Exact Solutions for Axisymmetric Vibration of Laminated Circular Plates
Publication: Journal of Engineering Mechanics
Volume 116, Issue 4
Abstract
Based on fundamental equations of three‐dimensional elasticity and giving up any assumptions about displacement models and stress distribution, the state equations for the axisymmetric free vibrations of transversely isotropic circular plates are established. Because the four quantities appearing in the state equations happen to be the compatibility quantities of the interfaces, it is extremely convenient to develop the state equations of laminated circular plates with transversely isotropic layers. The exact solutions for such problems with simply supported and clamped edges are presented in this paper. Every fundamental equation of three‐dimensional elasticity can be exactly satisfied and all five elastic‐flexibility constants can also be taken into account by the present method. No matter how many layers are considered, the calculation always leads to solving a set of linear algebraic equations of the second order. Numerical results are obtained and compared with the results calculated using the Reissner and Mindlin theories, respectively.
Get full access to this article
View all available purchase options and get full access to this article.
References
1.
Celep, Z. (1980). “Free vibration of some circular plates of arbitrary thickness.” J. Sound Vib., 70(3), 379–388.
2.
Poltorak, K., and Nagaya, K. (1985). “A method for solving free vibration problems of three‐layered plates with arbitrary shape.” J. Acoust. Soc. Am., 78(6), 2042–2048.
3.
Vlasov, V. Z. (1957). “The method of initial functions in problems of the theory of thick plates and shells.” 9th Cong. Appl. Mech., Brussels, Belgium, 6, 321–330.
Information & Authors
Information
Published In
Copyright
Copyright © 1990 ASCE.
History
Published online: Apr 1, 1990
Published in print: Apr 1990
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.