Static and free vibration analyses of functionally graded sandwich plates using state space differential quadrature method

• The governing equation of motion and constitutive relation are based on three-dimensional theory of elasticity.
• Closed form analytical solution for simply supported edges condition.
• Analytical solution along the thickness direction and DQM along the in-plane coordinates.

This study presents static and free vibration behaviors of two type of sandwich plates based on the three dimensional theory of elasticity. The core layer of one type is functionally graded material (FGM) with the isotropic face sheets whereas in second type, the core layer is isotropic with the face sheets FGM. The effective material properties of FGM layers are estimated to vary continuously through the thickness direction according to a power-law distribution of the volume fractions of the constituents. By using differential equilibrium equations and/or equations of motion as well as constitutive relations, state-space differential equation can be derived. In the case of simply supported condition, applying Fourier series to the quantities along the in-plane coordinates, governing equation can be solved analytically and for the other edges condition, a semi analytical solution can be obtained by using differential quadrature method (DQM) along the in-plane coordinate as well as state spaces technique in the thickness direction. Accuracy and exactness of the present approach is validated by comparing the numerical results with the results of published literature. Moreover, the influences of volume fraction, width-to-thickness ratios and aspect ratio on the vibration and static behaviors of plate are investigated.