Analysis of the free vibration of rectangular plates with central cut-outs using the discrete Ritz method |
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Authors: | K M Liew S Kitipornchai A Y T Leung C W Lim |
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Affiliation: | a School of Mechanical and Production Engineering, Nanyang Technological University, Nanyang Avenue, Singapore 639798, Singapore;b Department of Building and Construction, City University of Hong Kong, Tat Chee Avenue, Kowloon, Hong Kong |
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Abstract: | We present an analysis of the free vibration of plates with internal discontinuities due to central cut-outs. A numerical formulation for a basic L-shaped element which is divided into appropriate sub-domains that are dependent upon the location of the cut-out is used as the basic building element. Trial functions formed to satisfy certain boundary conditions are employed to define the transverse deflection of each sub-domain. Mathematical treatments in terms of the continuities in displacement, slope, moment, and higher derivatives between the adjacent sub-domains are enforced at the interconnecting edges. The energy functional results, from the proper assembly of the coupled strain and kinetic energy contributions of each sub-domain, are minimized via the Ritz procedure to extract the vibration frequencies and mode shapes of the plates. The procedures are demonstrated by considering plates with central cut-outs that are subjected to two types of boundary conditions. |
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Keywords: | Cut-out Free vibration Perforated plates Orthogonal polynomials Ritz method |
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