2017
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87
Synthesis and Characterization of Polymer/Nanosilicagel Nanocomposites
2
2
In this study, a polymersilica nanocomposite using the solgel method was synthesized in three steps at room temperature. The nanocomposite material was formed with an organic compound (polyethylene glycol) and inorganic silica nanoparticles. Furthermore, the size and the distribution of nanoparticles in the polymer matrix were characterized by a transmission electron microscope (TEM). In addition, the refractometer analysis was used to measure the refractive index of the nanocomposite. Following that, Fourier transform infrared (FTIR) spectroscopy and smallangle Xray diffraction and high Xray diffraction have also used to characterize the polymer and the inorganic part of the nanocomposite. TEM studies showed the distribution of nanoscale silica particles of the size of 50100 (nm) in the polymer matrix. Furthermore, the refractive index of the nanocomposite was measured about 1.4, which was very close to the refractive index of the natural lens (1.411). Additionally, the FTIR spectra showed OH groups in FTIR spectroscopy, which confirmed the hydrophilic property of silica nanoparticles and the two sharp peaks at the angles of 19° and 23° in the Xray diffraction analyses, which were in the nature of the crystallinity of polyethylene glycol. Finally, the results showed the surface modification of nanoparticles and their incorporation in a polymer matrix, which led to the formation of the desired nanocomposite that was made of inorganic (silica nanoparticles) and an organic (polyethylene glycol) compound.
1

1
8


F.
Shakooeea
Faculty of Materials and Metallurgical Engineering, Semnan University, Semnan, Iran
Faculty of Materials and Metallurgical Engineering
Iran
fshakouey@yahoo.com


Mardali
Yousefpoar
Faculty of Materials and Metallurgical Engineering, Semnan University, Semnan, Iran
Faculty of Materials and Metallurgical Engineering
Iran
myousefpor@semnan.ac.ir


Mohammad
Tajali
Faculty of Materials and Metallurgical Engineering, Semnan University, Semnan, Iran
Faculty of Materials and Metallurgical Engineering
Iran
mtajali@semnan.ac.ir
Nanocomposite
Biocompatible polymer
Silica
Solgel
Refractive index
Rheology
Intraocular lenses
[[1] Danieldasilva AL, Pinto F, Lopesdasilva JA, Trindade T, Goodfellow BJ, Gil AM. Rheological behavior of thermoreversible κcarrageenan / nanosilica gels. Colloid Interface Sci 2008; 320: 365614. ##[2] Kango S, Kalia S, Celli A, Njuguna J, Habibi Y, Kumar R. Surface modification of inorganic nanoparticles for development of organicinorganic nanocomposites  A review. Prog Polym Sci 2013; 38: 12321261. ##[3] Annaka M, Mortensen K, Matsuura T, Nochiokad MIK, Ogata N. Organicinorganic nanocomposite gels as an in situ gelation biomaterial for injectable accommodative intraocular lens. Soft Mater 2012; 8: 71857196. ##[4] Nagarwal CR, Kant S, Singh PN, Maiti P, Pandit JK. Polymeric nanoparticulate system: A potential approach for ocular drug delivery. J Control Rel 2009; 136: 213. ##[5] Hao X, Jeffery JL, Wilkie JS, Meijs GF, Clayton AB, Watling JD, Ho A, Fernandez V, Acosta C, Yamamoto H, Mohamed GM, Parel JM, Hughes TC. Functionalised polysiloxanes as injectable, in situ curable accommodating intraocular lenses. Biomaterials 2010; 31: 81538163. ##[6] Nishi O, Nishi Y, Chang S, Nishi K. Accommodation amplitudes after an accommodating intraocular lens refilling procedure: In vivo update. J Cataract Refract Surg 2014; 40: 295305. ##[7] Assia E. Accommodative intraocular lens: A challenge for future development. J Cataract Refract Surg 1997; 23: 332336. ##[8] Colthurst MJ, Williams RL, Hiscott PS, Grierson I. Biomaterials used in the posterior segment of the eye. Biomaterials 2000; 21: 649665. ##[9] DeBoer C, Wan Do H, Lee J, Humayun M, Tai YC. Biomimetic accommodating intraocular lens. IEEE; 2012. ##[10] Kayo ON, Nishi NY, Chang S. Capsular bag refilling using a new accommodating intraocular lens. J Cataract Refract Surg 2008; 34: 302309. ##[11] Reilly MA, Hamilton PD, Perry G, Ravi N. Comparison of the behavior of natural and refilled porcine lenses in a robotic lens stretcher. Experim Eye Res 2009; 88: 483494. ##[12] Nishi Y, Mireskandari K, Khaw P. Lens refilling to restore accommodation. J Cataract Refract Surg 2009; 35: 374382. ##[13] Nishi O, Nishi K, Mano C, Ichihara M, Honda T. Lens refilling with injectable silicone in rabbit eyes. J Cataract Refract Surg 1998; 24: 975982. ##[14] Hunter JJ, Melanie CW, Geraghty E. Optical analysis of an accommodating intraocular lens. J Cataract Refract Surg 2006; 32: 269278. ##[15] Vilupuru AS, Glasser A. Optical and biometric relationships of the isolated pig crystalline lens. Ophthal Physiol Opt 2001; 21: 296311. ##[16] Koopmans SA, Terwee T, Van Kooten TG. Prevention of capsular opacification after accommodative lens refilling surgery in rabbits. Biomaterials 2011; 32: 57435755. ##[17] Koopmans SA, Terwee T, Hanssen A, Martin H, Langner S, Stachs O, Van Kooten TG. Prevention of capsule opacification after accommodating lens refilling: Pilot study of strategies evaluated in a monkey model. J Cataract Refract Surg 2014; 40: 15211535. ##[18] Rana A, Miller D, Magnante P. Understanding the accommodating intraocular lens. J Cataract Refract Surg 2003; 29: 22842287. ##[19] Entabi M, Harman F, Lee N, Bloom PA. Injectable, 1piece hydrophilic acrylic toric intraocular lens for cataract surgery: Efficacy and stability. J Cataract Refract Surg 2011; 37: 235240. ##[20] Xu T, Jiaa Z, Luo Y, Jia D, Pengba Z. Interfacial interaction between the epoxidized natural rubber andsilica in natural rubber/silica composites. Appl Surf Sci 2015; 328: 306313. ##[21] Yousefpour MA, Taherian Z. The effects of ageing time on the microstructure and properties of mesoporous silicahydroxyapatite nanocomposite. Superlattices Microstruct 2013; 54: 7886. ##[22] He L, Li J, Zhou C, Zhu H, Cao Z, Tang B. Phase change characteristics of shapestabilized PEG/SiO2 composites using calcium chlorideassisted and temperatureassisted sol gel methods. Solar Energy 2014; 103: 448455. ##[23] Khanna L, Verma NK. Study on novel, superparamagnetic and biocompatible PEG/KFeO2 nanocomposite. J Appl Biomedicine 2014; 349: 116120. ##[24] Evora VMF, Shukla A. Fabrication, characterization, and dynamic behavior of polyester/TiO2 nanocomposites. Mater Sci Eng A 2003; 361(12): 358366. ##[25] Oh C, Ki CD, Chang JY, Oh SG. Preparation of PEGgrafted silica particles using emulsion method. Mater Letters 2005; 59: 929933. ##[26] Kiasat AR, Nazari S, Davarpanah J. Facile synthesis of an organicinorganic nanocomposite, PEGsilica, by solgel method; its characterization and application as an efficient catalyst in regioselective nucleophilic ring opening of epoxides: Preparation of bazido alcohols and bcyanohydrins. Chimie 2014; 17: 124130. ##[27] Kwon JW, Han YK, Lee WJ, Cho CS, Paik SJ, Cho D, Lee JH, Wee WR. Biocompatibility of poloxamer hydrogel as an injectable intraocular lens. J Cataract Refract Surg 2005; 31: 607613. ##[28] Hao X, Jeffery JL, Tam PT, McFarland G, Johnson G, Mulder RJ, Garrett Q, Nankivil FMD, Arrieta E, Ho A, Parel JM, Hughes TC. High refractive index polysiloxane as Injectable, in situ curable accommodating intraocular lens. Biomaterials 2012; 33: 56595671. ##[29] Kjoniksen AL, Nystro B, Lindman B. Dynamic viscoelasticity of gelling and nongelling aqueous mixtures of ethyl (hydroxyethyl) cellulose and an ionic surfactant. Macromolecules 1998; 31: 18521858. ##[30] Qian T, Li J, Yang H. The preparationofagreenshapestabilized composite phase change material of polyethyleneglycol/SiO2 with enhanced thermal performance based on oil shaleash via temperatureassisted solgel method, Solar Energy Mater Solar Cells 2015; 132: 2939.##]
Distribution of Residual Stresses in Polymer Reinforced Carbon Nanotubes and Laminated Carbon Fibers
2
2
In this study, the distribution of residual stress in fiberreinforced nanocomposites is investigated. Fiberreinforced nanocomposite is composed of three substances: carbon fiber, carbon nanotube (CNT), and polymer matrix. Unit cells in hexagonal packing array with different arrays as unit cell, 3*3 and 5*5 arrays have been selected as suitable for finite element analysis of residual stresses. Radial and tangential residual stress have been determined in different directions by finite element analysis using ABAQUS commercial software for each phase individually. The effect of the CNTs’ various volume fractions (0%, 1%, 2%, and 3%) on residual stress distribution has been studied in different directions and compared to one another for each phase. Results show that the 3*3 unit cells arrays are suitable for modeling microresidual stresses, and the results of this array are reliable. In addition, adding a 3% volume fraction of CNTs to the matrix is the best option for reduction of overall residual stresses with minimal fluctuation in local microresidual stresses.
1

