Vibration analysis of mindlin plates
About: This article is published in Journal of Sound and Vibration.The article was published on 1983-04-01. It has received None citation(s) till now. The article focuses on the topic(s): Vibration.
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4,291 citations
TL;DR: In this article, the correction for shear of the differential equation for transverse vibrations of prismatic bars is discussed, where the correction is based on the correction of the transverse vibration of a prismatic bar.
Abstract: (1921). LXVI. On the correction for shear of the differential equation for transverse vibrations of prismatic bars. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science: Vol. 41, No. 245, pp. 744-746.
2,047 citations
TL;DR: In this article, the free vibration of rectangular plates is analyzed using the Ritz method with 36 terms containing the products of beam functions, including clamped, simply-supported, and free edge conditions.
Abstract: This work attempts to present comprehensive and accurate analytical results for the free vibration of rectangular plates. Twenty-one cases exist which involve the possible combinations of clamped, simply-supported, and free edge conditions. Exact characteristic equations are given for the six cases having two opposite sides simply-supported. The existence of solutions to the various characteristic equations is carefully delineated. The Ritz method is employed with 36 terms containing the products of beam functions to analyze the remaining 15 cases. Accurate frequency parameters are presented for a range of aspect ratios (a/b = 0·4, 2/3, 1·0, 1·5, and 2·5) for each case. For the last 15 cases, comparisons are made with Warburton's useful, approximate formulas. The effects of changing Poisson's ratio are studied.
1,012 citations
TL;DR: In this paper, a 3D linear, small deformation theory of elasticity solution by the direct method is developed for the free vibration of simply-supported, homogeneous, isotropic, thick rectangular plates.
Abstract: A three-dimensional linear, small deformation theory of elasticity solution by the direct method is developed for the free vibration of simply-supported, homogeneous, isotropic, thick rectangular plates. The solution is exact and involves determining a triply infinite sequence of eigenvalues from a doubly infinite set of closed form transcendental equations. As no restrictions are placed on the thickness variation of stresses or displacements, this formulation yields a triply infinite spectrum of frequencies, instead of only one doubly infinite spectrum by thin plate theory and three doubly infinite spectra by Mindlin's thick plate theory. Further, the present analysis yields symmetric thickness modes which neither of the approximate theories can identify. Some numerical results from the two approximate theories are compared with those from the present solution and some important conclusions regarding the effect of the assumptions made in the approximate theories are drawn. The thickness variations of stresses and displacements are also discussed. The analysis is readily extended for laminated plates of isotropic materials. Numerical results are also given for three-ply laminates, and are used to assess the accuracy of thin plate theory predictions for laminates. Extension to general lateral surface conditions and forced vibrations is indicated.
434 citations