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We propose the semi and fully discrete finite element methods for investigating vibrations of elastic plate-plate structures. In the space, the longitudinal displacements of plates are discretized by conforming linear elements, and the corresponding transverse displacements are discretized by the Morley elements, leading to a semi-discrete finite e...
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Citations
... lved the differential equation of motion of a thin, isotropic, simply-supported, rectangular plate algebraically using separation of variables. He also used boundary characteristic orthogonal polynomials (BCOPs) in the Rayleigh-Ritz method to determine the free vibration frequencies of twenty-one rectangular plates with various boundary conditions.Lai and Huang (2009) proposed semi and fully discrete finite element methods for investigating vibration analysis of elastic plate structures. In the space directions, they discretized the longitudinal displacements on plates by conforming linear elements, and also discretized the corresponding transverse displacements by the Morley element, leading to a se ...
In this article, we derive error estimates for the Galerkin approximation of a general linear second order hyperbolic equation. The results can be applied to a variety of cases, for example, vibrating systems of linked elastic bodies. The results generalize the work of Baker [11.
G. A. Baker ( 1976 ). Error estimates for finite element methods for second order hyperbolic equations . SIAM J. Numer. Anal. 13 : 564 – 576 . [CrossRef], [Web of Science ®]View all references] and also allow for viscous type damping. Splitting the proofs for the semi-discrete and fully discrete cases not only simplifies the proofs but less restrictive regularity assumptions are required.