9
18


Ahmad Reza
Ghasemi
University of Kashan
University of Kashan
Iran
ghasemi@kashanu.ac.ir


Mohammad
MohammadiFesharaki
University of Kashan
University of Kashan
Iran
mohammadi.shirazu@gmail.com
Residual stresses
Carbon nanotube
Nanocomposite
Unit cell
[[1] Hahn HT, Pagano NJ. Curing stresses in composite laminates. J Compos Mater 1975; 9(1): 91106. ##[2] Shokrieh MM, Ghasemi AR. Simulation of central hole drilling process for measurement of residual Stresses in isotropic, orthotropic, and laminated composite plates .J Compos Mater 2007; 41(4): 435452. ##[3] Ghasemi AR, Shokrieh MM. Development of an integral method for determination of nonuniform residual stresses in laminated composites. Iran J Polym Sci & Tech 2008; 21(4): 347355. ##[4] Ghasemi A, TaheriBehrooz F, Shokrieh M. Determination of nonuniform residual stresses in laminated composites using integral hole drilling method: Experimental evaluation. J Compos Mater 2014; 48(4): 415425. ##[5] Ghasemi AR, Mohammadi M. Calculation of calibration factors for determination of residual stresses in fibermetal laminates using incremental holedrilling method. J Sci Tech Compos 2014; 1(1): 3544. ##[6] Ghasemi AR, Mohammadi M. Residual stress measurement of fiber metal laminates using incremental holedrilling technique in consideration of the integral method. Int J Mech Sci 2016; 114: 246256. ##[7] Abouhamzeh M, Sinke J, Jansen KMB, Benedictus R. Closed form expression for residual stresses and warpage during cure of composite laminates. Compos Struct 2015; 133: 902910. ##[8] Chen Y, Xia Z, Ellyin F. Evolution of Residual Stresses Induced During Curing Processing Using a Viscoelastic Micromechanical Model. Compos. Mater 2001; 35: 522542. ##[9] Aghdam MM, Khojeh A. More on the Effects of Thermal Residual and Hydrostatic Stresses on Yielding Behavior of Unidirectional Composites. Compos Struct 2003; 62: 285290. ##[10] Karami G, Garnich M. Micromechanical Study of Thermoelastic Behavior of Composites with Periodic Fiber Waviness, Compos Part B 2005; 36: 241248. ##[11] Zhao LG, Warrior N.A, Long AC. A ThermoViscoelastic Analysis of ProcessInduced Residual Stress in FibreReinforced Polymer–Matrix Composites, Mater Sci Eng 2007; 452: 483498. ##[12] Jin KK, Huang Y, Lee Y, Sung KH. Distribution of MicroStresses and Interfacial Tractions in Unidirectional Composites. Compos Mater 2008; 42: 18251849. ##[13] Quek M. Analysis of Residual Stresses in a Single Fibre–Matrix Composite. IntJ Adhes Adhes 2004; 24(5): 379388. ##[14] Hsueh C H, Becher PF, Sun EY. Analyses of thermal expansion behavior of intergranular twophase composites. J Mater Sci 2001; 36: 255261. ##[15] Jayaraman K, Reifsnider KL. Residual Stresses in a Composite with Continuously Varying Young’s Modulus in the Fiber/Matrix Interphase. Compos Mater 1992; 26: 770791. ##[16] Jayaraman K, Reifsnider KL. The Interphase in Unidirectional FiberReinforced Epoxies: Effect of Residual Thermal Stresses. Compos Sci Technol 1993; 47: 119129. ##[17] Bianchi V, Goursat P, Menessier E. CarbonFiberReinforced YMAS Glass Ceramic Matrix IV Thermal Residual Stresses and Fiber/Matrix Interfaces. Compos Sci Technol 1998; 58: 409418. ##[18] Quek MY, Yue CY. Axisymmetric Stress Distribution inthe Single Filament Pull outTest. Mater Sci Eng 1994; 189: 105116. ##[19] Zhang Y, Xia Z, Ellyin F. Evolution and Influence of Residual Stresses/Strains of Fiber Reinforced Laminates. Compos Sci Technol 2004; 64: 16131625. ##[20] Song DY, Takeda N, Ogihara S. A Method of Stress Analysis for Interfacial Property Evaluation in Thermoplastic Composites. Mater Sci Eng 2000; 278: 242246. ##[21] Levin I, Kaplan WD, Brandon D,Wieder T. Residual stresses in aluminaSiC nanocomposites. Acta Metall Mater 1994; 42(4): 11471154. ##[22] Todd R, Bourke M, Borsa C, Brook R. Neutron diffraction measurements of residual stresses in alumina/SiC nanocomposites. Acta Mater 1997; 45(4): 17911800. ##[23] Wu H. Residual stresses in composite materials. Woodhead Publishing; 2014. ##[24] Maligno AR. Finite element investigations on the microstructure of composite materials. Ph.D. Thesis, University of Nottingham, 2008. ##[25] Moreno MM, Marques FD. Influence of Boundary Conditions on the Determination of Effective Material Properties for Active Fiber Composites. 11th PanAmerican Cong Appl Mech; 2010. ##[26] Shokrieh MM, GhaneiMohammadi AR. Finite Element Modeling of Residual Thermal Stresses in FiberReinforced Composites Using Different Representative Volume Elements. World Cong Eng; 2010. ##[27] Shokrieh MM, Safarabadi M. Threedimensional analysis of micro residual stresses in fibrous composites based on the energy method: a study including interphase effects. J Com Mat 2012; 46(6): 727735. ##[28] Shokrieh M, Daneshvar A and Akbari S. Reduction of thermal residual stresses of laminated polymer composites by addition of carbon nanotubes. Mater Des 2014; 53: 209216. ##[29] Ghasemi AR, Mohammadi MM, Mohandes M. The role of carbon nanofibers on thermomechanical properties of polymer matrix composites and their effect on reduction of residual stresses. Compos Part B 2015; 77: 519527. ##[30] Ghasemi AR and Mohammadi M. Threedimensional residual stresses analysis of nanocomposite polymeric matrix based on fiber reinforced carbon nanotubes. J Sci Tech Comp 2016; 4(2): 2330. ##[31] Ghasemi AR, Mohammadi M. Development of Circular Disk Model for Polymeric Nanocomposites and Micromechanical Analysis of Residual Stresses in Reinforced Fibers with Carbon Nanotubes. Comput Methods Appl Mech Eng 2017; 35(2): 177196. ##[32] Ghasemi AR, MohammadiFesharaki M, Mohandes M. ThreePhase Micromechanical Analysis of Residual Stresses in Reinforced Fiber by Carbon Nanotubes. J Compos Mat 2016; DOI: 10.1177/0021998316669854. ##[33] Zhao LG, Warrior LA, Long AC. A Micromechanical Study of Residual Stress and Its Effect on Transverse Failure in Polymer–Matrix Composites. Int J sol struct 2006; 43: 54495467.##]
Study of Laminated Composite MEMS and NEMS Performance in Nano Metric Operations
2
2
Precision of nanometric operations is an important issue in nanoengineering studies. Several operative parameters might affect the quality of results. The parameters of the nano world are significant but not entirely controllable. However, the geometrical and mechanical properties of micro cantilevers are completely controllable. So, controlling the sensitivity of resulting image through t lamination design could be a proper approach. This paper analyses the effects of composite lamination on the performance of common Micro and Nano Electro Mechanical systems (MEMS and NEMS, respectively). Generalized Differential Quadrature (GDQ) and Generalized Differential Quadrature Element (GDQE) methods are used as semianalytic solutions for regular and irregular domains, respectively. Validity, applicability and accuracy of the proposed approach are demonstrated and then the lamination effects on the nanoimaging and manipulation of nano particles by micro cantilevers are studied. This study shows that some laminations of micro cantilevers resulted in a better performance in nanomanipulation and imaging. Furthermore, clarifying the dependency of system sensitivity on the profile of the substrate is remarkable.
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19
31


