An analytical approach for free vibrations analysis of viscoelastic circular and annular plates using FSDT

In this paper, free vibrations analysis of asymmetric viscoelastic annular and circular plates are studied using the first order shear deformation theory. The viscoelastic behavior is assumed standard linear solid in shear and elastic in bulk. Hamilton's principle is employed to derive governing equations which are five coupled partial differential equations with variable coefficients. Using the perturbation technique and the Fourier series, the equations of motion are solved analytically. Determination of the natural frequencies of the plate with different combinations of boundary conditions including simply supported, clamped, and free are considered. In addition, the sensitivity of the results to the geometrical and mechanical parameters is investigated. The results are compared with those obtained from the literature, classical plate theory, and finite elements package.