Abstract
Circular plates with radially varying thickness, stiffness, and density are widely used for the structural optimization in engineering. The axisymmetric flexural free vibration of such plates, governed by coupled differential equations with variable coefficients by use of the Mindlin plate theory, is very difficult to be studied analytically. In this paper, a novel analytical method is proposed to reduce such governing equations for circular plates to a pair of uncoupled and easily solvable differential equations of the Sturm-Liouville type. There are two important parameters in the reduced equations. One describes the radial variations of the translational inertia and flexural rigidity with the consideration of the effect of Poisson’s ratio. The other reflects the comprehensive effect of the rotatory inertia and shear deformation. The Heun-type equations, recently well-known in physics, are introduced here to solve the flexural free vibration of circular plates analytically, and two basic differential formulae for the local Heun-type functions are discovered for the first time, which will be of great value in enriching the theory of Heun-type differential equations.
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20 February 2018
The article “<Emphasis Type="Bold">Exact solutions for axisymmetric flexural free vibrations of inhomogeneous circular Mindlin plates with variable thickness</Emphasis>”, written by Jianghong YUAN and Weiqiu CHEN, was originally published Online First without open access. After publication in Volume 38, Issue 4, Page 505–526, the authors decided to opt for Open Choice and to make the article an open access publication. Therefore, the copyright of the article has been changed to © The Author(s) 2018 and the article is forthwith distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits use, duplication, adaptation, distribution, and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. The original article has been corrected.
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Acknowledgements
This paper is dedicated to the late Professor Y. H. PAO (1930–2013), who had been the supervisor, collaborator, and mentor of the two authors.
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Project supported by the National Natural Science Foundation of China (Nos. 11402133, 11620162, 11321202, and 11532001)
The original version of this article was revised due to a retrospective Open Access order.
A correction to this article is available at https://doi.org/10.1007/s10483-018-2270-6
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Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits use, duplication, adaptation, distribution, and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license and indicate if changes were made.
This article is published with open access at Springerlink.com, corrected publication 03/2018
The original article has been corrected.
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Yuan, J., Chen, W. Exact solutions for axisymmetric flexural free vibrations of inhomogeneous circular Mindlin plates with variable thickness. Appl. Math. Mech.-Engl. Ed. 38, 505–526 (2017). https://doi.org/10.1007/s10483-017-2187-6
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DOI: https://doi.org/10.1007/s10483-017-2187-6