Sadegh
Sadeghzadeh
School of new Technology, Iran University of Science and Technology
School of new Technology, Iran University
Iran
sadeghzadeh@iust.ac.ir


Moharram
Habibnejad Korayem
Iran University of Science and Technology
Iran University of Science and Technology
Iran
hkorayem@iust.ac.ir


Ahmad
Homayooni
Iran University of Science and Technology
Iran University of Science and Technology
Iran
homayooni@iust.ac.ir
Laminated Composite
MEMS and NEMS
GDQM
GDQEM
Nanomanipulation
[[1] Uchino K. Piezoelectric Actuators 2004–Materials, Design, Drive/Control, Modeling and Applications. Proc 9th Int Conf New Actuators; 2004. ##[2] Lee S, Kim J, Moon W, Choi J, Park I, Bae D. A multibodybased dynamic simulation method for electrostatic actuators. Nonlinear Dyn 2008; 54: 5368. ##[3] Lim YH, Varadan VV, Varadan VK. Finiteelement modeling of the transient response of MEMS sensors. Smart Mater Struct 1997; 6: 5361. ##[4] Beek JV, Puers R. A review of MEMS oscillators for frequency reference and timing applications. J Micromechanics Microengineering 2011; 22: 013001. ##[5] Korayem M, Rahneshin V, Sadeghzadeh S. Coarsegrained molecular dynamics simulation of automatic nanomanipulation process: The effect of tip damage on the positioning errors. Comput Mater Sci 2012; 60: 201211. ##[6] Korayem M, Rahneshin V, Sadeghzadeh S. Nano cluster manipulation success considering flexibility of system: Coarse grained molecular dynamics simulations. Scientia Iranica 2012; 19: 12881298. ##[7] Darvizeh M, Darvizeh A, Ansari R, Sharma C. Buckling analysis of generally laminated composite plates (generalized differential quadrature rules versus Rayleigh–Ritz method). Compos Struct 2004; 63: 6974. ##[8] HosseiniHashemi S, Fadaee M, Taher HRD. Exact solutions for free flexural vibration of Lévytype rectangular thick plates via thirdorder shear deformation plate theory. Appl Math Model 2011; 35: 708727. ##[9] Hashemi SH, Arsanjani M. Exact characteristic equations for some of classical boundary conditions of vibrating moderately thick rectangular plates. Int J Solids Struct 2005; 42: 819853. ##[10] Tornabene F. Free vibrations of anisotropic doublycurved shells and panels of revolution with a freeform meridian resting on Winkler–Pasternak elastic foundations. Compos Struct 2011; 94: 186206. ##[11] Balamurugan V, Narayanan S. A piezolaminated composite degenerated shell finite element for active control of structures with distributed piezosensors and actuators. Smart Mater Struct 2008; 17: 035031. ##[12] Benjeddou A. Advances in piezoelectric finite element modeling of adaptive structural elements: a survey. Comput Struct 2000; 76: 347363. ##[13] Tornabene F. 2D GDQ solution for free vibrations of anisotropic doublycurved shells and panels of revolution. Compos Struct 2011; 93: 18541876. ##[14] Hong C. Computational approach of piezoelectric shells by the GDQ method. Compos Struct 2010; 92: 811816. ##[15] Chen C. A differential quadrature element method. Proc 1st Int Conf Eng Comput Sim; 1995. ##[16] Korayem M, Sadeghzadeh S, Homayooni A. Semianalytical motion analysis of nanosteering devices, segmented piezotube scanners. Int J Mech Sci 2011; 53: 536548. ##[17] Korayem M, Homayooni A, Sadeghzadeh S, Safa M, Rahneshin V. A semianalytic modeling of nonlinearities for nanorobotic applications, macro and micro sized systems. 2nd Int Conf Control, Instrumentation Automation; 2011. ##[18] Sadeghzadeh S, Korayem MH, Rahneshin V, Homayooni A, Moradi M. Nanorobotic Applications of Finite Element Method. Computational Finite Element Methods in Nanotechnology, Editor: Musa S. CRC Press: Taylor and Francis Corporation; 2012. ##[19] Sadeghzadeh S, Korayem M, Rahneshin V, Homayooni A. A shapefeedback approach for more precise automatic nano manipulation process. 2nd Int Conf Control, Instrumentation and Automation; 2011. ##[20] Hamed S, Ghader R. Comparison of generalized differential quadrature and Galerkin methods for the analysis of microelectromechanical coupled systems. Commun Nonlinear Sci Numer Sim 2009; 14: 28072816. ##[21] Collinger J, Wickert JA, Corr L. Adaptive piezoelectric vibration control with synchronized switching. J Dyn Sys Measurement Control 2009; 131: 041006.##]
Improving Mechanical Properties of Nanocompositebased Epoxy by Highimpact Polystyrene and Multiwalled Carbon Nanotubes: Optimizing by a Mixture Design Approach
2
2
In the current study the influence of weight percentage of HIPS, weight percentage of CNT and hardener content on damping 1st and damping 2nd properties of epoxy/HIPS/CNT hybrid composite wase valuated. Mixture design methodology was employed to generate mathematical models for predicting damping 1st and damping 2nd behaviors of new mentioned hybrid nanocomposite as function of physical factors and optimizing desired mechanical properties. The maximum and minimum values of damping 1st occurred in run numbers 7 and 1 and were 3.71%and 1.64 % respectively, moreover maximum and minimum values of damping 2nd occurred in coded levels 9 and 1 with the values of 4.25% and 1.82 % respectively. Results of analysis of variance showed that input variables had linear effect on both of the studied responses, also two component interactions X1*X2, X1*X3 and X2*X3 affected damping 1st and damping 2nd due to their obtained Pvalues. Optimization results described that the highest value for damping 1st and damping 2nd were 3.53% and 4.11% respectively.Coded values were HIPS= 0.222, CNT= 0.301 and hardener= 0.476 and corresponding mixture components were HIPS=4.18wt%, CNT= 1.12 wt% and hardener= 25.75phr respectively.
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33
45


