New analytic solutions for free vibration of rectangular thick plates with an edge free

Seeking analytic free vibration solutions of rectangular thick plates without two parallel simply supported edges is of significance for an insight into the performances of related engineering devices and structures as well as their rapid design. A challenging set of problems concern the vibrating plates with a free corner, i.e., those with two adjacent edges free and the other two edges clamped or simply supported or one of them clamped and the other one simply supported. The main difficulty in solving one of such problems is to find a solution meeting both the boundary conditions at each edge and the condition at the free corner, which is unattainable using a conventional analytic method. In this paper, for the first time, we extend a novel symplectic superposition method to free vibration of rectangular thick plates with a free corner. The analytic frequency and mode shape solutions are both obtained and presented via comprehensive numerical and graphic results. The rigorousness in mathematical derivation and rationality of the method (without any predetermination for the solutions) guarantee the validity of our analytic solutions, which themselves are also validated by the reported results and refined finite element analysis.

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Free vibration analysis of rotating thick plates

Journal of Sound and Vibration ◽

10.1016/j.jsv.2008.12.007 ◽

2009 ◽

Vol 323 (1-2) ◽

pp. 366-384 ◽

Cited By ~ 48

Author(s):

S.H. Hashemi ◽

S. Farhadi ◽

S. Carra

Keyword(s):

Free Vibration ◽

Vibration Analysis ◽

Free Vibration Analysis ◽

Thick Plates

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Analytic solutions for a free vibration problem of a thin rectangular parallelepiped (plate) with free faces

Lobachevskii Journal of Mathematics ◽

10.1134/s1995080212040038 ◽

2012 ◽

Vol 33 (4) ◽

pp. 374-385 ◽

Cited By ~ 1

Author(s):

V. N. Paimushin ◽

T. V. Polyakova

Keyword(s):

Free Vibration ◽

Analytic Solutions ◽

Rectangular Parallelepiped ◽

Vibration Problem

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Eigenvector and eigenvalue analysis of thick plates resting on elastic foundation with first order finite element

Challenge Journal of Structural Mechanics ◽

10.20528/cjsmec.2018.02.004 ◽

2018 ◽

Vol 4 (2) ◽

pp. 61

Author(s):

Yaprak Itır Özdemir

Keyword(s):

Finite Element Method ◽

Finite Element ◽

Aspect Ratio ◽

Free Vibration ◽

Vibration Analysis ◽

Free Vibration Analysis ◽

Winkler Foundation ◽

Thick Plates ◽

First Order ◽

Element Method

The purpose of this paper is to study free vibration analysis of thick plates resting on Winkler foundation using Mindlin’s theory with first order finite element, to determine the effects of the thickness/span ratio, the aspect ratio, subgrade reaction modulus and the boundary conditions on the frequency parameters of thick plates subjected to free vibration. In the analysis, finite element method is used for spatial integration. Finite element formulation of the equations of the thick plate theory is derived by using first order displacement shape functions. A computer program using finite element method is coded in C++ to analyze the plates free, clamped or simply supported along all four edges. In the analysis, 4-noded finite element is used. Graphs are presented that should help engineers in the design of thick plates subjected to earthquake excitations. It is concluded that 4-noded finite element can be effectively used in the free vibration analysis of thick plates. It is also concluded that, in general, the changes in the thickness/span ratio are more effective on the maximum responses considered in this study than the changes in the aspect ratio.

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