Exact eigenvalue correspondences between laminated plate theories via membrane vibration

Based on Reddyʹs third-order theory, the ®rst-order theory and the classical theory, exact explicit eigenvalues are found for compression buckling, thermal 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 hydrostatic inplane force, an initial temperature increment and rotary inertias is incorporated. Bridged by the vibrating membrane, exact correspondences are readily established between any pairs of buckling and vibration eigenvalues associated with di€erent theories. Positive de®niteness of the critical hydrostatic pressure at buckling, the thermobukling temperature increment and, in the range of either tension loading or compression loading prior to occurrence of buckling, the natural vibration frequency is proved