2015
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Effect of Particle Size on the Structural and Mechanical Properties of Al–AlN Nanocomposites Fabricated by Mechanical Alloying
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Nanostructured Al composites with 2.5 wt.% aluminum nitride (AlN) were fabricated by powder metallurgy using mechanically milled aluminum powder mixed in a planetary ball mill with different particle sizes of AlN (50 nm and 1 μm) as reinforcement. After 20 h milling, the powders were diepressed uniaxially in a steel die and then sintered at 670 °C for 2 h. The morphologies and properties of the obtained powders were determined by scanning electron microscopy and Xray diffraction analysis. The results have indicated that the crystallite sizes of the composites decreased by increasing the milling time, resulting in sizes of 46 nm and 55 nm for the composites containing large (1 μm) and small (50 nm) AlN particles, respectively. After 20 h of milling, the microhardness of the nanocomposites with AlN particle sizes of 1 μm and 50 nm were 101 and 122, respectively. The flexural strength of the composite containing smaller AlN particles (50 nm) was higher than that of the composite containing larger AlN particles (1 μm). The testing results have indicated that the strength and hardness properties of the composite containing smaller AlN particles are better than those of the composite with larger AlN particles.
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73
78


H.
Ghods
Department of Materials Engineering, Islamic Azad University of Shahrood Branch, Shahrood, Iran
Department of Materials Engineering, Islamic
Iran


S.A.
Manafi
Department of Materials Engineering, Islamic Azad University of Shahrood Branch, Shahrood, Iran
Department of Materials Engineering, Islamic
Iran


E.
Borhani
Department of NanoTechnology, NanoMaterials Science and Engineering Group, Semnan University, Semnan, Iran
Department of NanoTechnology, NanoMaterials
Iran
Mechanical properties
Powder characteristics
Al/B4C nanocomposite
Mechanical alloying
[[1] Abdoli H, Asgharzadeh H, Salahi E. Sintering behavior of Al–AlNnanostructured composite powder synthesized by highenergy ball milling. J Alloy Compd 2009; 473: 116122. ##[2] Smagorinski ME, Tsantrizos PG, Grenier S, Cavasin A, Brzezinski T, Kim G. The properties and microstructure of Albased composites reinforced with ceramic particles. Mater Sci Eng A 1998; 244: 8690. ##[3] Sajjadi A, Ezatpour HR, Beygi H. Microstructure and mechanical properties of Al–Al2O3 micro and nano composites fabricated by stir casting. Mater Sci Eng A 2011; 528: 87658771. ##[4] Ezatpour HR, Beygi H, Sajjadi SA, Torabi M. Microstructure and mechanical properties of Al–Al2O3 micro and nano composites fabricated by a novel stir casting rout. 2nd Conferences on Application of nanotechnology in Science, Engineering and Medicine, Mashhad Iran 2001. ##[5] Comoro J, Salvador MD, Cambronero LEG. Hightemperature mechanical properties of aluminium alloys reinforced with boron carbide particles. Mater Sci Eng 2009; 499: 421426. ##[6] Han BQ, Agnew SR, Dunand DC. Highstrainrate deformation of pure aluminum reinforced with 25% alumina submicron particles near the solidus temperature. Scripta Mater 1999; 40: 801–8. ##[7] Kim SS, Haynes MJ, Gangloff RP. Localized deformation and elevatedtemperature fracture of submicrongrain aluminum with dispersoids. Mater Sci En A 1995; 203: 256–71. ##[8] Xiao YL, Li YL, Liang Y, Lu K, Zhou BL. Nanometre sized SiC particulates reinforced Al base composite material. Acta Metall Sin 1996; 6: 658–62. In Chinese. ##[9] Wu GH, Ma SL, Zhao YC, Yang DZ. Microyield deformation characteristic of Particle with Submicron scale reinforced 6061 Al matrix composite. Chinees J Mate Res 1998; 3: 307–10. in Chinese. ##[10] Troadec C, Goeuriot P, Verdieq P, Laurent Y, J. Vicenqc, Boitier G, Chermantc JL. AlN dispersed reinforced aluminum composite. Eur Ceram Soc 1997; 17: 18671875. ##[11] Fogagnolo JB, RuizNavas EM, Robert MH, Torralba JM. 6061 Al reinforced with silicon nitride particles processed by mechanical milling. Scripta Mater 2002; 47: 243248. ##[12] Fogagnolo JB, Robert MH, RuizNavas EM, Torralba JM. 6061 Al reinforced with zirconium diboride particles processed by conventional powder metallurgy and mechanical alloying. Mater Sci 2004; 39: 127132. ##[13] Benjamin JS. Mechanical Properties of Metallic Composites. Metall Transaction, 1970; 1: 29432951. ##[14] Suryanarayana C. Mechanical Alloying and Milling. Prog Mater Sci 2001; 46: 1184. ##[15] Lu L, Lai MO, Ng CW. Enhanced mechanical properties of an Al based metal matrix composite prepared using mechanical alloying. Mater Sci Eng A 1998; 252: 203211. ##[16] Bhaduri A, Gopinathan V, Ramakrishnan P, Miodownik AP. Processing and properties of SiC particulate reinforced A16.2Zn2.5MgI.7Cu alloy (7010) matrix composites prepared by mechanical alloying. Mater Sci En A 1996; 221: 94101. ##[17] Fogagnolo JB, Kiminami CS, Bolfarini C, Botta Filho WJ. Consolidation of Mechanically Alloyed Aluminium Matrix Composite Powders by Severe Plastic Deformation. JMNM 2003; 307: 1516. ##[18] Fogagnolo JB, Robert MH, Torralba JM. "Mechanically alloyed AlN particlereinforced Al6061 matrix composites: Powder processing, consolidation and mechanical strength and hardness of the asextruded materials." Mater Sci Eng A 2006; 426: 8594. ##[19] Wang J, Yi D, Su X, Yin F, Li H. Properties of submicron AlN particulate reinforced aluminum matrix composite. Mater Design 2009; 30: 78–81. ##[20] Abdoli H, Saebnouri E, Sadrnezhaad SK, Ghanbari M, Shahrabi T. Processing and surface properties of Al–AlN composites produced from nanostructured milled powders. J Alloy Compo 2010; 490: 624–630. ##[21] Razavi Hesabi Z, Simchi A, Seyed Reihani SM. Structural evolution during mechanical milling of nanometric and micrometric Al2O3 reinforced Al matrix composites. Mater Sci Eng A 2006; 428: 159168. ##[22] Simchi H, Kaflou A, Simchi A. Synergetic effect of Ni and Nb2O5 on dehydrogenation properties of nanostructured MgH2 synthesized by highenergy mechanical alloying. Int J Hydrogen Energ 2009; 34: 77247730. ##[23] Alizadeh A, TaheriNassaj E, Baharvandi HR. Preparation and investigation of Al–4 wt% B4C nanocomposite powders using mechanical milling. Mater Sci 2011; 34: 10391048. ##[24] Abdoli H, Salahi E, Farnoush H, Pourazrang K. Evolutions during synthesis of Al–AlNnanostructured composite powder by mechanical alloying. J Alloy Compo 2008; 461: 166172. ##[25] Mohammad Sharifi E, Karimzadeh F, Enayati M.H. Fabrication and evaluation of mechanical and tribological properties of boron carbide reinforced aluminum matrix nanocomposites. Mater Design 2011; 32: 32633271. ##[26] Fathy A, Wagih A, M. Abd ElHamid, Hassan A. Effect of Mechanical Milling on the Morphology and Structural Evaluation of AlAl2O3 Nanocomposite Powders. Int J Eng 2014; 27: 625632. ##[27] VD Mote VD, Purushotham Y, Dole BN. WilliamsonHall analysis in estimation of lattice strain in nanometersized ZnO particles. J theor appl phys 2012; 1: 511. ##[28] Borhani E. Microstructure and Mechanical Property of Heavily Deformed AlSc Alloy Having Different Starting Microstructures. PhD thesis, 2012, Kyoto University. ##[29] Abdoli H, Farnoush HR, Asgharzadeh H, Sadrnezhaad SK. Effect of high energy ball milling on compressibility of nanostructured composite powder. Powder Metall 2011; 54: 2429. ##[30] Razavi Tousi SS, Yazdani Rad R, Salahi E, Mobasherpour I, Razavi M. Production of Al20 wt.% Al2O3 composite powder using high energy milling. Powder Tech 2009; 192: 4651. ##[31] Nalwa HS. Nanoclusters and nanocrystals. Am Sci Pub 2003, los Angeles, California. ##[32] Sanghoon N, ByoungKwon C, Sukhoon K, Taekyu K. Influence of mechanical alloying atmosphere on the microstructures and mechanical properties of 15Cr ODS steels. Nucl Eng Tech 2014; 46: 857862.##]
Free Vibrations Analysis of Functionally Graded Rectangular Nanoplates based on Nonlocal Exponential Shear Deformation Theory
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In the present study the free vibration analysis of the functionally graded rectangular nanoplates is investigated. The nonlocal elasticity theory based on the exponential shear deformation theory has been used to obtain the natural frequencies of the nanoplate. In exponential shear deformation theory an exponential functions are used in terms of thickness coordinate to include the effect of transverse shear deformation and rotary inertia. The nonlocal elasticity theory is employed to investigate the effect of the small scale on the natural frequency of the functionally graded rectangular nanoplate. The govering equations and the corresponding boundary conditions are derived by implementing Hamilton’s principle. To show the accuracy of the formulations, the present results in specific cases are compared with available results in the literature and a good agreement is seen. Finally, the effect of the various parameters such as the nonlocal parameter, the power law indexes, the aspect ratio , and the thickness to lenghth ratio on the natural frequencies of the rectangular FG nanoplates is presented and discussed in detail.
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79
93


