Singh, Bani; Chakraverty, S. Transverse vibration of completely-free elliptic and circular plates using orthogonal polynomials in the Rayleigh-Ritz method. (English) Zbl 0747.73016 Int. J. Mech. Sci. 33, No. 9, 741-751 (1991). Summary: The Rayleigh-Ritz method using characteristic orthogonal polynomials has been applied to study the problem of transverse vibration of completely- free elliptic and circular plates of uniform thickness. A sequence of successive approximations has been generated to work out the frequencies and mode shapes. The process is continued until at least the first four frequencies converge to five significant digits. It has been found that the results agree completely with the known results for a circular plate. A comparison has also been made with some known experimental and theoretical results for an elliptic plate. Cited in 9 Documents MSC: 74H45 Vibrations in dynamical problems in solid mechanics 74K20 Plates 74S30 Other numerical methods in solid mechanics (MSC2010) 74P10 Optimization of other properties in solid mechanics Keywords:successive approximations; frequencies; mode shapes PDFBibTeX XMLCite \textit{B. Singh} and \textit{S. Chakraverty}, Int. J. Mech. Sci. 33, No. 9, 741--751 (1991; Zbl 0747.73016) Full Text: DOI