of Plate Deformation, Part-2: Laminated Plates, ASME J Appl Mech 1977; 44: 669–676.
34
[4] Levinson M. A New Rectangular Beam Theory. J Sound Vib 1981; 74: 81–87.
35
[5] Reddy JN. A Simple Higher Order Theory for Laminated Composite Plates. ASME J Appl Mech 1984; 51: 745–752.
36
[6] Touratier M. An Efficient Standard Plate Theory. Int J Eng Sci 1991; 29(8): 901–916.
37
[7] Soldatos KP. A Transverse Shear Deformation Theory for Homogeneous Monoclinic Plates. Acta Mech 1992; 94: 195–200.
38
[8] Karama M, Afaq KS, Mistou S. A Refinement of Ambartsumian Multi-layer Beam Theory. Comput Struct 2008; 86: 839–849.
39
[9] Sayyad AS. Comparison of Various Refined Beam Theories for the Bending and Free Vibration Analysis of Thick Beams. Appl Comput Mech 2011; 5: 217–230.
40
[10] Sayyad AS., Ghugal YM, Borkar RR. Flexural Analysis of Fibrous Composite Beams under Various Mechanical Loadings using Refined Shear Deformation Theories. Compos Mech Comput Appl 2014; 5(1): 1–19.
41
[11] Sayyad AS. Static Flexure and Free Vibration Analysis of Thick Isotropic Beams using Different Higher Order Shear Deformation Theories. Int J Appl Math Mech 2012; 8(14): 71–87.
42
[12] Mechab I, Tounsi A, Benatta MA, Bedia EAA. Deformation of Short Composite Beam using Refined Theories. J Math Anal Appl 2008; 346: 468–479.
43
[13] Carrera E, Giunta G. Refined Beam Theories based on A Unified Formulation, Int J Appl Mech 2010; 2(1): 117–143.
44
[14] Carrera E, Filippi M, Zappino E. Laminated Beam Analysis by Polynomial, Trigonometric, Exponential and Zig-zag Theories. Eur J Mech A Solids 2013; 41: 58–69.
45
[15] Carrera E, Filippi M, Zappino E. Free Vibration Analysis of Laminated Beam by Polynomial, Trigonometric, Exponential and Zig-zag Theories. J Compos Mater 2014; 48(19): 2299–2316.
46
[16] Giunta G, Metla N, Belouettar S, Ferreira AJM, Carrera E. A Thermo-Mechanical Analysis of Isotropic and Composite Beams via Collocation with Radial Basis Functions. J Therm Stresses 2013; 36: 1169–1199.
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[17] Chakrabarti A, Chalak HD, Iqbal MA, Sheikh AH. A New FE Model based on Higher Order Zigzag Theory for the Analysis of Laminated Sandwich Beam with Soft Core. Compos Struct 2011; 93: 271–279.
48
[18] Chalak HD, Chakrabarti A, Iqbal MA, Sheikh AH. Vibration of Laminated Sandwich Beams Having Soft Core, J Vib Control 2011; 18(10): 1422–1435.
49
[19] Gherlone M, Tessler A, Sciuva MD. A C0 Beam Elements based on the Refined Zig-zag Theory for Multi-layered Composite and Sandwich Laminates. Compos Struct 2011; 93: 2882–2894.
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[20] Shimpi RP, Ghugal YM. A New Layerwise Trigonometric Shear Deformation Theory for Two-layered Cross-ply Beams. Compos Sci Technol 2001; 61: 1271–1283.
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[21] Ghugal YM, Shinde SB. Flexural Analysis of Cross-ply Laminated Beams using Layerwise Trigonometric Shear Deformation Theory. Latin Am J Solids Struct2013; 10(4): 675–705.
52
[22] Arya H. A New Zig-zag Model for Laminated Composite Beams: Free Vibration Analysis. J Sound Vib 2003; 264: 485–490.
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[23] Sayyad AS, Ghugal YM. Effect of Transverse Shear and Transverse Normal Strain on Bending Analysis of Cross-ply Laminated Beams. Int J Appl Math Mech 2011; 7(12): 85–118.
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[24] Mantari JL, Oktem AS, Soares CG. A New Trigonometric Shear Deformation Theory for Isotropic, Laminated Composite and Sandwich Plates. Int J Solids Struct 2012; 49(1): 43–53.