Korosh
Khorshidi
Department of Mechanical Engineering, Faculty of Engineering, Arak, Iran
Department of Mechanical Engineering, Faculty
Iran
kkhorshidi@araku.ac.ir


Tahmoores
Asgari
Department of Mechanical Engineering, Faculty of Engineering, Arak, Iran
Department of Mechanical Engineering, Faculty
Iran
t_asgari@arshad.araku.ac.ir


Abolfazl
Fallah
Department of Mechanical Engineering, Faculty of Engineering, Arak, Iran
Department of Mechanical Engineering, Faculty
Iran
falahabolfazl67@gmail.com
vibration
Functionally graded nanoplates
Nonlocal elasticity
Exponential shear deformation theory
[[1] Iijima S. Helical microtubules of graphitic carbon. nature 1991; 354: 5658. ##[2] Miller RE, Shenoy VB. Sizedependent elastic properties of nanosized structural elements. Nanotechnology 2000; 11: 139. ##[3] Shen HS. Zhang CL. Torsional buckling and postbuckling of doublewalled carbon nanotubes by nonlocal shear deformable shell model. Compos Struct 2010; 92: 10731084. ##[4] Aydogdu M. Axial vibration of the nanorods with the nonlocal continuum rod model. Phys E 2009; 41: 861864. ##[5] Wang CM, Duan W. Free vibration of nanorings/arches based on nonlocal elasticity. Appl Phys 2008; 104: 014303. ##[6] Pradhan S, Phadikar J. Small scale effect on vibration of embedded multilayered graphene sheets based on nonlocal continuum models. Phys Lett A 2009; 373: 10621069. ##[7] Ma M, et al. Electrochemical performance of ZnO nanoplates as anode materials for Ni/Zn secondary batteries. J Power Sources 2008; 179: 395400. ##[8] Craighead HG. Nanoelectromechanical systems. Sci 2000; 290: 15321535. ##[9] SakhaeePour A, Ahmadian M, Vafai A. Applications of singlelayered graphene sheets as mass sensors and atomistic dust detectors. Solid State Commun 2008; 145: 168172. ##[10] SakhaeePour A, Ahmadian M, Vafai A. Potential application of singlelayered graphene sheet as strain sensor. Solid State Commun 2008; 147: 336340. ##[11] Aagesen M. Sorensen C. Nanoplates and their suitability for use as solar cells. Proceedings of Clean Technol 2008; 109112. ##[12] Ye C, et al. Thicknessdependent photocatalytic performance of ZnO nanoplatelets. J Phys Chem B 2006; 110: 1514615151. ##[13] Rafiee MA, et al. Fracture and fatigue in graphene nanocomposites. small 2010; 6: 179183. ##[14] Kong S, et al. The sizedependent natural frequency of Bernoulli–Euler microbeams. Int J Eng Sci 2008; 46: 427437. ##[15] Fleck N, Hutchinson J. Strain gradient plasticity. Adv Appl Mech 1997;33 :296361. ##[16] Yang F, et al. Couple stress based strain gradient theory for elasticity. Int J Sol Struct 2002; 39: 27312743. ##[17] Eringen AC, Edelen D. On nonlocal elasticity. Int J Eng Sci 1972; 10: 233248. ##[18] Peddieson J, Buchanan GR, McNitt RP. Application of nonlocal continuum models to nanotechnology. Int J Eng Sci 2003; 41: 305312. ##[19] Reddy J. Nonlocal theories for bending, buckling and vibration of beams. Int J Eng Sci 2007; 45: 288307. ##[20] Reddy J. Pang S. Nonlocal continuum theories of beams for the analysis of carbon nanotubes. J App Phys 2008; 103: 023511. ##[21] Heireche H, et al. Sound wave propagation in singlewalled carbon nanotubes using nonlocal elasticity. Phys E 2008; 40: 27912799. ##[22] Murmu T, Pradhan S. Buckling analysis of a singlewalled carbon nanotube embedded in an elastic medium based on nonlocal elasticity and Timoshenko beam theory and using DQM. Phys E 2009; 41: 12321239. ##[23] Murmu T, Pradhan S. Thermomechanical vibration of a singlewalled carbon nanotube embedded in an elastic medium based on nonlocal elasticity theory. Comput Mater Sci 2009; 46: 854859. ##[24] Wang L. Dynamical behaviors of doublewalled carbon nanotubes conveying fluid accounting for the role of small length scale. Comput Mater Sci 2009; 45: 584588. ##[25] Eringen AC. On differential equations of nonlocal elasticity and solutions of screw dislocation and surface waves. J appl phys 1983; 54: 47034710. ##[26] Chen Y, Lee JD, Eskandarian A. Atomistic viewpoint of the applicability of microcontinuum theories. Int j sol struct 2004; 41: 20852097. ##[27] Malekzadeh P, Heydarpour Y. Free vibration analysis of rotating functionally graded cylindrical shells in thermal environment. Compos Struct 2012; 94: 29712981. ##[28] Ungbhakorn V, Wattanasakulpong N. Thermoelastic vibration analysis of thirdorder shear deformable functionally graded plates with distributed patch mass under thermal environment. Appl Acoust 2013; 74: 10451059. ##[29] Kumar Y, Lal R. Prediction of frequencies of free axisymmetric vibration of twodirectional functionally graded annular plates on Winkler foundation. Eur J Mech A Solid 2013; 42: 219228. ##[30] Nie G, Zhong Z. Semianalytical solution for threedimensional vibration of functionally graded circular plates. Comput Method Appl M 2007; 196: 49014910. ##[31] Huang C, Yang P, Chang M. Threedimensional vibration analyses of functionally graded material rectangular plates with through internal cracks. Compos Struct 2012; 94: 27642776. ##[32] Matsunaga H. Free vibration and stability of functionally graded plates according to a 2D higherorder deformation theory. Compos