Yasser
Rostamiyan
Department of Mechanical Engineering, Sari Branch, Islamic Azad University, Sari, Iran
Department of Mechanical Engineering, Sari
Iran
y.rostamiyan@yahoo.com
Carbon fibre
Hybrid
Laminates
Mechanical properties
Mixture Design
[[1] Xu M, Hu J, Zou X, Liu M, Dong S, Zou Y. Mechanical and thermal enhancements of benzoxazinebased GF composite laminated by in situ reaction with carboxyl functionalized CNTs. J Appl Polym Sci 2013; 129(5): 26292637. ##[2] Eronat N, Candan U, Turkun M. Effects of glass fiber layering on the flexural strength of microfill and hybrid composites. J Esthetic Restorative Dentistry 2009; 21(3): 171178. ##[3] Wu X, Wang Y, Xie L, Yu J, Liu F, Jiang P. Thermal and electrical properties of epoxy composites at high alumina loadings and various temperatures. Iranian Polym J 2013; 22(1): 6173. ##[4] LeBaron PC, Wang Z, Pinnavaia TJ, Polymerlayered silicate nanocomposites: an overview. Appl Clay Sci 1999; 15(12): 1129. ##[5] Vallittu PK. Flexural properties of acrylic resin polymers reinforced with unidirectional and woven glass fibers. J Prosthetic Dentistry 2009; 81(3): 318326. ##[6] Rostamiyan Y, Fereidoon A, Rezaeiashtiyani M, Mashhadzadeh AH, Salmankhani A. Experimental and optimizing flexural strength of epoxybased nanocomposite: Effect of using nano silica and nano clay by using response surface design methodology. Mater Des 2015; 69: 96104. ##[7] Rostamiyan Y, Fereidoon A, Mashhadzadeh AH, Ashtiyani MR, Salmankhani A. Using response surface methodology for modeling and optimizing tensile and impact strength properties of fiber orientated quaternary hybrid nano composite. Compos Part B: Eng 2015; 69: 304316. ##[8] Panthapulakkal S, Sain M. Injectionmolded short hemp fiber/glass fiberreinforced polypropylene hybrid composites  Mechanical, water absorption and thermal properties. J Appl Polym Sci 2007; 103(4): 24322441. ##[9] Bekyarova E, Thostenson ET, Yu A, Kim H, Gao J, Tang J. Multiscale carbon nanotubecarbon fiber reinforcement for advanced epoxy composites. Langmuir 2007; 23(7): 39703974. ##[10] Godara A, Mezzo L, Luizi F, Warrier A, Lomov SV, van Vuure AW. Influence of carbon nanotube reinforcement on the processing and the mechanical behaviour of carbon fiber/epoxy composites. Carbon 2009; 47(12): 29142923. ##[11] Xu Y, Hoa SV. Mechanical properties of carbon fiber reinforced epoxy/clay nanocomposites. Compos Sci Technol 2008; 68(34): 854861. ##[12] Gojny FH, Wichmann MHG, Fiedler B, Bauhofer W, Schulte K. Influence of nanomodification on the mechanical and electrical properties of conventional fibrereinforced composites. Compos Part A: Appl Sci Manuf 2005; 36(11): 15251535. ##[13] Akbari R, Beheshty M, Shervin M. Toughening of dicyandiamidecured DGEBAbased epoxy resins by CTBN liquid rubber. Iran Polym J 2013; 22(5): 313324. ##[14] Ragosta G, Musto P, Scarinzi G, Mascia L, Epoxysilica particulatenanocomposites: Chemical interactions, reinforcement and fracture toughness Polym 2005; 46: 1050610516. ##[15] Mirmohseni A., Zavareh S. Epoxy/acrylonitrilebutadienestyrene copolymer/clay ternary nanocomposite as impact toughened epoxy. J Polym Res 2010; 17(2): 191201. ##[16] Becker O, Varley RJ, Simon GP. Thermal stability and water uptake of high performance epoxy layered silicate nanocomposites. Eur Polym J 2004; 40(1): 187195. ##[17] Zheng Y, Zheng Y, Ning R, Effects of nanoparticles SiO2 on the performance of nanocomposites. Mater Let 2003; 57(19): 29402944. ##[18] Uddin MF, Sun CT. Improved dispersion and mechanical properties of hybrid nanocomposites. Compos Sci Technol 2010; 70(2): 223230. ##[19] Rostamiyan Y, Fereidoon AB. Preparation, Modeling, and optimization of mechanical properties of epoxy/HIPS/silica hybrid nanocomposite using combination of central composite design and genetic algorithm. Part 1. Study of damping and tensile strengths. Strength Mater 2013; 45(5): 619634. ##[20] Fereidoon A, Mashhadzadeh HA, Rostamiyan Y, Experimental, modeling and optimization study on the mechanical properties of epoxy/highimpact polystyrene/multiwalled carbon nanotube ternary nanocomposite using artificial neural network and genetic algorithm, J Sci Eng Compos Mater 2013; 20(3): 265276. ##[21] Rostamiyan Y, Fereidoon AB, Mashhadzadeh AH, Khalili MA. Augmenting epoxy toughness by combination of both thermoplastic and nanolayered materials and using artificial intelligence techniques for modeling and optimization. J Polym Res 2013; 20(6): 111. ##[22] Mirmohseni A, Zavareh S. Modeling and optimization of a new impacttoughened epoxy nanocomposite using response surface methodology. J Polym Res 2011; 18(4): 509517. ##[23] Mirmohseni A, Zavareh S. Preparation and characterization of an epoxy nanocomposite toughened by a combination of thermoplastic, layered and particulate nanofillers. Mater Des 2010; 31(6): 26992706. ##[24] Leardi R. Experimental design in chemistry: A tutorial. Analytica Chimica Acta 2009; 652(12): 161172. ##[25] Zhang C, Wong WK. Optimal designs for mixture models with amount constraints. Statistics Probability Let 2013; 83(1): 196202. ##[26] Rostamiyan Y, Mashhadzadeh AH, Salman Khani A. Optimization of mechanical properties of epoxybased hybrid nanocomposite: Effect of using nano silica and highimpact polystyrene by mixture design approach. Mater Des 2014; 56: 10681077. ##[27] Rostamiyan Y, Fereidoon A, Ghasemi Ghalebahman A, Mashhadzadeh AH, Salmankhani A. Experimental study and optimization of damping properties of epoxybased nanocomposite: Effect of using nanosilica and highimpact polystyrene by mixture design approach. Mater Des 2015; 65: 12361244. ##[28] Rostamiyan Y, Mashhadzadeh AH, Fereidoon A. Investigation of damping and toughness properties of epoxybased nanocomposite using different reinforcement mechanisms: Polymeric alloying, nanofiber, nanolayered, and nanoparticulate materials. J Sci Eng Compos Mater 2015; 22(3): 223229. ##[29] Pionteck J, Muller Y, Haubler L. Reactive epoxyCTBN rubber blends: Reflection of changed curing mechanism in cure shrinkage and phase separation behaviour. Macromolecular Symposia 2011; 306307(1): 126140. ##[30] Lopez J, Ramirez C, Abad MJ, Barral L, Cano J, Diez FJ. Blends of acrylonitrilebutadienestyrene with an epoxy/cycloaliphatic amine resin: Phaseseparation behavior and morphologies. J ApplPolym Sci 2002; 85(6): 12771286.##]
On the Buckling the Behavior of a Multiphase Smart Plate based on a Higherorder Theory
2
2
Magnetoelectroelastic materials are multiphase smart materials that exhibit coupling among electrical, magnetic and mechanical energy fields. Due to this ability, they have been the topic of numerous research in the past decade. In this paper, buckling behavior of a multiphase magnetoelectroelastic rectangular plate with simply supported boundary conditions is investigated, based on Reddy’s higherorder shear deformation theory. Gauss’s laws for electrostatics and magnetostatics are used to model the electric and magnetic behaviors of the plate. The partial differential equations of motion are reduced to ordinary differential equations by using the Galerkin method. Then, the closedform expression for the critical buckling load of the plate considered is obtained. Some examples are presented to validate the study and to investigate the effects of some parameters on the critical buckling loads of the multiphase magnetoelectroelastic rectangular plates. It is found that the buckling behavior of the magnetoelectroelastic plate is dominated by the elastic properties of the plate, and magnetoelectric coefficients slightly increase the critical buckling load of the plate.
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47
58


