Damping Properties of Three-Layered Shallow Spherical Shells with a Constrained Viscoelastic Layer

Abstract

A theoretical study is presented for the damping of the flexural vibration of a three-layered shallow spherical shell with a constrained viscoelastic layer. Expressing in-plane displacements in terms of auxiliary functions, general solutions of the equations of motion for nonaxially symmetric modes are given in terms of Bessel functions. When the opening angle changes with a constant base diameter, natural frequencies and loss factors of shallow spherical are calculated for axially and nonaxially symmetric modes. Effects of the opening angle, the shear parameter, the thickness of each layer, and boundary conditions on the damping properties are investigated.