Free vibration analysis of a flat plate using the hierarchical finite element method

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Abstract

The hierarchical finite element method is used to determined the natural frequencies and modes of a flat, rectangular plate. Ten different boundary conditions—including free edges and point supports—are considered in this paper. Extensive results are presented for each case (including the variation of frequency with the aspect ratio and the Poisson ratio), and these are shown to be in very good agreement with the work of other investigators. This confirms both the applicability and accuracy of solution of the HFEM to problem of this type.

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  • Cited by (120)

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      Citation Excerpt :

      According to the open literature, the free vibration of intact plates has been widely investigated by various solution methods. Representative numerical methods include the finite element method (FEM), e.g., Bardell [1], the isogeometric analysis, e.g., Shojaee et al. [2,3], the boundary element method, e.g., Nardini and Brebbia [4], the finite difference method, e.g., Aksu and Felemban [5], the finite strip method, e.g., Cheung et al. [6], the meshless method, e.g., Chen et al. [7], the discrete singular convolution, e.g., Civalek et al. [8–11], and the differential quadrature method, e.g., Civalek et al. [11,12], Kong et al. [13], Wang and Wang [14], Szekrényes [15], and Trinh et al. [16]. In addition to the above-mentioned numerical methods, the classical semi-inverse analytical methods have also been used.

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