Modeling the vibration of a variable thickness ellipsoidal dish with central point clamp or concentric surface clamp

摘要

The vibration of shallow spherical and ellipsoidal dishes with variable thickness along the gradient from the apex is studied. The dishes are point-clamped at the apex or surface-clamped over concentric central regions which are modeled as singly and doubly connected domains, respectively. This model simulates domes, tank covers, radar dishes, or the antennas of certain communication satellites which are clamped over a finite region at the apex. The Ritz method is used to develop an efficient numerical procedure incorporating the boundary support characteristics intrinsically. Comparison with finite element and experimental results shows good consistency. Sets of useful vibration frequencies with additional mode shapes are presented to illustrate the capability of the method.