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March  2009, 11(2): 387-419. doi: 10.3934/dcdsb.2009.11.387

A finite element method for vibration analysis of elastic plate-plate structures

Junjiang Lai 1, and  Jianguo Huang 2,

1. 

Department of Mathematics, Shanghai Jiao Tong University, Shanghai 200240, China
2. 

Department of Mathematics, Shanghai Jiao Tong University, Shanghai 200240, Scientific Computing Key Laboratory of Shanghai Universities, Shanghai Normal University, Division of Computational Science, E–Institute of Shanghai Universities, Shanghai Normal University, China

Received  August 2007 Revised  October 2008 Published  December 2008

The semi and fully discrete finite element methods are proposed for investigating vibration analysis of elastic plate-plate structures. In the space directions, the longitudinal displacements on plates are discretized by conforming linear elements, and the corresponding transverse displacements are discretized by the Morley element, leading to a semi-discrete finite element method for the problem under consideration. Applying the second order central difference to discretize the time derivative, a fully discrete scheme is obtained, and two approaches for choosing the initial functions are also introduced. The error analysis in the energy norm for the semi and fully discrete methods are established, and some numerical examples are included to validate the theoretical analysis.
Keywords: Error analysis, Plate-plate structures, Vibration analysis.
Mathematics Subject Classification: Primary: 65M15, 65M60; Secondary: 70J35, 70J50.
Citation: Junjiang Lai, Jianguo Huang. A finite element method for vibration analysis of elastic plate-plate structures. Discrete and Continuous Dynamical Systems - B, 2009, 11 (2) : 387-419. doi: 10.3934/dcdsb.2009.11.387
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