Analytical method for free-damped vibration analysis of viscoelastic shear deformable annular plates made of functionally graded materials

This contribution aims to study the free vibrations behavior of viscoelastic functionally graded (VFGM) annular plates using the first-order shear deformation theory. The Zener three-parameter model is employed to model the time-dependent behavior of the plate which is assumed viscoelastic in shear and elastic in bulk. The functionally graded material properties vary through the thickness of the plate with a power law function and exponential distribution. Hamilton's principle is utilized to derive the governing equations which are three coupled partial differential equations with variable coefficients. The equations of motion are solved analytically using the perturbation technique. The natural frequencies of the plate are determined with different combinations of boundary conditions including simply supported, clamped and free. In addition, the effects of different viscoelastic and geometric parameters on the results are studied. The results are compared with those obtained from the literatures and the finite-element package. Investigation of the gradient index effect on the damping properties of VFGM plate shows that an increase in gradient index tends to decrease the damping behaviors of the VFGM plate.