Comparative Study of Frequencies for Plates Carrying Mass
Publication: Journal of Engineering Mechanics
Volume 119, Issue 5
Abstract
The present work is concerned with the determination of the fundamental frequencies of rectangular plates carrying a mass mounted at various positions. Although direct solution of the Navier and Lévy methods is not generally practical, an energy method involving double trigonometric functions was developed to obtain approximate closed‐form solutions. A finite element analysis is also presented for comparison. Extensive experimental investigation on the three plates through a shaker system was conducted to collect useful test data. Comparisons of experimental results with theoretical predictions of the finite element and energy methods are made. The results confirm that the frequency of the plate decreases as the weight of the component mass is increased, and the frequency increases as the mass moves away from the center of the plate. The work suggested that the tested plates can be approximately represented by plates with two opposite edges simply supported and the other two edges clamped (SCSC) boundary conditions. A set of comparisons also reveals that there is a need for improvement in the analytical methods for heavier masses.
Get full access to this article
View all available purchase options and get full access to this article.
References
1.
Gorman, D. J., and Singal, R. K. (1991). “Analytical and experimental study of vibration of rectangular plates on rigid point supports.” AIAA J., 29(5), 838–844.
2.
Hearmon, R. F. S. (1952). “The frequency of vibration of rectangular isotropic plates.” J. of Appl. Mech., 19(3), 402–403.
3.
Laura, P. A. A., Filipich, C. P., and Cortinez, V. H. (1987). “Vibrations of beams and plates carrying concentrated masses.” J. Sound and Vibration, 117(3), 459–465.
4.
Leissa, A. W. (1969). “Vibration of plates.” NASA SP‐160, Nat. Aeronautics and Space Admin., Washington, D.C.
5.
Leissa, A. W. (1973). “The free vibration of rectangular plates.” J. Sound and Vibration, 31(3), 257–293.
6.
Low, K. H., Ng, C. K., Lim, M. K., and Ong, Y. K. (1990). “Experiment and finite element method on the frequency analysis of loaded chassis.” Defence Technol. Dig., (Nov.), Singapore, 25–33.
7.
Steinberg, D. S. (1988). Vibration analysis for electronic equipment. 2nd Ed., John Wiley & Sons, Inc., New York, N.Y.
8.
Szilard, R. (1974). Theory and analysis of plates: classical and numerical methods. Prentice‐Hall, Englewood Cliffs, N.J.
9.
Warburton, G. B. (1954). “The vibration of rectangular plates.” Proc., Inst. of Mech. Engrs., Series A, 168(12), 371–384.
Information & Authors
Information
Published In
Copyright
Copyright © 1993 American Society of Civil Engineers.
History
Received: Jul 20, 1992
Published online: May 1, 1993
Published in print: May 1993
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.