Soheil
Razavi
Young Researchers and Elite Club, Tabriz Branch, Islamic Azad University, Tabriz, Iran
Young Researchers and Elite Club, Tabriz
Iran
soheilrazavi@outlook.com
analytical solution
Buckling load
Higherorder plate theory
Magnetoelectroelastic coupling
Smart plate
[[1] Brunelle EJ. Buckling of transversely isotropic Mindlin plates. AIAA Journal 1971; 9: 101822. ##[2] Mizusawa T. Buckling of rectangular Mindlin plates with tapered thickness by the spline strip method. Int J Solids Struct 1993; 30: 166377. ##[3] Dawe DJ, Wang S. Spline finite strip analysis of the buckling and vibration of rectangular composite laminated plates. Int J Mech Sci 1995; 37: 64567. ##[4] Wang W, Bert CW, Striz AG. Differential quadrature analysis of deflection, buckling, and free vibration of beams and rectangular plates. Comput Struct 1993; 48: 4739. ##[5] Teo TM, Liew KM. A differential quadrature procedure for threedimensional buckling analysis of rectangular plates. Int J Solids Struct 1999; 36: 114968. ##[6] Mohieddin Ghomshei MM, Mahmoudi A. Thermal buckling analysis of crossply laminated rectangular plates under nonuniform temperature distribution: A differential quadrature approach. J Mech Sci Tech 2010; 24: 251927. ##[7] Wang X, Wang Y, Ge L. Accurate buckling analysis of thin rectangular plates under locally distributed compressive edge stresses. ThinWalled Struct 2016; 100: 8192. ##[8] Wang X, Wang X, Shi X. Accurate buckling loads of thin rectangular plates under parabolic edge compressions by the differential quadrature method. Int J Mech Sci 2007; 49: 44753. ##[9] Cui S, Hao H, Cheong HK. Numerical analysis of dynamic buckling of rectangular plates subjected to intermediatevelocity impact. Int J Impact Eng 2001; 25(2): 14767. ##[10] Xiang Y, Wang CM. Exact buckling and vibration solutions for stepped rectangular plates. J Sound Vib 2002; 250(3): 50317. ##[11] Chen XL, Liew KM. Buckling of rectangular functionally graded material plates subjected to nonlinearly distributed inplane edge loads. Smart Mater Struct 2004; 13(6): 14307. ##[12] Wang D, Peng H. A Hermite reproducing kernel Galerkin meshfree approach for buckling analysis of thin plates. Comput Mech 2013; 51(6): 101329. ##[13] Javaheri R, Eslami MR. Thermal buckling of functionally graded plates based on higher order theory. J Thermal Stresses 2002; 25(7): 60325. ##[14] Matsunaga H. Thermal buckling of functionally graded plates according to a 2D higherorder deformation theory. Compos Struct 2009; 90(1): 7686. ##[15] Selim S, Akbarov SD. FEM analysis of the threedimensional buckling problem for a clamped thick rectangular plate made of a viscoelastic composite. Mech Compos Mater 2003; 39(6): 53140. ##[16] Ghorbanpour Arani A, Maghamikia Sh, Mohammadimehr M, Arefmanesh A. Buckling analysis of laminated composite rectangular plates reinforced by SWCNTs using analytical and finite element methods. J Mech Sci Technol 2011; 25(3): 80920. ##[17] Mohammadi M, Saidi AR, Jomehzadeh E. Levy solution for buckling analysis of functionally graded rectangular plates. Appl Compos Mater 2010; 17(2): 8193. ##[18] Kim SE, Thai HT, Lee J. Buckling analysis of plates using the two variable refined plate theory. ThinWalled Struct 2009; 47(4): 45562. ##[19] Thai HT, Kim SE. Levytype solution for buckling analysis of orthotropic plates based on two variable refined plate theory. Compos Struct 2011; 93(7): 173846. ##[20] Bodaghi M, Saidi AR. Levytype solution for buckling analysis of thick functionally graded rectangular plates based on the higherorder shear deformation plate theory. Appl Math Model 2010; 34(11): 365973. ##[21] Thai HT, Vo TP. A new sinusoidal shear deformation theory for bending, buckling, and vibration of functionally graded plates. Appl Math Model 2013; 37(5): 326981. ##[22] Kulkarni K, Singh BN, Maiti DK. Analytical solution for bending and buckling analysis of functionally graded plates using inverse trigonometric shear deformation theory. Compos Struct 2015; 134: 14757. ##[23] Bouazza M, Lairedj A, Benseddiq N, Khalki S. A refined hyperbolic shear deformation theory for thermal buckling analysis of crossply laminated plates. Mech Res Commun 2016; 73: 11726. ##[24] Grover N, Maiti DK, Singh BN. A new inverse hyperbolic shear deformation theory for static and buckling analysis of laminated composite and sandwich plates. Compos Struct 2013; 95: 66775. ##[25] Sayyad AS, Ghugal YM. Buckling and free vibration analysis of orthotropic plates by using exponential shear deformation theory. Latin American J Solids Struct 2014; 11(8): 1298314. ##[26] Fares ME, Zenkour AM. Buckling and free vibration of nonhomogeneous composite crossply laminated plates with various plate theories. Compos Struct 1999; 44(4): 27987. ##[27] Zenkour AM. Buckling of fiberreinforced viscoelastic composite plates using various plate theories. J Eng Math 2004; 50(1): 7593. ##[28] Ranjbaran A, Khoshravan MR, Kharazi M. Buckling analysis of sandwich plate using layerwise theory. J Mech Sci Technol 2014; 28(6): 276977. ##[29] Cetkovic M. Thermal buckling of laminated composite plates using layerwise displacement model. Compos Struct 2016; 142: 23853. ##[30] Jabbari M, Farzaneh Joubaneh E, Khorshidvand AR, Eslami MR. Buckling analysis of porous circular plate with piezoelectric actuator layers under uniform radial compression. Int J Mech Sci 2013; 70: 506. ##[31] Jandaghian AA, Rahmani O. On the buckling behavior of piezoelectric nanobeams: An exact solution. J Mech Sci Technol 2015; 29(8): 317582. ##[32] Pan E. Exact solution for simply supported and multilayered magnetoelectroelastic plates. J Appl Mech 2001; 68(4): 60818. ##[33] Pan E, Heyliger PR. Free vibrations of simply supported and multilayered magnetoelectroelastic plates. J Sound Vib 2002; 252(3): 42942. ##[34] Xue CX, Pan E, Zhang SY, Chu HJ. Large deflection of a rectangular magnetoelectroelastic thin plate. Mech Res Commun 2011; 38(7): 51823. ##[35] Razavi S, Shooshtari A. Nonlinear free vibration of magnetoelectroelastic rectangular plates. Compos Struct 2015; 119: 37784. ##[36] Kattimani SC, Ray MC. Smart damping of geometrically nonlinear vibrations of magnetoelectroelastic plates. Compos Struct 2014; 114: 5163. ##[37] Xu XJ, Deng ZC, Zhang K, Meng JM. Surface effects on the bending, buckling and free vibration analysis of magnetoelectroelastic beams. Acta Mech 2016; 227(6): 155773. ##[38] Li YS, Ma P, Wang W. Bending, buckling, and free vibration of magnetoelectroelastic nanobeam based on nonlocal theory. J Intelligent Mater Sys Struct 2016; 27(9): 113949. ##[39] Li YS. Buckling analysis of magnetoelectroelastic plate resting on Pasternak elastic foundation. Mech Res Commun 2014; 56: 10414. ##[40] Kumaravel A, Ganesan N, Sethuraman R. Buckling and vibration analysis of layered and multiphase magnetoelectroelastic cylinders subjected to uniform thermal loading. Multidiscipline Model Mater Struct 2010; 6(4): 47592. ##[41] Lang Z, Xuewu L. Buckling and vibration analysis of functionally graded magnetoelectrothermoelastic circular cylindrical shells. Appl Math Model 2013; 37(4): 227992. ##[42] Ansari R, Gholami R, Rouhi H. Sizedependent nonlinear forced vibration analysis of magnetoelectrothermoelastic Timoshenko nanobeams based upon the nonlocal elasticity theory. Compos Struct 2015; 126: 216226. ##[43] Ebrahimi F, Barati MR. Magnetoelectroelastic buckling analysis of nonlocal curved nanobeams. Eur Phys J Plus 2016; 131: 346 (13 pages). ##[44] Jamalpoor A, AhmadiSavadkoohi A, HosseiniHashemi Sh. Free vibration and biaxial buckling analysis of magnetoelectroelastic microplate resting on viscoPasternak substrate via modified strain gradient theory. Smart Mater Struct 2016; 25(10): 105035. ##[45] Farajpour A, Hairi Yazdi MR, Rastgoo A, Loghmani M, Mohammadi M. Nonlocal nonlinear plate model for large amplitude vibration of magnetoelectroelastic nanoplates. Compos Struct 2016; 140: 323336. ##[46] Xu X, Deng Z, Zhang K, Meng J. Surface effects on the bending, buckling and free vibration analysis of magnetoelectroelastic beams. Acta Mech 2016; 227(6): 15571573. ##[47] Liu J, Zhang P, Lin G, Wang W, Lu S. High order solutions for the magnetoelectroelastic plate with nonuniform materials. Int J Mech Sci 2016; 115116: 532551. ##[48] Zhou Y, Zhu J. Vibration and bending analysis of multiferroic rectangular plates using thirdorder shear deformation theory. Compos Struct 2016; 153: 712723. ##[49] Wenjun W, Peng L, Feng J. Twodimensional linear elasticity theory of magnetoelectroelastic plates considering surface and nonlocal effects for nanoscale device applications. Smart Mater Struct 2016; 25(9): 095026 (15 pages). ##[50] Reddy JN. Mechanics of laminated composite plates and shells: theory and analysis. 2nd ed. CRC Press; 2004. ##[51] Razavi S, Shooshtari A. Free vibration analysis of a magnetoelectroelastic doublycurved shell resting on a Pasternaktype elastic foundation. Smart Mater Struct 2014; 23(10): 105003 (9 pages). ##[52] Wu CP, Lu YC. A modified Pagano method for the 3D dynamic responses of functionally graded magnetoelectroelastic plates. Compos Struct 2009; 90(3): 36372.##]
Free Vibration and Buckling Analyses of Functionally Graded Nanocomposite Plates Reinforced by Carbon Nanotube
2
2
This paper describes the application of refined plate theory to investigate free vibration and buckling analyses of functionally graded nanocomposite plates reinforced by aggregated carbon nanotube (CNT). The refined shear deformation plate theory (RSDT) uses four independent unknowns and accounts for a quadratic variation of the transverse shear strains across the thickness, satisfying the zero traction boundary conditions on the top and bottom surfaces of the plate without using shear correction factors. The motion equations are derived from Hamilton’s energy principle and Navier’s method is applied to solve this equation. The material properties of the functionally graded carbon nanotube reinforced composites (FGCNTRCs) are assumed to vary along the thickness and estimated with the Mori–Tanaka approach. Effects on the natural frequency and critical buckling load of the FGCNTRC plates by CNT volume fraction, CNT distribution, CNT cluster distribution, and geometric dimensions of the plate are investigated. Effects of loading conditions on the critical buckling load are also examined.
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59
73


