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Structural Engineering and Mechanics Volume 34, Number 4, March10 2010 , pages 491-505 DOI: https://doi.org/10.12989/sem.2010.34.4.491 |
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Nonlinear free vibration of heated corrugated annular plates with a centric rigid mass |
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Yong-Gang Wang, Dan Li and Ze-Jun Feng
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| Abstract | ||
| A computational analysis of the nonlinear free vibration of corrugated annular plates with shallow sinusoidal corrugations under uniformly static ambient temperature is examined. The governing equations based on Hamilton\'s principle and nonlinear bending theory of thin shallow shell are established for a corrugated plate with a concentric rigid mass at the center and rotational springs at the outer edges. A simple harmonic function in time is assumed and the time variable is eliminated from partial differential governing equations using the Kantorovich averaging procedure. The resulting ordinary equations, which form a nonlinear two-point boundary value problem in spatial variable, are then solved numerically by shooting method, and the temperature-dependent characteristic relations of frequency vs. amplitude for nonlinear vibration of heated corrugated annular plates are obtained. Several numerical results are presented in both tabular and graphical forms, which demonstrate the accuracy of present method and illustrate the amplitude frequency dependence for the plate under such parameters as ambient temperature, plate geometry, rigid mass and elastic constrain. | ||
| Key Words | ||
| corrugated annular plate; nonlinear vibration; temperature change; elastic constraint; central rigid mass; shooting method. | ||
| Address | ||
| Yong-Gang Wang: Department of Applied Mechanics, China Agricultural University, Beijing 100083, P.R. China Dan Li: Department of Applied Mechanics, China Agricultural University, Beijing 100083, P.R. China Ze-Jun Feng: Department of Applied Mechanics, China Agricultural University, Beijing 100083, P.R. China | ||