struct 2008; 82: 499512. ##[33] Malekzadeh P, Beni AA. Free vibration of functionally graded arbitrary straightsided quadrilateral plates in thermal environment. Compos Struct 2010; 92: 27582767. ##[34] Ke L, et al. Axisymmetric nonlinear free vibration of sizedependent functionally graded annular microplates. Compos Part B: Engineering 2013; 53: 207217. ##[35] Ke LL, et al. Bending, buckling and vibration of sizedependent functionally graded annular microplates. Compos struct 2012; 94: 32503257. ##[36] Asghari M, Taati E. A sizedependent model for functionally graded microplates for mechanical analyses. J Vib Cont 2013; 19: 16141632. ##[37] Natarajan S, et al. Sizedependent free flexural vibration behavior of functionally graded nanoplates. Comput Mater Sci 2012; 65: 7480. ##[38] Thai HT, Choi DH. Sizedependent functionally graded Kirchhoff and Mindlin plate models based on a modified couple stress theory. Compos Struct 2013; 95: 142153. ##[39] Reddy J. Microstructuredependent couple stress theories of functionally graded beams. J Mech Phys of Solids 2011; 59: 23822399. ##[40] HosseiniHashemi S, Zare M, Nazemnezhad R. An exact analytical approach for free vibration of Mindlin rectangular nanoplates via nonlocal elasticity. Compos Struct 2013; 100: 290299. ##[41] Sahoo R, Singh B. A new trigonometric zigzag theory for static analysis of laminated composite and sandwich plates. Aerosp sci technol 2014; 35: 1528. ##[42] Narendar S. Buckling analysis of micro/nanoscale plates based on twovariable refined plate theory incorporating nonlocal scale effects. Compos Struct 2011; 93: 30933103. ##[43] HosseiniHashemi S, Bedroud M. Nazemnezhad R. An exact analytical solution for free vibration of functionally graded circular/annular Mindlin nanoplates via nonlocal elasticity. Compos Struct 2013; 103: 108118. ##[44] Sayyad AS, Ghugal YM. Bending and free vibration analysis of thick isotropic plates by using exponential shear deformation theory. Appl Comput mech 2012; 6: 112. ##[45] Shufrin I, Eisenberger M. Stability and vibration of shear deformable plates––first order and higher order analyses. Int j sol struc 2005; 42: 12251251. ##[46] HosseiniHashemi S, et al. Free vibration of functionally graded rectangular plates using firstorder shear deformation plate theory. Appl Math Model 2010; 34: 12761291. ##[47] Zhao X, Lee Y, Liew KM. Free vibration analysis of functionally graded plates using the elementfree kpRitz method. J sound Vibration 2009; 319: 918939. ##[48] Vel SS, Batra R. Threedimensional exact solution for the vibration of functionally graded rectangular plates. J Sound Vibration 2004; 272: 703730. ##[49] Pradyumna S, Bandyopadhyay J. Free vibration analysis of functionally graded curved panels using a higherorder finite element formulation. J Sound Vibration 2008; 318: 176192. ##[50] Mori T, Tanaka K. Average stress in matrix and average elastic energy of materials with misfitting inclusions. Acta metallurgica 1973; 21: 571574. ##[51] Benveniste Y. A new approach to the application of MoriTanaka's theory in composite materials. Mech mater 1987; 6: 147157. ##[52] Hill R. A selfconsistent mechanics of composite materials. J Mech Phys Sol 1965; 13: 213222. ##[53] HosseiniHashemi S, Fadaee M, Atashipour SR. Study on the free vibration of thick functionally graded rectangular plates according to a new exact closedform procedure. Compos Struc 2011; 93: 722735.##]
Free Vibration Analysis of 2D Functionally Graded Annular Plate considering the Effect of Material Composition via 2D Differential Quadrature Method
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This study investigates the free vibration of the TwoDimensional Functionally Graded Annular Plates (2DFGAP). The theoretical formulations are based on the threedimensional elasticity theory with small strain assumption. The TwoDimensional Generalized Differential Quadrature Method (2DGDQM) as an efficient and accurate semianalytical approach is used to discretize the equations of motion and to implement the various boundary conditions. The fast rate of convergence for this method is shown and the results are compared with the existing results in the literature. The material properties are assumed to be continuously changing along thickness and radial directions simultaneously, which can be varied according to the power law and exponential distributions, respectively. The effects of the geometrical parameters, the material graded indices in thickness and radial directions, and the mechanical boundary conditions on the frequency parameters of the twodimensional functionally graded annular plates are evaluated in detail. The results are verified to be against those given in the literature.
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95
111


Mohammad
Nejati
Young Researchers and Elite Club, Islamic Azad University, Arak Branch, Arak, Iran
Young Researchers and Elite Club, Islamic
Iran


Hamid
Mohsenimonfared
Department of Mechanical Engineering, Islamic Azad University, Arak Branch, Arak, Iran
Department of Mechanical Engineering, Islamic
Iran
hmohsenimonfared@iauarak.ac.ir