Rasool
Moradidastjerdi
Young Researchers and Elite Club,Khomeinishahr Branch, Islamic Azad University, Khomeinishahr, Iran
Young Researchers and Elite Club,Khomeinishahr
Iran
rasoul.moradi@iaukhsh.ac.ir


Hosein
MalekMohammadi
Department of Mechanical Engineering, BuAli Sina University, Hamedan
Department of Mechanical Engineering, BuAli
Iran
hoseinmm15@yahoo.com
Mori–Tanaka approach
Refined plate theory
Aggregated carbon nanotubes
Free Vibration
Buckling
[[1] Esawi AMK, Farag MM, Carbon nanotube reinforced composites: potential and current challenges. Mate Des, 2007; 28: 23942401. ##[2] Lau AKT, Hui D, The revolutionary creation of new advanced materialscarbon nanotube composites. Compos Part B, 2002; 33: 263277. ##[3] Thostenson ET, Ren Z, Chou TW, Advances in the science and technology of carbon nanotubes and their composites: a review. Compos Sci Technol, 2001; 61: 18991912. ##[4] Han Y, Elliott J, Molecular dynamics simulations of the elastic properties of polymer/carbon nanotube composites. Comput Mater Sci, 2007; 39: 315323. ##[5] Alian, AR, Kundalwal, SI, Meguid, SA, Multiscale modeling of carbon nanotube epoxy composites, Polym, 2015; 70, 149160. ##[6] Kundalwal, SI, Ray MC, Smart damping of fuzzy fiber reinforced composite plates using 13 piezoelectric composites, J Vib Control, 2016; 22: 15261546. ##[7] Kundalwal, SI, Meguid, SA, Effect of carbon nanotube waviness on active damping of laminated hybrid composite shells, Acta Mech, 2015; 226, 20352052. ##[8] Ray, MC, Kundalwal, SI, Effect of Carbon Nanotube Waviness on the Load Transfer Characteristics of Short Fuzzy FiberReinforced Composite, J Nanomech Micromech, 2013; 4, A4013010. ##[9] Wuite J, Adali S, Deflection and stress behaviour of nanocomposite reinforced beams using a multiscale analysis. Compos struct, 2005; 71: 388396. ##[10] Formica G, Lacarbonara W, Alessi R, Vibrations of carbon nanotube reinforced composites. J Sound Vib, 2010; 329: 18751889. ##[11] Vodenitcharova T, Zhang LC, Bending and local buckling of a nanocomposite beam reinforced by a singlewalled carbon nanotube. Inter J Solid Struct, 2006; 43: 30063024. ##[12] Reddy JN, Analysis of functionally graded plates. Int J Numerical Methods Eng, 2000; 47: 663684. ##[13] Zenkour AM, A comprehensive analysis of functionally graded sandwich plates. Part 2buckling and free vibration deflection and stresses. Inter J Solid Struc, 2005; 42: 52435258. ##[14] Cheng ZQ, Batra RC, Deflection relationships between the homogeneous Kirchhoff plate theory different functionally graded plate theories. Archive Mech, 2000; 52: 143158. ##[15] Cheng ZQ, Batra RC, Exact correspondence between eigenvalues of membranes and functionally graded simply supported polygonal plates. J Sound Vib, 2000; 229: 879895. ##[16] Amabili, M, Karazis, K, Khorshidi, K, Nonlinear vibrations of rectangular laminated composite plates with different boundary conditions, Inter J Struct Stab Dyn, 2011; 11, 673695. ##[17] Khorshid, K, Farhadi, S, Free vibration analysis of a laminated composite rectangular plate in contact with a bounded fluid, Compos struct, 2013; 104, 176186. ##[18] Khorshidi, K, Bakhsheshy, A, Free vibration analysis of a functionally graded rectangular plate in contact with a bounded fluid, Acta Mech, 2015; 226, 34013423. ##[19] Tahouneh, V, Naei, MH, SemiAnalytical Solution for Free Vibration Analysis of Thick Laminated Curved Panels with PowerLaw Distribution FG Layers and Finite Length Via TwoDimensional GDQ Method, J solid mech, 2016; 8, 334347. ##[20] Tahouneh, V, Naei, MH, Free vibration and vibrational displacements analysis of thick elastically supported laminated curved panels with powerlaw distribution functionally graded layers and finite length via 2D GDQ method, JSandw Struct Mater, 2016; 18, 263293. ##[21] Tahouneh, V, Yas, MH, Tourang, H, Kabirian, M, Semianalytical solution for threedimensional vibration of thick continuous grading fiber reinforced (CGFR) annular plates on Pasternak elastic foundations with arbitrary boundary conditions on their circular edges, Meccanica, 2013; 48, 13131336. ##[22] Tahouneh, V, Yas, MH, Semianalytical solution for threedimensional vibration analysis of thick multidirectional functionally graded annular sector plates under various boundary conditions, J Eng Mech, 2013, 140, 3146. ##[23] Shen HS, Postbuckling of nanotubereinforced composite cylindrical shells in thermal environments, Part I: Axiallyloaded shells. Compos struct, 2011; 93: 209620108. ##[24] Mehrabadi SJ, Sobhani Aragh B, Khoshkhahesh V, Taherpour A, Mechanical buckling of nanocomposite rectangular plate reinforced by aligned and strait singlewalled carbon nanotubes. Compos Part B, 2012; 43: 20312040. ##[25] Mori T, Tanaka K, Average stress in matrix and average elastic energy of materials with Misfitting inclusions. Acta Metallurgica, 1973; 21: 571574. ##[26] Yas MH, Heshmati M, Dynamic analysis of functionally graded nanocomposite beams reinforced by randomly oriented carbon nanotube under the action of moving load. Applied Math Modelling, 2012; 36: 13711394. ##[27] Sobhani Aragh B, Nasrollah Barati AH, Hedayati H, Eshelby–Mori–Tanaka approach for vibrational behavior of continuously graded carbon nanotube–reinforced cylindrical panels. Compos Part B, 2012; 43: 19431954. ##[28] Pourasghar A, Yas MH, Kamarian S, Local aggregation effect of CNT on the vibrational behavior of fourparameter continuous grading nanotubereinforced cylindrical panels. Polymer Compos, 2013; 34: 707721. ##[29] MoradiDastjerdi R, Pourasghar A, Foroutan M, The effects of carbon nanotube orientation and aggregation on vibrational behavior of functionally