Analysis of the free vibration of rectangular plates with central cut-outs using the discrete Ritz method

• Published in: International journal of mechanical sciences 2003-05, Vol.45 (5), p.941-959
• Main Authors: Liew, K.M., Kitipornchai, S., Leung, A.Y.T., Lim, C.W.
• Format: Article
• Language: English
• Subjects: Cut-out; Exact sciences and technology; Free vibration; Fundamental areas of phenomenology (including applications); Orthogonal polynomials; Perforated plates; Physics; Ritz method; Solid mechanics; Structural and continuum mechanics; Vibration, mechanical wave, dynamic stability (aeroelasticity, vibration control...); Vibrations and mechanical waves
• ISSN: 0020-7403; 1879-2162
• DOI: 10.1016/S0020-7403(03)00109-7

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.