An analytical solution of transverse vibration of rectangular plates simply supported at two opposite edges with arbitrary number of elastic line supports in one way
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This paper presents a new analytical solution of transverse vibration of rectangular plates simply supported at two opposite edges with arbitrary number of elastic line supports in one way. The reaction forces of the elastic line supports are regarded as the unknown external forces acted on the plate. The analytical solution of the differential equation of motion of the rectangular plate, which includes the unknown reaction forces, is gained. The frequency equation is derived by using the linear relutionships between the reaction forces of the elastic line supports and the transverse displacements of the plate along the elastic line supports. The representations of the frequency equation and the mode shape functions are different from those obtained by other methods.
Key wordsrectangular plate eigen-frequency elastic line support analytical solution
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- A. S. Veletsos and N. M. Newmark, Determination of natural frequencies of continuous plates hinged along two opposite edges, Journal of Applied Methanics, 23 (1956).Google Scholar
- S. Azimi, J. F. Hamilton and W. Soedel, The receptance method applied to the free vibration of continuous rectangular plates, Journal of Sound and Vibration, 93 (1984).Google Scholar
- M. Mukhopadhyay, A. semi-analytic solution for free vibration of rectangular plates, Journal of Sound and Vibration, 60 (1978).Google Scholar
- E. E. Ungar, Free oscillations of edge-connected simply supported plate system, Journal of Engineering for Industry, 83 (1961).Google Scholar
- Y. K. Cheung and M. S. Cheung, Flexural vibrations of rectangular and other polygonal plates, Journal of the Engineering Mechanics Division, ASCE, 97 (1971).Google Scholar
- Ren Yongtai and Shi Xifu, Ordinary Differential Equation, Liaoning People's Press (1984). (in Chinese)Google Scholar
- Vibration group of Tsing Hua University, Mechanical Vibration, Vol. 1, Mechanical Industry Press (1980). (in Chinese)Google Scholar