Three-dimensional vibration analysis of sandwich and multilayered plates with general ply stacking sequences by a spectral-sampling surface method

Abstract This paper investigates the three-dimensional (3-D) vibration characteristics of sandwich and multilayered plates with general ply stacking sequences and arbitrary restraints based on a spectral-sampling surface method. The theoretical formulation is undertaken by the 3-D theory of elasticity such that it is able to study the dynamic behavior of sandwich and multilayered plates very well, even in the presence of soft layers. Under the current framework, a set of sampling surfaces along the thickness direction of each plate layer are primarily selected and the displacements of these surfaces are chosen as basic plate variables. Consequently, vibration solutions for sandwich and multilayered plates with different thicknesses, material properties and ply stacking sequences can be derived up to desired accuracy by selecting sufficient number of sampling surfaces. In addition, the penalty technique and Lagrange multiplier method are adopted to relax the enforcement of the boundary conditions. As a result, the proposed formulation can be applied efficiently to the 3-D vibration analysis of sandwich and multilayered plates with general restraints. The final solutions are determined by a modified variational principle, in which each of the basic plate variables is approximated by the spectral method. Results show that the present method is capable of calculating highly accurate numerical results for thick sandwich and multilayered plates with general ply stacking sequences and arbitrary boundary conditions.

[1]  K. Liew,et al.  Three-dimensional vibration analysis of multilayered piezoelectric composite plates , 2006 .

[2]  Liz G. Nallim,et al.  An analytical–numerical approach to simulate the dynamic behaviour of arbitrarily laminated composite plates , 2008 .

[3]  Gennady M. Kulikov,et al.  Exact 3D stress analysis of laminated composite plates by sampling surfaces method , 2012 .

[4]  E. Carrera.  Theories and finite elements for multilayered, anisotropic, composite plates and shells , 2002 .

[5]  M. Gharib,et al.  A state space augmented generalised RKPM for three-dimensional analysis of thick and laminated composite plates , 2015 .

[6]  K. M. Liew,et al.  Vibration analysis of symmetrically laminated thick rectangular plates using the higher-order theory and p-Ritz method , 1997 .

[7]  Gennady M. Kulikov,et al.  Three-dimensional exact analysis of piezoelectric laminated plates via a sampling surfaces method , 2013 .

[8]  Arthur W. Leissa,et al.  On the three‐dimensional vibrations of the cantilevered rectangular parallelepiped , 1983 .

[9]  S. Kapuria,et al.  Three-dimensional extended Kantorovich solution for Levy-type rectangular laminated plates with edge effects , 2014 .

[10]  Erasmo Carrera,et al.  CZ° requirements—models for the two dimensional analysis of multilayered structures , 1997 .

[11]  Ding Zhou,et al.  Free vibrations of rectangular unsymmetrically laminated composite plates with internal line supports , 2001 .

[12]  G. Kulikov,et al.  Heat conduction analysis of laminated shells by a sampling surfaces method , 2014 .

[13]  Sinniah Ilanko,et al.  Penalty methods for finding eigenvalues of continuous systems: Emerging challenges and opportunities , 2012 .

[14]  Guang Meng,et al.  Three-dimensional elasticity solution for vibration analysis of composite rectangular parallelepipeds , 2013 .

[15]  Erasmo Carrera,et al.  Finite deformation higher-order shell models and rigid-body motions , 2008 .

[16]  Tiangui Ye,et al.  A spectral-sampling surface method for the vibration of 2-D laminated curved beams with variable curvatures and general restraints , 2016 .

[17]  Tiangui Ye,et al.  Structural vibration : a uniform accurate solution for laminated beams, plates and shells with general boundary conditions , 2015 .

[18]  J. R. Banerjee,et al.  An exact spectral-dynamic stiffness method for free flexural vibration analysis of orthotropic composite plate assemblies – Part I: Theory , 2015 .

[19]  Erasmo Carrera,et al.  Plates and Shells for Smart Structures: Classical and Advanced Theories for Modeling and Analysis , 2011 .

[20]  K. M. Liew,et al.  Vibration analysis of symmetrically laminated plates based on FSDT using the moving least squares differential quadrature method , 2003 .

[21]  Ding Zhou,et al.  Three-dimensional free vibration analysis of doubly-curved shells , 2015 .

[22]  Metin Aydogdu,et al.  A new shear deformation theory for laminated composite plates , 2009 .

[23]  G. Kulikov.  Refined Global Approximation Theory of Multilayered Plates and Shells , 2001 .

[24]  Bo Liu,et al.  Exact solutions for free vibrations of orthotropic rectangular Mindlin plates , 2011 .

[25]  Arcangelo Messina,et al.  Vibration of completely free composite plates and cylindrical shell panels by a higher-order theory , 1999 .

[26]  Erasmo Carrera,et al.  Analysis of thickness locking in classical, refined and mixed multilayered plate theories , 2008 .

