Forced vibration experiments of a rotating extremely thin circular membrane

Abstract

Vibration modes of a rotating circular membrane with extremely small thickness are investigated. In the previous papers, the author has conducted theoretical analysis of the membrane's equilibrium states and small vibration modes under gravity, employing the membrane theory of shell of revolution and von Karman's vibration equation and taking buckling of the thin membrane into account. In this paper, the vibration mode analysis is briefly summarized and the vibration modes are experimentally investigated in detail. An experimental system that can rotate and vibrate the circular membrane simultaneously in vacuum is created, and forced vibration experiments are performed with a wide range of rotation and excitation frequencies. Several vibration modes are observed and two kinds of resonance points are obtained by the experiments. Experimental results are compared with analytical results, and the resonance points and a few basic vibration modes are found to appear similarly in both. It is also found that the frequencies of the lowest vibration mode observed in the experiment are higher than those of the vibration mode analysis. In view of the compressive stress, i.e. wrinkling in circumferential direction due to finite amplitude vibration of the thin membrane, the vibration mode analysis is modified and the difference of the mode frequency is explained.

Keywords

• rotating membrane
• vibration mode
• theoretical analysis
• forced vibration experiment
• wrinkling