An analytical approach for dynamic response of viscoelastic annular sector plates

Abstract

Accurate and profound comprehension of the dynamical behavior of viscoelastic plates is a key task in designing these structures, and also optimizing their mechanical/vibrational behavior. In the present research, the dynamic response of the annular sector plates under asymmetric impulsive and harmonic transverse loads is determined analytically. The boundary conditions for the radial edges are simply supported, but for the circular boundaries, different cases are investigated. By employing Hamilton’s principle, the governing equations of motion are derived based on the first-order shear deformation theory. The viscoelastic behavior of the polymer sector plate is considered as the standard linear solid in shear and elastic in bulk. An analytical method based on the perturbation technique and the Fourier series is adopted to solve the equations of motion which include a system of partial differential equations with variable coefficients. Moreover, in parallel, the classical plate theory is obtained in the same procedure to examine the influence of each theory. Then, the sensitivity of the results to the geometrical and mechanical parameters is declared. The results are compared with those obtained from the classical plate theory and the finite element method.