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[25] Ferreira AJM, Roque CMC, Jorge RMN. Analysis of Composite Plates by Trigonometric Shear Deformation Theory and Multi-quadrics. Comput Struct 2005; 83(27): 2225–2237.
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[26] Zenkour AM. Benchmark Trigonometric and 3-D Elasticity Solutions for an Exponentially Graded Thick Rectangular Plate. Arch Appl Mech 2007; 77: 197–214.
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[27] Sayyad AS, Ghugal YM, Naik NS. Bending Analysis of Laminated Composite and Sandwich Beams according to Refined Trigonometric Beam Theory. Curved and Layered Struct 2015; 2: 279–289.
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[28] Dahake AG, Ghugal YM. A Trigonometric Shear Deformation Theory for Flexure of Thick Beams. Procedia Eng 2013; 51: 1–7.
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[29] Dahake AG, Ghugal YM. A Trigonometric Shear Deformation Theory for Flexure of Thick Beams. Int J Sci Res Publ 2012; 2(11): 1–7.
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[30] Ghugal YM, Dahake AG. Flexure of Cantilever Thick Beams using Trigonometric Shear Deformation Theory. Int J Mech Aerosp Ind Mechatronic Manuf Eng2013; 7(5): 380–389.
61
[31] Pagano NJ. Exact Solutions for Composite Laminates in Cylindrical Bending. Compos Mater 1969; 3: 398–411.
62
ORIGINAL_ARTICLE
Adaptive Tunable Vibration Absorber using Shape Memory Alloy
This study presents a new approach to control the nonlinear dynamics of an adaptive absorber using shape memory alloy (SMA) element. Shape memory alloys are classified as smart materials that can remember their original shape after deformation. Stress and temperature-induced phase transformations are two typical behaviors of shape memory alloys. Changing the stiffness associated with phase transformations causes these properties of SMA. A thermo-mechanical model (based on the transformation strain which is a measure of strain indicating the phase transformation) is used to constrain the general thermo-mechanical features of the SMA. Here, the one-dimensional SMA model is adopted to calculate both the pseudo-elastic response and the shape memory effects. The dynamic behavior of shape memory alloys is then investigated, and a Newmark method is adopted to analyze the nonlinear dynamic equations. Results demonstrate that the vibration of an initial system can be tuned using the SMA absorber in a wide range of frequencies. Therefore, SMAs as adaptive tuned vibration absorbers provide an excellent performance to control vibrations.
http://macs.journals.semnan.ac.ir/article_332_463d027d2ba350431b148b55adec59c9.pdf
2015-04-01T11:23:20
2018-10-18T11:23:20
55
60
10.22075/macs.2015.332
Shape memory alloy
Vibration absorber
Phase transformation
Nonlinear dynamic
Shirko
Faroughi
sh.faroughi@uut.ac.ir
true
1
Faculty of Mechanical Engineering, Urmia University of Technology, Urmia, Iran
Faculty of Mechanical Engineering, Urmia University of Technology, Urmia, Iran
Faculty of Mechanical Engineering, Urmia University of Technology, Urmia, Iran
LEAD_AUTHOR
[1] Meirovitch L. Elements of Vibration Analysis. McGraw-Hill; 1986.
1
[2] Brennan MJ. Some Recent Developments in Adaptive Tuned Vibration Absorbers/Neutralisers. Shock Vib 2006; 13(4): 531–543, 2006.
2
[3] Rustighi E, Brennan MJ, Mace BR. A Shape Memory Alloy Adaptive Tuned Vibration Absorber: Design and Implementation. Smart Mater Struct 2005; 14: 19–28.
3
[4] Rustighi E, Brennan MJ, Mace BR., Real-time Control of A Shape Memory Alloy Adaptive Tuned Vibration Absorber, Smart Mater Struct 2005; 14(6) 1184–1195.
4
[5] Wang L, Melnik RVN. Nonlinear Dynamics of Shape Memory Alloy Oscillators in Tuning Structural Vibration Frequencies. Mechatronics 2012; 22(8): 1085–1096.
5
[6] Inman DJ. Vibration: with Control, Measurement and Stability. Prentice Hall; 1989.
