Application of Reissner’s Variational Principle to Cantilever Plate Deflection and Vibration Problems

Plass, H. J.; Gaines, J. H.; Newsom, C. D.

doi:10.1115/1.3636444

Cited by 23 publications

(2 citation statements)

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“…Besides, some other approximate analysis of the bending of a rectangular cantilever plate by uniform normal pressure was presented by Nash [13]. The generalized variational principle was applied to rectangular thin plates by Shu and Shih [24], and the principle was then used by Plass et al [25] for deflection and vibration problems of cantilever plates. Leissa and Niedenfuhr [26] obtained the solution for uniformly loaded cantilevered square plates using the technique of point matching and the Rayleigh -Ritz method.…”

Section: Introductionmentioning

confidence: 99%

Exact bending solutions of orthotropic rectangular cantilever thin plates subjected to arbitrary loads

Zhong

Tian

et al. 2011

Int Appl Mech

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Abstract. Exact bending solutions of orthotropic rectangular cantilever thin plates subjected to arbitrary loads are derived by using a novel double finite integral transform method. Since only the basic elasticity equations for orthotropic thin plates are used, the method presented in this paper eliminates the need to predetermine the deformation function and is hence completely rational thus more accurate than conventional semi-inverse methods, which presents a breakthrough in solving plate bending problems as they have long been bottlenecks in the history of elasticity. Numerical results are presented to demonstrate the validity and accuracy of the approach as compared with those previously reported in the literature.

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Section: Introductionmentioning

confidence: 99%

Exact bending solutions of orthotropic rectangular cantilever thin plates subjected to arbitrary loads

Zhong

Tian

et al. 2011

Int Appl Mech

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“…In this note, the method developed in ref. 7 on the basis of Reissner's modified variational theory' 9 ' is extended to include trapezoidal cantilever plates ( Fig. 1).…”

Section: Introductionmentioning

confidence: 99%

A Note on the Free Vibrations of Cantilever Plates with Swept-Back Leading Edge

Kornecki

Maimon

1966

J. R. Aeronaut. Soc.

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Free vibrations of triangular and trapezoidal plates have been analysed recently theoretically and experimentally by many authors. Some of them applied the Rayleigh-Ritz procedure, while others proposed to use the Kantorovich-Vlasov method, reducing the problem to solution of an ordinary differential equation.In this note, the method developed in ref. 7 on the basis of Reissner’s modified variational theory is extended to include trapezoidal cantilever plates (Fig. 1).Comparison of theory and experiment shows that, retaining four terms in the deflection function, one obtains three natural frequencies to a high degree of accuracy.

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Vibrations of cantilevered skewed plates with corner stress singularities

McGee¹,

Leissa²,

Huang³

1992

Numerical Meth Engineering

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SUMMARYAccurate natural frequencies of skewed cantilevered thin plates are determined using the Ritz method. The present work is the first known vibrational study of the effects of stress singularities at the reentrant corner of skewed plates. In conjunction with classical thin plate theory, the Ritz trial space of assumed transverse displacement functions consists of algebraic polynomials, which are mathematically complete, and corner functions, which account for the singular behaviour of bending stresses at the reentrant corner. The corner functions were derived approximately four decades ago to study the nature of the stress singularities which occur at sharp interior corners or crack tips of typical plane elasticity and plate bending problems. Accurate non-dimensional frequencies are calculated for thin plates having various side ratios and arbitrary degrees of skewness. Detailed numerical studies show that augmenting the Ritz trial space of polynomials with corner functions, having a co-ordinate origin at the reentrant corner, enhances the convergence of the upper-bound frequencies. The importance of using corner functions in skew plate vibrations is found to increase as the skew angle increases and as the side ratio decreases. Results obtained using the present method are compared with those obtained by other investigators using both theoretical and experimental methods.

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Application of Reissner’s Variational Principle to Cantilever Plate Deflection and Vibration Problems

Cited by 23 publications

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Exact bending solutions of orthotropic rectangular cantilever thin plates subjected to arbitrary loads

Exact bending solutions of orthotropic rectangular cantilever thin plates subjected to arbitrary loads

A Note on the Free Vibrations of Cantilever Plates with Swept-Back Leading Edge

Vibrations of cantilevered skewed plates with corner stress singularities

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