Membrane Analogy of Buckling and Vibration of Inhomogeneous Plates

Abstract

Exact explicit eigenvalues are found for compression buckling, hygrothermal buckling, and vibration of sandwich plates with dissimilar facings and functionally graded plates via analogy with membrane vibration. These results apply to simply supported polygonal plates using the first-order shear deformation theory and the classical theory. A Winkler-Pasternak elastic foundation, a hydrostatic inplane force, hygrothermal effects, and rotary inertias are incorporated. Bridged by the vibrating membrane, exact correspondence is readily established between any pairs of eigenvalues associated with buckling and vibration of sandwich plates, functionally graded plates, and homogeneous plates. Positive definiteness is proved for the critical buckling hydrostatic pressure and, in the range of either tension loading or compression loading prior to occurrence of buckling, for the natural vibration frequency.