Ali
Asanjarani
Young Researchers and Elite Club, Islamic Azad University, Arak Branch, Arak, Iran
Young Researchers and Elite Club, Islamic
Iran
Functionally graded material
Generalized differential quadrature
Free Vibration
Annular plate
[[1] Brush DO, Almorth BO. Buckling of bars, plates and shells, McGrawHill, 1975. ##[2] Finot M, Suresh S. Small and large deformation of thick and thinfilm multilayers: effect of layer geometry, plasticity and compositional gradients, J Mech Phys Solids 1996; 44(5): 683–721. ##[3] Pan E, Han F. Exact solution for functionally graded and layered magnetoelectro elastic plates, Int J Eng Sci 2005; 43(34): 321–339. ##[4] Cheng ZQ, Batra RC. Deflection relationships between the homogeneous Kirchhoff plate theory and different functionally graded plate theories, Arch Mech 2000; 52(1): 143–158. ##[5] Bhangale RK, Ganesan N. Static analysis of simply supported functionally graded and layered magnetoelectroelastic plates, Int J Solid Struct 2006; 43(10): 3230–3253. ##[6] Ramirez F, Heyliger PR, Pan E. Discrete layer solution to free vibrations of functionally graded magnetoelectroelastic plates, Mech Adv Mater Struct 2006; 13(3): 249–266. ##[7] Abrate S. Free vibration, buckling, and static deflections of functionally graded plates, Compos Sci Technol 2006; 66(14): 2383–2394. ##[8] HosseiniHashemi S, Rokni Damavandi Taher H, Akhavan H, Omidi M. Free vibration of functionally graded rectangular plates using firstorder shear deformation plate theory, Appl Math Modell 2010; 34(5): 1276–1291. ##[9] Kim YW. Temperature dependent vibration analysis of functionally graded rectangular plates, J Sound Vib 2005; 284(35): 531–549. ##[10] Malekzadeh P. Threedimensional free vibration analysis of thick functionally graded plates on elastic foundations, Compos Struct 2009; 89(3): 367–373. ##[11] Yas MH, Sobhani Aragh B. Free vibration analysis of continuous grading fiber reinforced plates on elastic foundation, Int J Eng Sci 2010; 48(12): 1881–1895. ##[12] Chiroiu V, Munteanu L. On the free vibrations of a piezoceramic hollow sphere, Mech Res Commun 2007; 34(2): 123–129. ##[13] Chen WQ. Vibration theory of nonhomogeneous, spherically isotropic piezoelastic bodies, J Sound Vib 2000; 236(5): 833–860. ##[14] Haddadpour H, Mahmoudkhani S, Navazi HM. Free vibration analysis of functionally graded cylindrical shells including thermal effects, ThinWalled Struct 2007; 45(6): 591–599. ##[15] Sobhani Aragh B, Yas MH. Threedimensional free vibration of functionally graded fiber orientation and volume fraction cylindrical panels, Mater Des 2010; 31(9): 4543–4552. ##[16] Yas MH, SobhaniAragh B. Threedimensional analysis for thermoelastic response of functionally graded fiber reinforced cylindrical panel, Compos Struct 2010; 92(10): 2391–2399. ##[17] Bahtui A, Eslami MR. Coupled thermoelasticity of functionally graded cylindrical shells, Mech Res Commun 2007; 34(1): 1–18. ##[18] Prakash T, Ganapathi M. Asymmetric flexural vibration and thermoelastic stability of FGM circular plates using finite element method, Compos Part B 2006; 37(78): 642–649. ##[19] Eraslan AN, Akis T. On the plane strain and plane stress solutions of functionally graded rotating solid shaft and solid disk problems, Acta Mech 2006; 181(12): 43–63. ##[20] Efraim E, Eisenberger M. Exact vibration analysis of variable thickness thick annular isotropic and FGM plates, J Sound Vib 2007; 299(45):720–738. ##[21] Nie GJ, Zhong Z. Semi analytical solution for threedimensional vibration of functionally graded circular plates, Comput. Methods Appl Mech Eng 2007; 196(4952): 4901–4910. ##[22] Dong CY. Threedimensional free vibration analysis of functionally graded annular plates using the Chebyshev–Ritz method, Mater Des 2008; 29(8): 1518–1525. ##[23] Tahouneh V, Yas MH. 3D Free vibration analysis of thick functionally graded annular plates on Pasternak elastic foundation via differential quadrature method (DQM), Acta Mech 2012; 223(9): 18791897. ##[24] HosseiniHashemi S, Fadaee M, Atashipour SR. A new exact analytical approach for free vibration of ReissnerMindlin functionally graded rectangular plates, Int J Mech Sci 2011; 53(1): 11–22. ##[25] Jodaei A, Jalal M, Yas MH. Free vibration analysis of functionally graded annular plates by statespace based differential quadrature method and comparative modeling by ANN, Compos Part B 2012; 43(2): 340–353. ##[26] Malekzadeh P, Shahpari SA, Ziaee HR. Threedimensional free vibration of thick functionally graded annular plates in thermal environment. J Sound Vib 2010; 329(4): 425–42. ##[27] Rad AB, Shariyat M. A threedimensional elasticity solution for twodirectional FGM annular plates with nonuniform elastic foundations subjected to normal and shear tractions, Acta Mech Solida Sinica 2013; 26(6): 671–90. ##[28] Malekzadeh P, Safaeian Hamzehkolaei N. A 3D discrete layerdifferential quadrature free vibration of multilayered FG annular plates in thermal environment, Mech Adv Mater Struct 2013; 20(4):31630. ##[29] Liang X, Kou H, Wang L, Palmer AC, Wang Z, Liu G. Threedimensional transient analysis of functionally graded material annular sector plate under various boundary conditions. Compos Struct 2015; 132(15): 584–596. ##[30] Nie G, Zhong Z. Dynamic analysis of multidirectional functionally graded annular plates, Appl Math Modell 2010; 34(3): 608–616. ##[31] Asgari M, Akhlaghi M. Natural frequency analysis of 2DFGM thick hollow cylinder based on threedimensional elasticity equations, Eur J Mech A/Solids 2011; 30(2):72–81. ##[32] Bert CW, Malik M. Differential quadrature method in computational mechanics: A review, Appl Mech 1996; 49(1): 1–28. ##[33] Bellman RF, Kashef BG, Casti J. Differential quadrature: A technique for the rapid solution of nonlinear partial differential equations, Comput Phys 1972; 10(1): 40–52. ##[34] Shu C. Differential Quadrature and Its Application in Engineering, Springer Publication, 2000. ##[35] Zhou D, Au FTK, Cheung YK, Lo SH. Threedimensional vibration analysis of circular and annular plates via the ChebyshevRitz method, Int J Solid Struct 2003; 40(12): 3089–3105.##]
Nonlocal Buckling and Vibration Analysis of TripleWalled ZnO Piezoelectric Timoshenko Nanobeam Subjected to MagnetoElectroThermoMechanical Loadings
2
2
In this study, using the nonlocal elasticity theory, the buckling and vibration analysis of triple walled ZnO piezoelectric Timoshenko beam on elastic Pasternak foundation is analytically investigated under magnetoelectrothermomechanical loadings. Using the Timoshenko beam free body diagram, the equilibrium equation of Timoshenko nanobeam model is obtained and solved by Navier’s method for a simplysupported nanobeam. The surrounding elastic mediums are simulated by Winkler and Pasternak models and interlayer forces are considered by LenardJones potential. The effects of various parameters including the elastic medium, small scale, length, thickness, van der Waals force on the critical buckling load and nondimensional natural frequency of triple walled ZnO nanobeam are investigated. The results of this study show that the critical buckling load reduces with increasing the temperature change, direct electric field, magnetic field, and length of nanotube, and vice versa for the thickness of nanotubes, and two parameters elastic foundations. Also, the nonlocal critical buckling load and nondimensional natural frequency of Timoshenko nanobeam are smaller than the local critical buckling load and nondimensional natural frequency. The results can be useful for designing the smart nanobeam for MEMS and NEMS.
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113
126


