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Structural Engineering and Mechanics Volume 28, Number 1, January10 2008 , pages 53-67 DOI: https://doi.org/10.12989/sem.2008.28.1.053 |
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Free vibrations of anisotropic rectangular plates with holes and attached masses |
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C. A. Rossit and P. M. Ciancio
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| Abstract | ||
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Anisotropic materials are increasingly required in modern technological applications. Certainly, civil, mechanical and naval engineers frequently deal with the situation of analyzing the dynamical behaviour of structural elements being composed of such materials. For example, panels of anisotropic materials must sometimes support electromechanical engines, and besides, holes are performed in them for operational reasons e.g., conduits, ducts or electrical connections. This study is concerned with the natural frequencies and normal modes of vibration of rectangular anisotropic plates supported by different combinations of the classical boundary conditions: clamped, simply . supported and free, and with additional complexities such holes of free boundaries and attached concentrated masses. A variational approach (the well known Ritz method) is used, where the displacement amplitude is approximated by a set of beam functions in each coordinate direction corresponding to the sides of the rectangular plate. Consequently each coordinate function satisfies the essential boundary conditions at the outer edge of the plate. The influence of the position and magnitude of both hole and mass, on the natural frequencies and modal shapes of vibration are studied for a generic anisotropic material. The classical Ritz method with beam functions as spatial approximation proved to be a suitable procedure to solve a problem of such analytical complexity. | ||
| Key Words | ||
| vibration of plates; anisotropic plates; concentrated mass; holes of free edge; Ritz method. | ||
| Address | ||
| C. A. Rossit: Dpto. de Ingenieria, Instituto de Mecanica Aplicada, Universidad Nacional del Sur, 8000, Bahia Blanca, Argentina P. M. Ciancio: Facultad de Ingenieria, Universidad Nacional del Centro de la Provincia de Buenos Aires, 7400, Olavarria, Argentina | ||