Vibration Mode Analysis of a Rotating Circular Membrane under Transverse Distributed Load

Abstract

Vibration modes of an extremely thin rotating circular membrane subjected to trans-verse distributed load are investigated. In the previous paper, the author proposed an analytical method to obtain equilibrium states with large transverse deformations em-ploying the von Karman theory and taking account of buckling under the assumptions of rotationally symmetric deformations. In this paper, transverse vibration equation around the equilibrium state under transverse load is derived and modal equation is for-mulated. The equation is numerically solved and modal frequencies and modal shapes are obtained. Typical vibration modes are illustrated. In order to confirm the validity of the analysis, eigenvalue analysis of a spring-mass system model for the membrane are performed to obtain vibration modes. A fairly good agreement is found between the theoretical and numerical results. Experiments of thin rotating circular membranes under gravity in vacuum are also conducted and transverse vibration frequencies are measured for a variety of rotation speed and air pressure. Analytical results are com-pared with the experimental results to verify the validity of the present analysis.