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

Abstract

Vibration modes of an extremely thin rotating circular membrane subjected to transverse distributed load are investigated. In the previous paper, the author proposed an analytical method to obtain equilibrium states with large transverse deformations employing 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 formulated. 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 compared with the experimental results to verify the validity of the present analysis.

Forced vibration experiments of a rotating extremely thin circular membrane

“…In this section, the analysis of the equilibrium states and vibration modes of a rotating circular membrane subjected to a uniform transverse load performed in the previous papers (Okuizumi, 2007(Okuizumi, , 2010 is summarized and the analysis of wave motions is added.…”

“…The equilibrium state of the membrane under gravity was studied by theoretical analysis using the membrane theory of shell of revolution (Clark and Narayanaswamy, 1967) and the result was confirmed by conducting experiment in vacuum (Okuizumi, 2007). Small vibration modes of the membrane were also studied by theoretical and numerical analyses and the results were partially examined in the experiment (Okuizumi, 2010).…”

Wrinkling of transversely loaded spinning membranes

“…Hence, he evaluated the load at which the circumferential stress on the outer edge becomes 40 negative, and assumed this load to be equal to the critical buckling load of the membrane. Okuizumi (2007) carried out experiments in a vacuum chamber on thin, spinning membranes loaded by gravity and vibrating under axisymmetric excitation (Okuizumi, 2009(Okuizumi, , 2014, using Simmonds' stress criterion to predict buckling.…”