6
[7] Lagoudas DC. Introduction to Modeling and Engineering Applications of Shape Memory Alloys. Springer; 2007.
7
[8] Elahinia MH, Koo JH, Tan H. Improving Robustness of Tuned Vibration Absorbers using Shape Memory Alloys. Shock Vib 2005; 12(5): 349–361.
8
[9] Van JH. Damping Capacity of Thermoelastic Martensite in Shape Memory Alloys. J Alloys Compd 2003; 355 (1–2): 58–64.
9
[10] Sitnikova E, Pavlovskaia E, Wiercigroch M. Dynamics of An Impact Oscillator with SMA Constraint, Eur Phys J Special Topics 2008; 165(1): 229–238.
10
[11] Sitnikova E, Pavlovskaia E, Wiercigroch M, Savi MA. Vibration Reduction of The Impact System by An SMA Restraint: Numerical Studies. Int J Non-linear Mech 2010; 45(9): 837–849.
11
[12] Santos DD, Cardozo B, Savi MA. Nonlinear Dynamics of A Non-smooth Shape Memory Alloy Oscillator. Chaos Solitons Fractals 2009; 40(1): 197–209.
12
[13] Saadat S, Salichs J, Noori M, Hou Z, Davoodi H, Baron I, Suzuki Y, Masuda A. An Overview of Vibration and Seismic Applications of NiTi Shape Memory Alloy. Smart Mater Struct 2002; 11(2): 218–229.
13
[14] Lagoudas DC, Machado LG, Lagoudas M. Nonlinear Vibration of A One-degree of Freedom Shape Memory Alloy Oscillator: A Numerical-Experimental Investigation. Proc AIAA Conf 2005.
14
[15] Savi M, Paula A, Lagoudas D. Numerical Investigation of An Adaptive Vibration Absorber Using Shape Memory Alloys. J Intell Mater Sys Struct 2011; 22(1): 67–80.
15
[16] Wang LX, Melnik RVN. Tuning Vibration Frequencies with Shape Memory Alloy Oscillators. Proc Int Conf Comput Struct Technol 2006.
16
[17] Souza AG, Mamiya EN, Zouain N. Three-dimensional Model for Solids Undergoing Stress-induced Phase Transformations. Eur J Mech A Solids 1998; 17(5): 789–806.
17
[18] Auricchio F, Petrini L. Improvements and Algorithmical Considerations on A Recent Three-dimensional Model Describing Stress-induced Solid Phase Transformations. Int J Numer Methods Eng 2002; 55(11): 1255–1284.
18
[19] Crisfield MA, Non-linear Finite Element Analysis of Solids and Structures. John Wiley & Sons; 1997.
19
ORIGINAL_ARTICLE
Free Vibration of Lattice Cylindrical Composite Shell Reinforced with Carbon Nano-tubes
The free vibration of the lattice cylindrical composite shell reinforced with Carbon Nano-tubes (CNTs) was studied in this study. The theoretical formulations are based on the First-order Shear Deformation Theory (FSDT) and then by enforcing the Galerkin method, natural frequencies are obtained. In order to estimate the material properties of the reinforced polymer with nano-tubes, the modified Halpin-Tsai equations were used and the results were checked with an experimental investigation. Also, the smeared method is employed to superimpose the stiffness contribution of the stiffeners with those of the shell in order to obtain the equivalent stiffness of the whole structure. The effect of the weight fraction of the CNTs and also the ribs angle on the natural frequency of the structure is investigated in two types of length to diameter ratios in the current study. Finally, the results which are obtained from the analytical solution are checked with the FEM method using ABAQUS CAE software, and a good agreement has been seen between the FEM and the analytical results.
http://macs.journals.semnan.ac.ir/article_333_825faf81bc6a84f4eeac81358f548552.pdf
2015-04-01T11:23:20
2018-10-18T11:23:20
61
72
10.22075/macs.2015.333
Carbon nano-tubes
Lattice structures
Modified Halpin-Tsai equations
Free Vibration
J.
Emami
javademami90@gmail.com
true
1
Composite Materials and Technology Center, Malek-Ashtar University of Technology, Tehran, Iran
Composite Materials and Technology Center, Malek-Ashtar University of Technology, Tehran, Iran
Composite Materials and Technology Center, Malek-Ashtar University of Technology, Tehran, Iran
LEAD_AUTHOR
J.