graded nanocomposite cylinders by a meshfree method. Acta Mech, 2013; 224: 28172832. ##[30] 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, 113130. ##[31] Tahouneh, V, Yas, MH, Influence of equivalent continuum model based on the EshelbyMoriTanaka scheme on the vibrational response of elastically supported thick continuously graded carbon nanotubereinforced annular plates, Polym Compos, 2014; 35, 16441661. ##[32] Tahouneh, V, Naei, MH, The effect of multidirectional nanocomposite materials on the vibrational response of thick shell panels with finite length and rested on twoparameter elastic foundations, Int J Adv Struct Eng, 2016; 8, 1128. ##[33] Tahouneh, V, Using an equivalent continuum model for 3D dynamic analysis of nanocomposite plates, Steel Compos Struct, 2016; 20, 623649. ##[34] Tahouneh, V, Naei, MH, Using EshelbyMoriTanaka scheme for 3D free vibration analysis of sandwich curved panels with functionally graded nanocomposite face sheets and finite length, Polym Compos, 2016; DOI: 10.1002/pc. 23929. ##[35] AM Zenkour, Generalized shear deformation theory for bending analysis of functionally graded plates. Applied Math Modelling, 2006; 30: 6784. ##[36] Zenkour AM, The refined sinusoidal theory for FGM plates on elastic foundations, Inter J Mech Sci, 2009; 51, 869880. ##[37] Merdaci S, Tounsi A, Houari MS, Mechab I, Hebali H, Benyoucef S, Two new refined shear displacement models for functionally graded sandwich plates. Archive Applied Mech, 2011; 81: 15071522. ##[38] Thai HT, Choi DH, A refined plate theory for functionally graded plates resting on elastic foundation. Compos Sci Technol, 2011; 71: 18501858. ##[39] Akavci SS, Buckling and free vibration analysis of symmetric and antisymmetric laminated composite plates on an elastic foundation. J Reinf Plast Compos, 2007; 26: 19071919. ##[40] Benyoucef S, Mechab I, Tounsi A, Fekrar A, Ait Atmane H, Adda Bedia EA, Bending of thick functionally graded plates resting on WinklerPasternak elastic foundations. Mech Compos Mater, 2010; 46: 425434. ##[41] MoradiDastjerdi, R, Payganeh, G, MalekMohammadi, H, Free Vibration Analyses of Functionally Graded CNT Reinforced Nanocomposite Sandwich Plates Resting on Elastic Foundation, J solid mech, 2015; 7, 158172 ##[42] Khorshid, K, Fallah, A, Buckling analysis of functionally graded rectangular nanoplate based on nonlocal exponential shear deformation theory, Inter J Mech Sci, 2016; 113, 94104. ##[43] Khorshidi, K, Asgari, T, Fallah, A, Free Vibrations Analysis of Functionally Graded Rectangular Nanoplates based on Nonlocal Exponential Shear Deformation Theory, Mech Adv Compos Struct, 2015; 2, 7993. ##[44] Khorshidi, K, Khodadadi, M, Precision Closedform Solution for Outofplane Vibration of Rectangular Plates via Trigonometric Shear Deformation Theory, Mech Adv Compos Struct, 2016; 3, 3143. ##[45] Ait Atmane H, Tounsi A, Mechab I, Adda Bedia EA, Free vibration analysis of functionally graded plates resting on WinklerPasternak elastic foundations using a new shear deformation theory. Inter J Mech Mater Des, 2010; 6: 113121. ##[46] Shi DL, Feng XQ, Yonggang YH, Hwang KC, Gao, H, The effect of nanotube waviness and agglomeration on the elastic property of carbon nanotube reinforced composites. J Eng Mater Technol, 2004; 126, 250257. ##[47] Prylutskyy YI, Durov SS, Ogloblya OV, Buzaneva EV, Scharff P, Molecular dynamics simulation of mechanical, vibrational and electronic properties of carbon nanotubes. Comput Mater Sci, 2000; 17: 352355. ##[48] Odegard GM, Gates TS, Wise KE, Park C, Siochi EJ, Constitutive modeling of nanotubereinforced polymer composites. Compos Sci Technol, 2003; 63: 16711687. ##[49] Barai P, Weng GJ, A theory of plasticity for carbon nanotube reinforced composite. Inter J Plast Technol, 2011; 27: 539559. ##[50] Matsunaga H, Free vibration and stability of functionally graded plates according to a 2D higherorder deformation theory. Compos struct, 2008; 82: 499512. ##[51] Bodaghi M, Saidi AR, Levytype solution for buckling analysis of thick functionally graded rectangular plates based on the higherorder shear deformation plate theory. Appl Math Modelling, 2010; 34, 36593673. ##[52] Thai, HT, Choi, DH, An efficient and simple refined theory for buckling analysis of functionally graded plates. Appl Math Modelling, 2012; 36: 10081022. ##]
A Numerical and Analytical Solution for the Free Vibration of Laminated Composites Using Different Plate Theories
2
2
An analytical and numerical solution for the free vibration of laminated polymeric composite plates with different layups is studied in this paper. The governing equations of the laminated composite plates are derived from the classical laminated plate theory (CLPT) and the firstorder shear deformation plate theory (FSDT). General layups are evaluated by the assumption of crossply and angleply laminated plates. The solver is coded in MATLAB. As a verification method, a finite element code using ANSYS is also developed. The effects of lamination angle, plate aspect ratio and modulus ratio on the fundamental natural frequencies of a laminated composite are also investigated and good agreement is found between the results evaluated and those available in the open literature. The results show that the fundamental frequency increases with the modular ratio and the bendingstretching coupling lowers the vibration frequencies for both crossply and angleply laminates with the CLPT. Also it is found that the effect of bendingstretching coupling, transverse shear deformation and rotary inertia is to lower the fundamental frequencies.
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75
87


