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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. [ABSTRACT FROM AUTHOR]

This paper investigates flexural vibration of functionally graded sandwich microbeams supported by different axially immovable boundary conditions. The governing equations of free vibration problem are based on Timoshenko beam theory and the modified couple stress theory which are taking into account the important effects of shear deformation, rotary inertia and material length scale parameter. To solve the governing equations presented in the forms of coupled differential equations for vibration analysis of the beams with various boundary conditions, an effective tool, namely Chebyshev collocation method, is employed to find out accurate solutions with many important parametric studies. The effects of material volume fraction index, layer thickness ratio, slenderness ratio, boundary condition, temperature rise, etc. on natural frequencies of the beams are taken into account and discussed in details. The numerical results of the beams in ambient temperature and high thermal environment are presented in several tables and figures that can serve as benchmarks for further investigations in the field of FG sandwich microbeam analysis. [ABSTRACT FROM AUTHOR]

An improved third-order shear deformation theory is employed to investigate free and forced vibration responses of functionally graded plates. A power law distribution is used to describe the variation of material compositions across the plate thickness. The governing equations for vibration analysis obtained using an energy approach are then solved using the Ritz method. Two types of solutions, temperature independent and dependent material properties, are considered. Many effects of the volume fraction index, temperature, material pairs, thickness, plate aspect ratio, etc., which have significant impact on dynamic behaviour of the plates, are considered in the numerical illustrations of free and forced vibration results. At high temperatures, it is observed that the maximum deflections of the functionally graded plates subjected to the dynamic loading increase with the increase of frequency ratio and temperature. [ABSTRACT FROM PUBLISHER]