VIBRATION ANALYSIS OF RECTANGULAR ISOTROPIC THICK PLATES USING MINDLIN PLATE CHARACTERISTIC FUNCTIONS

The Modified Vlasov Model is applied to the free vibration analysis of thick plates resting on elastic foundations. The effects of the subsoil depth, plate dimensions and their ratio, the value of the vertical deformation parameter within the subsoil on the frequency parameters of plates on elastic foundations are investigated. A four-noded, twelve degrees of freedom quadrilateral finite element (PBQ4) is used for plate bending analysis based on Mindlin plate theory which is effectively applied to the analysis of thin and thick plates when selective reduced integration technique is used. The first ten natural frequency parameters are presented in tabular and graphical forms to show the effects of the parameters considered in the study. It is concluded that the effect of the subsoil depth on the frequency parameters of the plates on elastic foundation is generally larger than that of the other parameters considered in the study.

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Analytical Approaches to Vibration Analysis of Thick Plates Subjected to Different Supports, Loadings and Boundary Conditions - A Literature Survey

International Journal of Engineering Research in Africa ◽

10.4028/www.scientific.net/jera.17.43 ◽

2015 ◽

Vol 17 ◽

pp. 43-53 ◽

Cited By ~ 1

Author(s):

Fazl E. Ahad ◽

Dong Yan Shi

Keyword(s):

Vibration Analysis ◽

Plate Theory ◽

Relevant Literature ◽

Research Work ◽

Vibration Characteristics ◽

Mindlin Plate ◽

Orthotropic Plates ◽

Thick Plates ◽

Vibrational Characteristics ◽

Analytical Approaches

Plates are one of the most important structural components used in many industries like aerospace, marine and various other engineering fields and thus motivate designers and engineers to study the vibrational characteristics of these structures. A lot of research work and studies have been done to study its vibration characteristics. This paper is a review of existing literature on vibration analysis of plates. Focus has been kept on prominent studies related to isotropic plates based on Mindlin plate theory; however few citations on orthotropic plates and higher order shear deformation theories have also been included. All citations are in English language. This review is aimed to provide contemporarily relevant survey of papers on vibrational characteristics of thick plates and identification of various methods and approaches that have been used to study the vibration characteristics. This paper will not only be useful for scientists, designers and researchers to locate important and relevant literature/research quickly but will also help them to identify and apply some of these methods and approaches to study the vibration characteristics of various other 2D and 3D structures.

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Free vibration analysis of rectangular and annular Mindlin plates with undamaged and damaged boundaries by the spectral collocation method

Journal of Vibration and Control ◽

10.1177/1077546311422242 ◽

2011 ◽

Vol 18 (11) ◽

pp. 1722-1736 ◽

Cited By ~ 12

Author(s):

Ma’en S Sari ◽

Eric A Butcher

Keyword(s):

Free Vibration ◽

Boundary Conditions ◽

Collocation Method ◽

Vibration Analysis ◽

Natural Vibration ◽

Numerical Technique ◽

Free Vibration Analysis ◽

Mindlin Plate ◽

Grid Points ◽

Matrix Vector

The objective of this paper is the development of a new numerical technique for the free vibration analysis of isotropic rectangular and annular Mindlin plates with damaged boundaries. For this purpose, the Chebyshev collocation method is applied to obtain the natural frequencies of Mindlin plates with damaged clamped boundary conditions, where the governing equations and boundary conditions are discretized by the presented method and put into matrix vector form. The damaged boundaries are represented by distributed translational and torsional springs. In the present study the boundary conditions are coupled with the governing equation to obtain the eigenvalue problem. Convergence studies are carried out to determine the sufficient number of grid points used. First, the results obtained for the undamaged plates are verified with previous results in the literature. Subsequently, the results obtained for the damaged Mindlin plate indicate the behavior of the natural vibration frequencies with respect to the severity of the damaged boundary. This analysis can lead to an efficient technique for structural health monitoring of structures in which joint or boundary damage plays a significant role in the dynamic characteristics. The results obtained from the Chebychev collocation solutions are seen to be in excellent agreement with those presented in the literature.

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Sharp Corner Functions for Mindlin Plates

Journal of Applied Mechanics ◽

10.1115/1.1795221 ◽

2005 ◽

Vol 72 (1) ◽

pp. 1-9 ◽

Cited By ~ 19

Author(s):

O. G. McGee ◽

J. W. Kim ◽

A. W. Leissa

Keyword(s):

Plate Theory ◽

Thin Plates ◽

Mode Shapes ◽

Mindlin Plate ◽

Transverse Displacement ◽

Thick Plates ◽

Thin Plate Theory ◽

Mindlin Plate Theory ◽

Moderately Thick Plates ◽

Sharp Corners

Transverse displacement and rotation eigenfunctions for the bending of moderately thick plates are derived for the Mindlin plate theory so as to satisfy exactly the differential equations of equilibrium and the boundary conditions along two intersecting straight edges. These eigenfunctions are in some ways similar to those derived by Max Williams for thin plates a half century ago. The eigenfunctions are called “corner functions,” for they represent the state of stress currently in sharp corners, demonstrating the singularities that arise there for larger angles. The corner functions, together with others, may be used with energy approaches to obtain accurate results for global behavior of moderately thick plates, such as static deflections, free vibration frequencies, buckling loads, and mode shapes. Comparisons of Mindlin corner functions with those of thin-plate theory are made in this work, and remarkable differences are found.

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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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Nanoscale mass nanosensor based on the vibration analysis of embedded magneto-electro-elastic nanoplate made of FGMs via nonlocal Mindlin plate theory

Microsystem Technologies ◽

10.1007/s00542-017-3654-8 ◽

2017 ◽

Vol 24 (5) ◽

pp. 2295-2316 ◽

Cited By ~ 11

Author(s):

M. Hosseini ◽

M. R. Mofidi ◽

A. Jamalpoor ◽

M. Safi Jahanshahi

Keyword(s):

Vibration Analysis ◽

Plate Theory ◽

Mindlin Plate ◽

Mindlin Plate Theory

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Vibration Analysis of Discontinuous Mindlin Plates by Differential Quadrature Element Method

Journal of Vibration and Acoustics ◽

10.1115/1.2893965 ◽

1999 ◽

Vol 121 (2) ◽

pp. 204-208 ◽

Cited By ~ 33

Author(s):

F.-L. Liu ◽

K. M. Liew

Keyword(s):

Free Vibration ◽

Vibration Analysis ◽

Differential Quadrature Method ◽

Free Vibration Analysis ◽

Differential Quadrature ◽

Mindlin Plate ◽

Quadrature Method ◽

Differential Quadrature Element Method ◽

Quadrature Element Method ◽

Element Method

A new numerical technique, the differential quadrature element method (DQEM), has been developed for solving the free vibration of the discontinuous Mindlin plate in this paper. By the DQEM, the complex plate domain is decomposed into small simple continuous subdomains (elements) and the differential quadrature method (DQM) is applied to each continuous subdomain to solve the problems. The detailed formulations for the DQEM and the connection conditions between each element are presented. Several numerical examples are analyzed to demonstrate the accuracy and applicability of this new method to the free vibration analysis of the Mindlin plate with various discontinuities which are not solvable directly using the differential quadrature method.

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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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