Flexural vibration analysis of functionally graded sandwich plates resting on elastic foundation with arbitrary boundary conditions: Chebyshev collocation technique

Abstract

This paper aims to present accurate solutions for flexural vibration of functionally graded sandwich plates resting on two-parameter elastic foundation with any combined boundary conditions. The governing equations of free vibration problem are derived from the first-order shear deformation theory that covers the important effects of shear deformation and rotary inertia. To solve the coupled differential equations governing vibration behavior of the plates with various boundary conditions, an effective tool, namely Chebyshev collocation method, is implemented to obtain the accurate solutions with several parametric studies. The influences of material volume fraction index, layer thickness ratio, side-to-height ratio, boundary conditions, etc., on natural frequencies of the plates are taken into investigation and discussed in details. Our numerical experiments reveal that the proposed method can offer the accurate frequency results of the plates as compared to those available in the literature. Additionally, the spring constants of elastic foundation have a significant impact on frequency changes of the plates. Increasing the values of spring constants leads to considerable increases of the frequencies.