Exact eigenvalue correspondences between laminated plate theories via membrane vibration

Based on Reddy's third-order theory, the first-order theory and the classic al theory, exact explicit eigenvalues are found for compression buckling, t hermal buckling and vibration of laminated plates via analogy with membrane vibration, These results apply to symmetrically laminated composite plates with transversely isotropic laminae and simply supported polygonal edges, Comprehensive consideration of a Winkler-Pasternak elastic foundation, a hy drostatic inplane force, an initial temperature increment and rotary inerti as is incorporated. Bridged by the vibrating membrane, exact correspondence s are readily established between any pairs of buckling and vibration eigen values associated with different theories. Positive definiteness of the cri tical hydrostatic pressure at buckling, the thermobukling temperature incre ment and, in the range of either tension loading or compression loading pri or to occurrence of buckling, the natural vibration frequency is proved. (C ) 2000 Elsevier Science Ltd. All rights reserved.