Steady-state response of an internally damped spherical shell translationally or rotationally driven at an edge.

Abstract

The steady-state response of an internally damped spherical shell translationally or rotationally driven at an edge is determined by the transfer matrix analysis method. For this purpose, the applicability of the thin shell theory is assumed and the governing equations of vibration of the shell are written as a coupled set of first order differential equations by using the transfer matrix of the shell. Once the transfer matrix has been determined by quadrature of the equations, the steady-state response is calculated numerically together with the natural frequencies in terms of the elements of the transfer matrix of the shell under any combination of boundary conditions. By the application of the method, the dynamic response and the resonant frequencies are calculated numerically for the shells driven by sinusoidally varying axial, transverse deflection, or angular rotation at an edge.