Mehdi
Mohammadimehr
Department of Solid Mechanics, Faculty of Mechanical Engineering, University of Kashan, Kashan, Iran
Department of Solid Mechanics, Faculty of
Iran
mmohammadimehr@kashanu.ac.ir


Seyyed Amir Mohammad
Managheb
Department of Solid Mechanics, Faculty of Mechanical Engineering, University of Kashan, Kashan, Iran
Department of Solid Mechanics, Faculty of
Iran
s.am_managheb@yahoo.com


Sajad
Alimirzaei
Department of Solid Mechanics, Faculty of Mechanical Engineering, University of Kashan, Kashan, Iran
Department of Solid Mechanics, Faculty of
Iran
salimirzaie69@gmail.com
Nonlocal buckling and vibration analysis
Triplewalled ZnO piezoelectric
Timoshenko nanobeam
Elastic foundation
Magnetoelectrothermomechanical loadings
[[1] Eringen AC, on differential equations of nonlocal elasticity and solutions of screw dislocation and surface waves. J Appl Phys 1983; 54: 47034710. ##[2] Ying Chen, Piezoelectricity in ZnOBased multilayer structures for applications, New Brunswick, New Jersey May, 2008; Dissertation Director: Professor Yicheng Lu. ##[3] Narendar S, Gupta SS, Gopalakrishnan S, Wave propagation in singlewalled carbon nanotube under longitudinal magnetic field using nonlocal Euler–Bernoulli beam theory. Appl Math Modell 2012; 36: 4529–4538. ##[4] Kiani K, Magnetothermoelastic fields caused by an unsteady longitudinal magnetic field in a conducting nanowire accounting for eddycurrent loss Materials. Chemis Phys 2012; 136: 589–598. ##[5] Ghorbanpour Arani A, Abdollahian M, Kolahchi R, Rahmati AH, Electrothermo torsional buckling of an embedded armchair DWBNNT using nonlocal shear deformable shell model. Compos Part B: Eng 2013; 51: 291–299. ##[6] Ghorbanpour Arani A, Rahnama Mobarakeh M, Shams Sh, Mohammadimehr M, The effect of CNT volume fraction on the magnetothermoelectromechanical behavior of smart nanocomposite cylinder. J Mech Sci Tech 2012; 26(8): 2565–2572. ##[7] Kong T, Li DX, Wanga X, Thermomagnetodynamic stresses and perturbation of magnetic fieldvector in a nonhomogeneous hollow cylinder. Appl Math Modell 2009; 33: 2939–2950. ##[8] Murmu1 T, Adhikari S, McCarthy MA, Axial vibration of embedded nanorods under transverse magnetic field effects via nonlocal elastic continuum theory. J Comput Theor Nanos 2014; 11: 1–7. ##[9] Wang YiZe, Li FM, Nonlinear primary resonance of nano beam with axial initial load by nonlocal continuum theory. Int J NonLinear Mech 2014; 61: 74–79. ##[10] Mohammadimehr M, Rahmati AH, Small scale effect on electrothermomechanical vibration analysis of singlewalled boron nitride nanorods under electric excitation. Turkis J Env Sci 2014; 37: 1–15. ##[11] Zhang J, Wang R, Wang C, Pezoelectric ZnOCNT nanotubes under axial strain and electrical voltage. Physica E 2012; 46: 105–112. ##[12] Akbari Alashti R, Khorsand M, Tarahhomi MH, Thermoelastic analysis of a functionally graded spherical shell with piezoelectric layers by differential quadrature method. Scientia Iranica 2013; 20 (1):109–119. ##[13] Jomehzade E, Afshar MK, Galiotis C, Shi X, Pugno NM, Nonlinear softening and hardening nonlocal bending stiffness of an initially curved monolayer grapheme. Int J NonLinear Mech 2013; 56: 123–131. ##[14] Lei Y, Adhikari S, Murmu T, Friswell MI, Asymptotic frequencies of various damped nonlocal beams and plates. Mech Res Commun 2014; 62: 94–101. ##[15] Mohammadimehr M, Rousta Navi B, Ghorbanpour Arani A, Biaxial buckling and bending of smart nanocomposite plate reinforced by carbon nanotube under electromagnetomechanical loadings based on the extended mixture rule approach. Mech Advan Compos Struct 2014; 1: 17–26. ##[16] Ansari R, Gholami R, Sahmani S, Free vibration of sizedependent functionally graded microbeams based on the strain gradient Reddy beam theory. Int J Comput Meth Eng Sci Mech 2014; 15:401–412. ##[17] Najar F, ElBorgi S, Reddy JN, Mrabet K, Nonlinear nonlocal analysis of electrostatic nanoactuators. Compos Struct 2015; 120:117–128. ##[18] Reddy JN, ElBorgi S, Eringen’s nonlocal theories of beams accounting for moderate rotations. Int J Eng Sci 2014; 82: 159–177. ##[19] Adhikari S, Gilchrist D, Murmu T, McCarthy MA, Nonlocal normal modes in nanoscale dynamical systems. Mech Syst Signal Pr 2015; 60: 583–603. ##[20] Ghorbanpour Arani A, Fereidoon A, Kolahchi R, Nonlocal DQM for a nonlinear buckling analysis of DLGSs integrated with Zno piezoelectric layers. J Appl Mech 2014; 45(1): 922. ##[21] Ansari R, Faghih Shojaei M, Gholami R, Mohammadi V, Darabi MA, Thermal postbuckling behavior of sizedependent functionally graded Timoshenko microbeams. Int J NonLinear Mech 2013; 50: 127–135. ##[22] Karlicic D, Murmu T, Cajic M, KozicP, Adhikari S, Dynamics of multiple viscoelastic carbon nanotube based nanocomposites with axial magnetic field. J Appl Phys 2014; 115: 234–303. ##[23] Yu R, Pan C, Chen J, Zhu G, Wang ZL, Enhanced Performance of a ZnO NanowireBased SelfPowered Glucose Sensor by Piezotronic Effect. Advan Func Mater, 2013; doi:10.1002/adfm.201300593/j.adv.funct.mat.2013. ##[24] Liew KM, Lei ZX, Yu JL, Zhang LW, Postbuckling of carbon nanotubereinforced functionally graded cylindrical panels under axial compression using a meshless approach. Comput Methods Appl Mech Eng 2014; 268: 1–17. ##[25] Mohammadimehr M, Rousta Navi B, Ghorbanpour Arani A, The free vibration of viscoelastic doublebonded polymeric nanocomposite plates reinforced by FGSWCNTs using modified strain gradient theory (MSGT) sinusoidal shear deformation theory and meshless method. Compos Struct 2015; 131: 654–671. ##[26] Mohammadimehr M, Mohandes M, Moradi M, Size dependent effect on the buckling and vibration analysis of doublebonded nanocomposite piezoelectric plate reinforced by boron nitride nanotube based on modified couple stress theory. J Vib Control; doi:10.1177/1077546314544513/j.vib.cont. 2014. ##[27] Eltaher MA, Abdelrahman AA, AlNabawy A, Khater M, Mansour A, Vibration of nonlinear graduation of nanoTimoshenko beam considering the neutral axis position. Appl Math Comput 2014; 235: 512–529. ##[28] Le Grognec P, Nguyen Q, Hjiaj M, Exact buckling solution for twolayer Timoshenko beams with interlayerslip. Int J Solids Struct, 2012; 49: 143–150. ##[29] Aydogdu M, Longitudinal wave propagation in multiwalled carbon nanotubes. Compos Struct 2014; 107: 578–584. ##[30] Ghorbanpour Arani A, Kolahchi R, Zarei ShM, Viscosurfacenonlocal piezoelasticity effects on nonlinear dynamic stability of graphene sheets integrated with ZnO sensors and actuators using refined zigzag theory. Compos Struct 2015; 132: 506–526. ##[31] Ghannadpour SAM, Mohammadi B, Fazilati J, Bending, buckling and vibration problems of nonlocal Euler beams using Ritz method. Compos Struct 2013; 96: 584–589. ##[32] Wang ChY, Adhikari S, ZnOCNT composite nanotubes as nanoresonators. Phys Lett A 2011; 375: 2171–2175. ##[33] Rahmati AH, Mohammadimehr M, Vibration analysis of nonuniform and nonhomogeneous boron nitride nanorods embedded in an elastic medium under combined loadings using DQM. Physica B 2014; 440: 88–98. ##[34] Yas MH, Samadi N, Free vibrations and buckling analysis of carbon nanotubereinforced composite Timoshenko beams on elastic foundation. Int J Pres Ves Pip 2012; 98: 119–128. ##[35] Rao SS, Mechanical Vibration: Theory and Analysis, Prentice Hall, 2011. ##[36] Wang CM, Tan VBC, Zhang YY, Timoshenko beam model for vibration analysis of multiwalled carbon nanotubes. J Sound Vib 2012; 294:1060–1072. ##[37] Mohammadimehr M, Saidi AR, Ghorbanpour Arani A, Arefmanesh A, Han Q, Buckling analysis of doublewalled carbon nanotubes embedded in an elastic medium under axial compression using nonlocal Timoshenko beam theory. J Mech Eng Sci 2011; 225: 498–506. ##[38] Ghorbanpour Arani A, Hashemian M, Kolahchi R, Time discretization effect on the nonlinear vibration of embedded SWBNNT conveying viscous fluid. Compos: Part B 2013; 54: 298–306. ##[39] Wu CP, Lai ww. Free vibration of an embedded singlewalled carbon nanotube with various boundary conditions using the RMVTbased nonlocal Timoshenko beam theory and DQ method. Physica E 2015; 68: 8–21.##]
Damage Energy Evaluation in [55/55]9 Composite Pipes using Acoustic Emission Method
2
2
In this study, the longitudinal and hoop tensile strengths of an industrial ±55° Glass Reinforced Epoxy (GRE) pipe with eighteen layers as well as the associated failure mechanisms are determined. To obtain the longitudinal and hoop tensile strengths values, three specimens are cut from the studied GRE pipe in each direction. A comparison is done between both the strength values, and the fracture pattern of the specimens is studied. Determining the different failure mechanisms which are created during both of the tests, the acoustic emission technique is used. The acoustic emission energy as an important damage parameter in determining the different failure mechanisms of the specimens is depicted for both of the tests and is related to the obtained results from the stresstime curve. A high magnification camera is used to verify the failure mechanisms characterized by the acoustic emission method.
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127
134


