Vibrations and stability analysis of multiple rectangular plates coupled with elastic layers based on different plate theories

• Vibrations and stability of multiple plate systems are investigated.
• Different plate theories (CPT, FSDT and HSDT) are used in frequency analysis.
• Stability regions are determined.
• General mode shapes are presented.

Analytical solutions of natural frequencies and critical buckling loads for a set of homogenous plates in the complex plate system are determined in this paper. A different layerwise approach is found via interconnecting several plates into one kind of layered block. For this determination, the classical, first order and high order shear deformation theories are used to present rotary inertia and shear effects on systems with different numbers of elastically connected plates. Closed form solutions are determined in the form of explicit expressions of natural frequencies and critical buckling loads. General mode shapes are presented for systems of elastically connected plates. The stability of the complex system is determined and discussed for different stiffnesses of the support, layers and various geometric dimensions. These results are of considerable practical interest and have a wide application in the engineering practice of frameworks. The range of frequencies depending on number of elastically connected plates in the block is discovered.