Eskandari Jam
eskandari@mut.ac.ir
true
2
Composite Materials and Technology Center, Malek-Ashtar University of Technology, Tehran, Iran
Composite Materials and Technology Center, Malek-Ashtar University of Technology, Tehran, Iran
Composite Materials and Technology Center, Malek-Ashtar University of Technology, Tehran, Iran
AUTHOR
M.R.
Zamani
true
3
Composite Materials and Technology Center, Malek-Ashtar University of Technology, Tehran, Iran
Composite Materials and Technology Center, Malek-Ashtar University of Technology, Tehran, Iran
Composite Materials and Technology Center, Malek-Ashtar University of Technology, Tehran, Iran
AUTHOR
A.
Davar
true
4
Composite Materials and Technology Center, Malek-Ashtar University of Technology, Tehran, Iran
Composite Materials and Technology Center, Malek-Ashtar University of Technology, Tehran, Iran
Composite Materials and Technology Center, Malek-Ashtar University of Technology, Tehran, Iran
AUTHOR
Vasiliev VV, Barynin VA, Rasin AF. Anisogrid Lattice Structures - Survey of Development and Application. Compos Struct 2001; 54: 361–370.
1
[2] KhaliliS MR, Azarafza R, Davar A. Transient Dynamic Response of Initially Stressed Composite Circular Cylindrical Shells under Radial Impulse Load. Compos Struct 2009; 89: 275–284.
2
[3] Hemmatnezhad M, Rahimi GH, Ansari R. On the Free Vibrations of Grid-stiffened Composite Cylindrical Shells. Springer 2014; 225: 609–623.
3
[4] Zhang H, Sun F, Fan H, Chen H, Chen L, Fang D. Free Vibration Behaviors of Carbon Fiber Reinforced Lattice-core Sandwich Cylinder. Compos Sci Technol 2014; 100: 26–33.
4
[5] Zhu P, Lei ZX, Liew KM. Static and Free Vibration Analyses of Carbon Nano-tube-reinforced Composite Plates using Finite Element Method with First-order Shear Deformation Plate Theory. Compos Struct 2012; 94: 1450–1460.
5
[6] Reddy BR, Ramji K, Satyanarayana B. Free Vibration Analysis of Carbon Nano-tube Reinforced Laminated Composite Panels. World Acad Sci Eng Technol 2011; 5: 8–29.
6
[7] Sobhani Aragh B, Borzabadi Farahani E, Nasrollah Barati AH. Natural Frequency Analysis of Continuously Graded Carbon Nano-tube-reinforced Cylindrical Shells based on Third-order Shear Deformation Theory. Math Mech Solids 2013; 18: 264–284.
7
[8] Arasteh R, Omidi M, Rousta AHA, Kazerooni H. A Study on Effect of Waviness on Mechanical Properties of Multi-Walled Carbon Nano-tube/Epoxy Composites Using Modified Halpin–Tsai Theory. J Macromolecular Sci Part: B Physics 2011; 50(12): 2464–2480.
8
[9] Asadi E. Manufacturing and Experimental Study of Vibration of Laminated Composite Plates Reinforced by Carbon Nano-tube. MSc Thesis, Malek-Ashtar Uuniversity of Technology, Iran, 2013.
9
[10] Kidane S, Li G, Helms J, Pang S, Woldesenbet E. Buckling Load Analysis of Grid Stiffened Composite Cylinders. Compos 2003; 34: 1–9.
10
[11] Wodesenbet E, Kidane S, Pang S. Optimization for Buckling Loads of Grid Stiffened Composite Panels. Compos 2003; 60: 159–169.
11
[12] Ghasemi MA, Yazdani M, Hoseini SM. Analysis of Effective Parameters on the Buckling of Grid Stiffened Composite Shells based on First-order Shear Deformation Theory. Modares Mech Eng J 2013; 13(10): 51–61.
12
[13] Reddy JN. Mechanics of laminated composite plates and shells: theory and analysis, CRC Press; 2004.
13
[14] Qatu MS, Vibration of laminated shells and plates: Academic Press; 2004.
14