[27]  A. S. Sarigül,et al.  Free vibration analysis of symmetrically laminated thin composite plates by using discrete singular convolution (DSC) approach: Algorithm and verification , 2008 .

[28]  Ashraf M. Zenkour,et al.  Bending of orthotropic plates resting on Pasternak’s foundations using mixed shear deformation theory , 2011 .

[29]  Luigi Iurlaro,et al.  The (3,2)-Mixed Refined Zigzag Theory for generally laminated beams: Theoretical development and C0 finite element formulation , 2015 .

[30]  Abdullateef M. Al-Khaleefi,et al.  Free vibration analysis of thin arbitrarily laminated anisotropic plates using boundary-continuous displacement Fourier approach , 2001 .

[31]  Wei Chen,et al.  3D free vibration analysis of cross-ply laminated plates with one pair of opposite edges simply supported , 2005 .

[32]  Parviz Malekzadeh,et al.  A two-dimensional layerwise-differential quadrature static analysis of thick laminated composite circular arches , 2009 .

[33]  Guang Meng,et al.  A variational method for free vibration analysis of joined cylindrical-conical shells , 2013 .

[34]  Jianqiao Ye,et al.  A three-dimensional free vibration analysis of cross-ply laminated rectangular plates with clamped edges , 1997 .

[35]  Dhanjoo N. Ghista,et al.  Mesh-free radial basis function method for static, free vibration and buckling analysis of shear deformable composite laminates , 2007 .

[36]  Zhendong Hu,et al.  Free vibration of simply supported and multilayered magneto-electro-elastic plates , 2015 .

[37]  Ghodrat Karami,et al.  Static, free vibration and buckling analysis of anisotropic thick laminated composite plates on distributed and point elastic supports using a 3-D layer-wise FEM , 2004 .

[38]  Simon Wang,et al.  Free vibration analysis of skew fibre-reinforced composite laminates based on first-order shear deformation plate theory , 1997 .

[39]  Warna Karunasena,et al.  Free vibration analysis of laminated composite plates based on FSDT using one-dimensional IRBFN method , 2011 .

[40]  K. M. Liew,et al.  Three-dimensional analysis of the coupled thermo-piezoelectro-mechanical behaviour of multilayered plates using the differential quadrature technique , 2005 .

[41]  E. Carrera.  Theories and Finite Elements for Multilayered Plates and Shells:A Unified compact formulation with numerical assessment and benchmarking , 2003 .

[42]  J. Hodgkinson,et al.  Layerwise optimisation for maximising the fundamental frequencies of point-supported rectangular laminated composite plates , 2005 .

[43]  K. M. Liew,et al.  Buckling and vibration analysis of isotropic and laminated plates by radial basis functions , 2011 .

[44]  Ernian Pan,et al.  FREE VIBRATIONS OF SIMPLY SUPPORTED AND MULTILAYERED MAGNETO-ELECTRO-ELASTIC PLATES , 2002 .

[45]  J. N. Reddy,et al.  Energy principles and variational methods in applied mechanics , 2002 .

[46]  Gregory E. Fasshauer,et al.  Computation of natural frequencies of shear deformable beams and plates by an RBF-pseudospectral method , 2006 .

[47]  C. Guedes Soares,et al.  A new trigonometric shear deformation theory for isotropic, laminated composite and sandwich plates , 2012 .

[48]  Guang Meng,et al.  A Domain Decomposition Method for Vibration Analysis of Conical Shells With Uniform and Stepped Thickness , 2013 .

[49]  Xiong Zhang,et al.  Linear statics and free vibration sensitivity analysis of the composite sandwich plates based on a layerwise/solid-element method , 2013 .

[50]  Tiangui Ye,et al.  Elasticity solution for vibration of generally laminated beams by a modified Fourier expansion-based sampling surface method , 2016 .

[51]  Hongguang Li,et al.  Three-dimensional free and transient vibration analysis of composite laminated and sandwich rectangular parallelepipeds: Beams, plates and solids , 2015 .

[52]  L. Fox,et al.  Chebyshev polynomials in numerical analysis , 1970 .

[53]  Huu-Tai Thai,et al.  A simple refined theory for bending, buckling, and vibration of thick plates resting on elastic foundation , 2013 .

[54]  H. Razi,et al.  Three-dimensional dynamic analysis of laminated composite plates subjected to moving load , 2009 .

[55]  Yogesh M. Desai,et al.  Analytical solutions for vibrations of laminated and sandwich plates using mixed theory , 2004 .

[56]  Zhu Su,et al.  A modified Fourier solution for vibration analysis of moderately thick laminated plates with general boundary restraints and internal line supports , 2014 .

[57]  J. Reddy.  Mechanics of laminated composite plates and shells : theory and analysis , 1996 .

[58]  A. R. Setoodeh,et al.  A hybrid layerwise and differential quadrature method for in-plane free vibration of laminated thick circular arches , 2008 .