THE ANALYTICAL SOLUTION OF THE FREE VIBRATIONOF CIRCLE MEMBRANE

PDF(674 KB)

Journal of Vibration and Shock ›› 2009, Vol. 28 ›› Issue (5) : 84-86.

论文

THE ANALYTICAL SOLUTION OF THE FREE VIBRATIONOF CIRCLE MEMBRANE

LIN Wen-jing, CHEN Shu-hui, LI Sen

Author information +

History +

Abstract

The free vibration of circle membrane is studied in this paper. Firstly, the governing differential equation of membrane is set up by Hamilton’s principle. Then, by employing the method of separated variables, two second order differential equations regarding the time t, the radial direction coordinate r and one Bessel equation regarding the circumferential direction coordinate are derived. These equations are solved respectively. Therefore, the analytical solution of natural frequencies and modals of circle membrane and fan-shaped membrane are obtained. Finally, the numerical calculations are also taken by using the finite element software ANSYS. Two examples show that the theoretical results are pretty good agreement with those numerical results obtained by ANSYS. The theoretical results are lower limits of the numerical results.

Key words

circle membrane / free vibration / Hamilton’s principle / the method of separated variables / Bessel function

Cite this article

EndNote

Ris (Procite)

Bibtex

Download Citations

LIN Wen-jing;CHEN Shu-hui;LI Sen. THE ANALYTICAL SOLUTION OF THE FREE VIBRATIONOF CIRCLE MEMBRANE [J]. Journal of Vibration and Shock, 2009, 28(5): 84-86