A refined model for dynamic analysis of circular plates on elastic foundations

• Published in: Journal of sound and vibration 1992-09, Vol.157 (2), p.233-241
• Main Authors: Sargand, S.M., Das, Y.C., Jayasuriya, A.M.
• Format: Article
• Language: English
• Subjects: Exact sciences and technology; Fundamental areas of phenomenology (including applications); Physics; Solid mechanics; Structural and continuum mechanics; Vibration, mechanical wave, dynamic stability (aeroelasticity, vibration control...)
• ISSN: 0022-460X; 1095-8568
• DOI: 10.1016/0022-460X(92)90678-Q

A two-parameter model is developed to represent the supporting foundation in analyzing the axially symmetric free vibrations of a finite circular plate resting on an elastic foundation of finite depth. In this analytical process, a rigorous theoretical basis is presented, using Hamilton's principle, for deriving the equations governing the interaction between the plate and the elastic foundation. Here, the decay rate of the foundation displacement components through the depth appears as a new parameter. This new parameter, normally taken as contant by other researchers, is shown to depend on other foundation parameters. The incoming waves in the horizontal direction are eliminated by considering the foundation to be infinite in the horizontal direction and a general solution is presented in terms of Bessel functions. The application of the model is illustrated by examples and the effect of foundation parameters on the natural frequencies and corresponding decay rates are studied for the first and second modes of vibrations.