期刊
APPLIED MATHEMATICAL MODELLING
卷 33, 期 9, 页码 3523-3532出版社
ELSEVIER SCIENCE INC
DOI: 10.1016/j.apm.2008.11.016
关键词
Corrugated circular plate; Large amplitude vibration; Temperature change; Shooting method
This paper presents a nonlinear free vibration analysis of corrugated circular plates with shallow sinusoidal corrugations under uniformly static ambient temperature. Based on the nonlinear bending theory of thin shallow shells, the governing equations for corrugated plates are established from Hamilton's principle. These partial differential equations are reduced to corresponding ordinary ones by elimination of the time variable with Kantorovich method following an assumed harmonic time mode. The resulting 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 plates are obtained successfully. The comparison with available published results shows that the numerical analysis here is of good reliability. A detailed parametric study is conducted involving the dependency of nonlinear frequency on the depth and density of corrugations along with the temperature change. Effects of these variables on the trend of nonlinearity are plotted and discussed. (C) 2008 Elsevier Inc. All rights reserved.
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