Hamid Reza
Mahdavi
Faculty of MechanicalEengineering, Tarbiat Modares University, Tehran, Iran
Faculty of MechanicalEengineering, Tarbiat
Iran


Gholam Hosein
Rahimi
Faculty of MechanicalEengineering, Tarbiat Modares University, Tehran, Iran
Faculty of MechanicalEengineering, Tarbiat
Iran
rahimi_gh@modares.ac.ir


Amin
Farrokhabadi
Faculty of MechanicalEengineering, Tarbiat Modares University, Tehran, Iran
Faculty of MechanicalEengineering, Tarbiat
Iran
aminfarrokh@modares.ac.ir


Hossein
Saadatmand
Department of Engineering Design, National Iranian Gas Company, Boushehr, Iran
Department of Engineering Design, National
Iran
saadatmand_h@nigcboushehr.ir
GRE composite pipe
Longitudinal strength
Hoop strength
Acoustic emission
Failure mechanisms
[[1] Cohen D. Influence of filament winding parameters on composite vessel quality and strength. Compos Part A 1997; 28: 10351047. ##[2] Cohen D, Mantell SC, Zhao L. The effect of fiber volume fraction on filament wound composite pressure vessel strength. Compos Part B 2001; 32: 413429. ##[3] Xia M, Takayanagi H, Kemmochi K. Analysis of multilayered filamentwound composite pipes under internal pressure. Compos Struct 2001; 53: 483491. ##[4] Hwang TK, Hong CS, Kim CG. Size effect on the fiber strength of composite pressure vessels. Compos Struct 2003; 59: 489498. ##[5] Baranger E, Allix O, Blanchard L. A computational strategy for the analysis of damage in composite pipes. Compos Sci Technol 2009; 69: 8892. ##[6] Melo JDZ, Neto FL, de Araujo Barros G, de Almeida Mesquita FN. Mechanical behavior of GRP pressure pipes with addition of quartz sand filler. J Compos Mater 2010; 45(6): 717726. ##[7] Rafiee R. Experimental and theoretical investigations on the failure of filament wound GRP pipes. Compos Part B 2013; 45: 257267. ##[8] Prosser WH. Acoustic emission, In Shull PJ (Ed) Nondestructive Evaluation, theory, techniques and applications. Taylor and Francis, 2002. ##[9] Curtis GJ. Acoustic emission energy relates to bond strength. Nondestr Test Eval 1975: 249257. ##[10] Groot PJ, Wijnen PAM, Janssen RBF. Realtime frequency determination of acoustic emission for different fracture mechanisms in carbon/epoxy composites. Compos Sci Technol 1995; 55: 405412. ##[11] Yu YH, Choi JH, Kweon JH, Kim DH. A study on the failure detection of composite materials using an acoustic emission. Compos Struct 2006; 75: 163169. ##[12] Bourchak M, Farrow IR, Bond IP, Rowland CW, Menan F. Acoustic emission energy as a fatigue damage parameter for CFRP composites. Int J Fatigue 2007; 29: 457470. ##[13] Bussiba A, Kupiec M, Ifergane S, Piat R, Bohlke T. Damage evolution and fracture events sequence in various composites by acoustic emission technique. Compos Sci Technol 2008; 68: 11441155. ##[14] De Rosa LM, Santulli C, Sarasini F. Acoustic emission for monitoring the mechanical behavior of natural fibre composites: A literature review. Compos Part A 2010; 40: 14561469. ##[15] Liu PF, Chu JK, Liu YL, Zheng JY. A study on the failure mechanisms of carbon fiber/epoxy composite laminates using acoustic emission. Mater Des 2012; 37: 228235. ##[16] Aggelis DG, Barkoula NM, Matikas TE, Paipetis AS. Acoustic structural health monitoring of composite materials: Damage identification and evaluation in cross ply laminates using acoustic emission and ultrasonics. Compos Sci Technol 2012; 72: 11271133. ##[17] Zarif Karimi N, Heidary H, Ahmadi M, Rahimi A. M. Farajpur. Monitoring of residual tensile strength in drilled composite laminates by acoustic emission. Modares Mech Eng 2013; 13(15): 169183 (in Persian). ##[18] Belalpour dastjerdi P, Fotouhi M, Fotouhi S, Ahmadi M. Acoustic emission based study to investigate the initiation and growth of delamination in composite materials. Modares Mech Eng 2014; 14(3): 7884 (in Persian). ##[19] Saeedifar M, Fotouhi M, Mohammadi R, Hajikhani M, Ahmadinajafabadi M. Classification of damage mechanisms during delamination growth in sandwich composites byacoustic emission. Modares Mech Eng 2014; 14(6): 144152 (in Persian). ##[20] Ben Ammar I, Karra C, El Mahi A, El Guerjouma R, Haddar M. Mechanical behavior and acoustic emission technique for detecting damage in sandwich structures. Appl Acoust 2014; 86: 106117. ##[21] Zarif Karimi N, Minak G, Kianfar P. Analysis of damage mechanisms in drilling of composite materials by acoustic emission. Compos Struct 2015; 131: 107114. ##[22] Standard Test Method for tensile properties of polymer matrix composite materials. Annual Book of ASTM Standard. D 303900; 2000. ##[23] Standard Test Method for Apparent Hoop Tensile Strength of Plastic or Reinforced Plastic Pipe by Split Disk Method. Annual Book of ASTM Standard. D 229004; 2004. ##[24] Standard Test Method for Ignition Loss of Cured Reinforced Resins. Annual Book of ASTM Standard. D 258402; 2002. ##[25] Behroozi H. National Iranian Gas Company (NIGC), Boushehr, Iran, 2015. ##[26] Nondestructive testing Acoustic emission Equipment characterization Part 2: Verification of operating characteristic. BSI Standards Publication. BS EN 134772; 2010. ##[27] Vidya Sagar R. An experimental Study on Acoustic Emission Energy and Fracture Energy of Concrete. Proc National Semin Exhibition on NonDestr Eval 2009: 1012. ##[28] Nondestructive testing Terminology Part 9: Terms used in acoustic emission testing. Brithish Standard. BS EN 13309; 2009.##]
Buckling Analysis of Spherical Composite Panels Reinforced by Carbon Nanotube
2
2
In this study, the buckling behavior of moderately thick Carbon NanoTube (CNT)reinforced spherical composite panels subjected to both uniaxial and biaxial loads is examined. The uniform and various kinds of functionally graded distributions of the CNT are considered. The mechanical properties of the nanocomposite panels are estimated using the modified rule of mixture. Based on the firstorder shear deformation theory and the von Karmantype of kinematic nonlinearity, the governing differential equations are derived and the solutions are determined using Galerkin’s method. The suggested model is justified by a good agreement between the present results and those reportedin the literature. The numerical results are performed to elucidate the influences of volume fraction, aspect ratio, thickness ratio and sidetoradius ratio on the critical buckling loads of the spherical nanocomposite panels. One of the main contributions of the current study is to investigate the effectiveness of functionally graded distributions.The effectiveness of functionally graded distributions with respect to various parameters are also investigated.
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144


Saleh
Pouresmaeeli
School of Mechanical Engineering, Shiraz University, Shiraz, Iran
School of Mechanical Engineering, Shiraz
Iran
pouresmaeeli@gmail.com


S. Ahmad
Fazelzadeh
School of Mechanical Engineering, Shiraz University, Shiraz, Iran
School of Mechanical Engineering, Shiraz
Iran
fazelzad@shirazu.ac.ir


