Axisymmetric natural frequencies of statically loaded annular plates

Article type: Research Article

Authors: Abdel-Rahman, Eihab M. | Faris, Waleed F. | Nayfeh, Ali H.

Affiliations: Department of Engineering Science and Mechanics, MC 0219, Virginia Polytechnic Institute and State University, Blacksburg, VA 24061, USA. E-mail: [email protected]

Abstract: We present a numerical procedure to solve the axisymmetric vibration problem of statically loaded annular plates. We use the von Kármán nonlinear plate model to account for large deformations and study the effect of static deflections on the natural frequencies and mode shapes for six combinations of boundary conditions. The shooting method is used to solve the resulting eigenvalue problem. Our results show that static deformations have a significant effect on the natural frequencies and small effect on the mode shapes of the plate. Further, the results show that the presence of in-plane stresses has a significant effect on the natural frequencies.

Journal: Shock and Vibration, vol. 10, no. 5-6, pp. 301-312, 2003