Mohammad Amin
Torabizadeh
University of Applied Science and Technology
University of Applied Science and Technology
Iran
torabizadeh@yahoo.com


Abdolhossein
Fereidoon
University of Semnan
University of Semnan
Iran
ab.fereidoon@gmail.com
Free Vibration
laminated composites
plate theories
numerical method
analytical method
[[1] Campbell FC. Structural composite materials, ASM international; 2011. ##[2] Tan p, Nie JG. Free and forced vibration of variable stiffness composite annular thin plates with elastically restrained edges. Compos Struct 2016; 149: 398407. ##[3] Zhang LW, Zhang Y, Zou GL, Liew KM. Free vibration analysis of triangular CNTreinforced composite plates subjected to inplane stresses using FSDT elementfree method. Compos Struct 2016; 149: 247260. ##[4] Chakraborty S, Mandal B, Chowdhury R, Chakrabarti A. Stochastic free vibration analysis of laminated composite plates using polynomial correlated function expansion. Compos Struct 2016; 135: 236249. ##[5] Ganesh S, Kumar KS, Mahato PK. Free Vibration Analysis of Delaminated Composite Plates Using Finite Element Method. Int Conf Vib Problems; 2015. 10671075. ##[6] Mantari JL, Ore M. Free vibration of single and sandwich laminated composite plates by using a simplified FSDT. Compos Struct 2015; 132: 952959. ##[7] Su Z, Jin G, Wang X. Free vibration analysis of laminated composite and functionally graded sector plates with general boundary conditions. Compos Struct 2015; 132: 720736. ##[8] Zhang LW, Lei ZX, Liew KM. Free vibration analysis of functionally graded carbon nanotubereinforced composite triangular plates using the FSDT and elementfree IMLSRitz method. Compos Struct 2015; 120: 189199. ##[9] Marjanivic M, Vuksanovic D. Layerwise solution of free vibrations and buckling of laminated composite and sandwich plates with embedded delamination. Compos Struct 2014; 108: 920. ##[10] Boscolo M. Analytical solution for free vibration analysis of composite plates with layerwise displacement assumptions. Compos Struct 2013; 100: 493510. ##[11] Qu Y, Wu S, Li H, Meng G. Threedimensional free and transient vibration analysis of composite laminated and sandwich rectangular parallelepipeds: Beams, plates and solids. Compos Part B: Eng 2015; 73: 96110. ##[12] Rafiee M, Liu XF, He XQ, Kitipornchai S. Geometrically nonlinear free vibration of shear deformable piezoelectric carbon nanotube/fiber/polymer multiscale laminated composite plates. J Sound Vib 2014; 333 (14): 32363251. ##[13] Akhras G, Li W. Stability and free vibration analysis of thick piezoelectric composite plates using spline finite strip method. Int J Mech Sci 2011; 53 (8): 575584. ##[14] Grover N, Singh BN, Maiti DK. Analytical and finite element modeling of laminated composite and sandwich plates: An assessment of a new shear deformation theory for free vibration response. Int J Mech Sci 2013; 67: 8999. ##[15] Jafari RA, Abedi M, Kargarnovin MH, Ahmadian MT. An analytical approach for the free vibration analysis of generally laminated composite beams with shear effect and rotary inertia. Int J Mech Sci 2012; 65 (1): 97104. ##[16] Tai H, Kim S. Free vibration of laminated composite plates using two variable refined plate theories. Int J Mech Sci 2010; 52 (4): 626633. ##[17] Srinivasa CV, Suresh JY, kumar WP. Experimental and finite element studies on free vibration of skew plates. Int J Adv Struct Eng 2014; 48 (6): 123129. ##[18] Ramu I, Mohanty SC. Study on Free Vibration Analysis of Rectangular Plate Structures Using Finite Element Method. Proc Eng2012; 38: 27582766. ##[19] Chandrashekhara K. Free vibration of composite beams including rotary inertia and shear deformation. Compos Struct 1990; 14 (4): 269279. ##[20] Ke L, Yang J, Kitipornchai S. Nonlinear free vibration of functionally graded carbon nanotubereinforced composite beams. Compos Struct 2010; 92 (3): 676683. ##[21] Song O. Free Vibration of Anisotropic Composite ThinWalled Beams of Closed CrossSection Contour. J Sound Vib 1993; 167 (1): 129147. ##[22] Lee J. Free vibration analysis of delaminated composite beams. Comput Struct 2000; 74 (2): 121129. ##[23] Reddy JN. Mechanics of laminated composite plates and shells, theory and analysis. 2nd ed. CRC Press; 2003. ##[24] Bathe KJ. Finite element procedures. PrentieHall, Englewood cliffs; 1996.##]