Esmaeal
Ghavanloo
School of Mechanical Engineering, Shiraz University, Shiraz, Iran
School of Mechanical Engineering, Shiraz
Iran
ghavanloo@shirazu.ac.ir
Buckling
Carbon nanotubereinforced
Nanocomposite
Spherical panel
[[1] Iijima S. Helical Microtubules of Graphitic Carbon. Nature 1991; 354: 56–58. ##[2] Cadek M, Coleman JN, Barron V, Hedicke K, Blau WJ. Morphological and Mechanical Properties of CarbonNanotubeReinforced Semicrystalline and Amorphous Polymer Composites. Appl Phys Lett 2002; 81: 5123–5125. ##[3] ThostensonET, ChouTW. On The Elastic Properties of Carbon NanotubeBased Composites: Modelling and Characterization. J Phys D: Appl Phys 2003; 36: 573–582. ##[4] LauKT, GuC, GaoGH, LingHY, ReidSR. Stretching Process of Single and Multiwalled Carbon Nanotubes for Nanocomposite Applications. Carbon 2004; 42: 426–428. ##[5] Coleman JN, Khan U, Blau WJ, Gunko YK. Small but Strong: A Review of the Mechanical Properties of Carbon NanotubePolymer Composites. Carbon 2006; 44: 1624–1652. ##[6] Qian D, Dickey EC, Andrews R, Rantell T. Load Transfer and Deformation Mechanisms in Carbon NanotubePolystyrene Composites. Appl Phys Lett 2000; 76: 2868–2870. ##[7] Ruan SL, Gao P, Yang XG, Yu TX. Toughening High Performance Ultrahigh Molecular Weight Polyethylene Using Multiwalled Carbon Nanotubes. Polymer 2003; 44: 5643–5654. ##[8] Rafiee R, FirouzbakhtV.Predicting Young’s Modulus of Aggregated Carbon Nanotube Reinforced Polymer, Mech Adv Compos Struct 2014; 1: 9–16. ##[9] Mohammadimehr M, RoustaNavi B, GhorbanpourArani A.Biaxial Buckling and Bending of Smart Nanocomposite Plate Reinforced by CNTs Using Extended Mixture Rule Approach. Mech Adv Compos Struct 2014; 1: 17–26. ##[10] Alibeigloo A. Elasticity Solution of Functionally Graded Carbon Nanotube Reinforced Composite CylindricalPanel. Mech Adv Compos Struct 2014; 1: 49–60. ##[11] Tahouneh V, EskandariJam J. A Semianalytical Solution for 3D Dynamic Analysis of Thick Continuously Graded Carbon NanotubeReinforced Annular Plates Resting on a TwoParameter Elastic Foundation. Mech Adv Compos Struct 2014; 1: 113–130. ##[12] ShenHS. Postbuckling of NanotubeReinforced Composite Cylindrical Shells in Thermal Environments, Part I: AxiallyLoaded Shells. Compos Struct 2011; 93: 2096–2108. ##[13] ShenHS.Postbuckling of NanotubeReinforced Composite Cylindrical Shells in Thermal Environments, Part II: PressureLoaded Shells. Compos Struct 2011; 93: 2496–503. ##[14] ShenHS.Thermal Buckling and Postbuckling Behavior of Functionally Graded Carbon NanotubeReinforced Composite Cylindrical Shells. Compos Part BEng 2012; 43: 1030–1038. ##[15] Shen HS, Xiang Y.Postbuckling of NanotubeReinforced Composite Cylindrical Shells under Combined Axial and Radial Mechanical Loads in Thermal Environment, Compos Part BEng 2013; 52: 311–322. ##[16] Liew KM, Lei ZX, Yu JL, Zhang LW. Postbuckling of Carbon NanotubeReinforced Functionally Graded Cylindrical Panels under Axial Compression Using a Meshless Approach. Comput Method Appl 2014; 268: 1–17. ##[17] Shen HS. Torsional Postbuckling of NanotubeReinforced Composite Cylindrical Shells in Thermal Environments. Compos Struct 2014; 116: 477–488. ##[18] Shen HS, Xiang Y. Postbuckling of Axially Compressed NanotubeReinforced Composite Cylindrical Panels Resting on Elastic Foundations in Thermal Environments. Compos Part BEng 2014; 67: 50–61. ##[19] JamJE, KianiY.Buckling of Pressurized Functionally Graded Carbon Nanotube Reinforced Conical Shells. Compos Struct 2015; 125: 586–595. ##[20] RabaniBidgoli M, Karimi MS, GhorbanpourArani A. Nonlinear Vibration and Instability Analysis of Functionally Graded CNTReinforced Cylindrical Shells Conveying Viscous Fluid Resting on Orthotropic Pasternak Medium. Mech Adv Mater Struct 2016; 23: 819–831. ##[21] Mohammadimehr M, RoustaNavi B, GhorbanpourArani A. Free Vibration of Viscoelastic DoubleBonded Polymeric Nanocomposite Plates Reinforced by FGSwcnts Using MSGT, Sinusoidal Shear Deformation Theory and Meshless Method. Compos Struct 2015; 131: 654–671. ##[22] Mohammadimehr M, RoustaNavi B, GhorbanpourArani A. Modified Strain Gradient Reddy Rectangular Plate Model for Biaxial Buckling and Bending Analysis of DoubleCoupled Piezoelectric Polymeric Nanocomposite Reinforced by FGSWNT. Compos Part BEng 2016; 87: 132–148. ##[23] Mohammadimehr M, Salemi M, RoustaNavi B. Bending, Buckling, and Free Vibration Analysis of MSGT Microcomposite Reddy Plate Reinforced by FGSwcntswith TemperatureDependent Material Properties