Free vibration analysis of a rectangular plate with Kelvin type boundary conditions

Article type: Research Article

Authors: Kırışık, R. | Yüksel, Ş.

Affiliations: Turkish Atomic Energy Authority, Eskişehir Yolu 9.km 06530 Lodumlu, Ankara, Turkey | Department of Mechanical Engineering, Faculty of Engineering and Architecture, Gazi University, 06570 Maltepe, Ankara, Turkey

Note: [] Corresponding author. Fax: +90 312 287 8761; E-mail: [email protected]

Abstract: The transverse vibrations of a rectangular plate with the Kelvin type boundary conditions at four corners are investigated. The plate is modeled as being attached to four lumped spring-damper systems at the corners. An analytical procedure is proposed based on the modal analysis. The completely free case of the plate is first studied. The expressions for the eigenfrequencies and eigenfunctions of the plate are obtained by utilizing the separation of variables. Then, the case in which the stiffness and the viscous damping as external forces acting at the corners of the plate is studied. Following the modal analysis procedure, the general solution for the equation of motion of the rectangular plate is derived. Some numerical results are presented.

Journal: Shock and Vibration, vol. 14, no. 6, pp. 447-457, 2007