Parametric vibration analysis of sector plates using perturbation technique

This paper aims to investigate the in-plane and out-of-plane free vibrations analysis of both solid and annular sector plates with time-dependent properties. The Fourier expansion and the perturbation technique are employed to solve the partial differential equations based on the first-order shear deformation theory. By defining a new parameter, the motion equations which have variable coefficients convert to equations with constant coefficients that lead to a closed-form solution for each order of the perturbation expansion. Due to the use of this displacement field, rapid convergence and high accuracy results can be easily obtained for both in-plane and out-of-plane natural frequencies. The influences of some key parameters including the inner to outer radius ratios, sector angle, thickness to radius ratios, and damping parameters on free vibration of the viscoelastic sector plates are illustrated and analyzed, which may serve as benchmark solutions in the future. Besides, the results are compared with the actual results from the literature, classic theory of plates, and finite element analysis. The present formulation yields many new and accurate results at a low computational cost for the study of mechanical and geometrical parameters.