under HydroThermoMechanical Loadings Using DQM. Compos Struct 2016; 138: 361–380. ##[24] Ghorbanpour Arani A, Jamali M, Mosayyebi M, Kolahchi R. Analytical Modeling of Wave Propagation in Viscoelastic Functionally Graded Carbon Nanotubes Reinforced Piezoelectric Microplate under ElectroMagnetic Field. Mech Eng J NanoEng NanoSys, Doi: 1740349915614046. ##[25] Shen HS. Nonlinear Bending of Functionally Graded Carbon NanotubeReinforced Composite Plates in Thermal Environments. Compos Struct 2009; 91: 9–19. ##[26] Fazelzadeh SA, Pouresmaeeli S, Ghavanloo E. Aeroelastic Characteristics of Functionally Graded CarbonNanotubeReinforced Composite Plates undera Supersonic Flow. Comput Methods Appl Mech Eng 2015; 285: 714–729. ##[27] Lei ZX, Liew KM, Yu JL. Buckling Analysis of Functionally Graded Carbon NanotubeReinforced Composite Plates Using the ElementFree KpRitz Method. Compos Struct 2013; 98: 160–168. ##[28] AmabiliM. Nonlinear vibrations and stability of shells and plates. Cambridge University Press; 2008. ##[29] Kiani Y, Akbarzadeh AH, Chen ZT, Eslami MR. Static and Dynamic Analysis of an FGM Doubly Curved Panel Resting on the PasternakType Elastic Foundation. Compos Struct 2012; 94: 2474–2484. ##[30] MatsunagaH. Free Vibration and Stability of Functionally Graded Shallow Shells According to a2D HigherOrder Deformation Theory. Compos Struct 2008; 84: 132–146. ##[31] Zhang LW, Lei ZX, Liew KM. An ElementFree IMLSRitz Framework for Buckling Analysis of FGCNT Reinforced Composite Thick Plates Resting on Winkler Foundations. Eng Anal Bound Elem 2015; 58: 7–17. ##[32] Matsunaga H. Vibration and Stability of Thick Simply Supported Shallow Shells Subjected to InPlane Stresses. J Sound Vib 1999; 225: 41–60.##]
Dynamic Stability of Moderately Thick Composite Laminated Skew Plates using Finite Strip Method
2
2
The dynamic instability regions of composite laminated skew flat plates subjected to uniform inplane axial endloading are investigated. The inplane loading is assumed as a combination of a timeinvariant component and a harmonic timevarying component uniformly distributed along two opposite panel ends’ width. In case of some loading frequencyamplitude pairconditions, the model is subjected to instabilities. The dynamic instability margins of the skewed flat panel have been extracted using a developed semianalytical finite strip formulation. The method has been developed based on a fullenergy approach through the principle of the virtual work. The effects of thickness have been included by utilizing a thirdorder Reddy type shear deformation theory. The effects of boundary conditions as well as geometry on the instability loadfrequency regions are derived using the Bolotin's firstorder approximation. In order to demonstrate the capabilities of the developed method in predicting the structural dynamic behavior, some representative results are obtained and compared with those in the literature wherever available.
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145
150


Jamshid
Fazilati
Aerospace Research Institute, Tehran, Iran
Aerospace Research Institute, Tehran, Iran
Iran
jfazilati@ari.ac.ir
Parametric instability
Finite strip method
Skew plate
Third order shear deformation theory
[[1] Heuer R, Irschik H, Ziegler F. Nonlinear Random Vibrations of Thermally Buckled Skew Plates. Probab Eng Mech 1993; 8(3–4): 265–271. ##[2] Hu HT, Tzeng WL. Buckling Analysis of Skew Laminate Plates Subjected to Uniaxial Inplane Loads. ThinWalled Struct 2000; 38: 53–77. ##[3] Dey P, Singha MK. Dynamic Stability Analysis of Composite Skew Plates Subjected to Periodic InPlane Load. ThinWalled Struct 2006; 44: 937–942. ##[4] Lee SY. Finite element dynamic stability analysis of laminated composite skew plates containing cutouts based on HSDT. Comp Sci Technol 2010; 70: 1249–1257. ##[5] Tahmasebinejad A, Shanmugam NE. Elastic Buckling of Uniaxially Loaded Skew Plates Containing Openings. ThinWalled Struc 2011; 49: 1208–1216. ##[6] Noh MH, Lee SY. Dynamic Instability of Delaminated Composite Skew Plates Subjected to Combined Static and Dynamic Loads Based on HSDT. Compos Part B 2014; 58: 113–121. ##[7] Singha MK, Daripa R. Nonlinear Vibration of Symmetrically Laminated Composite Skew Plates by Finite Element Method. Int J NonLinear Mech 2007; 42: 1144–1152. ##[8] Wang S. Free Vibration Analysis of Skew FibreReinforced Composite Laminates Based on FirstOrder Shear Deformation Plate Theory. Comput Struct 1997; 63: 525–538.##]