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

2015 ◽  
Vol 17 ◽  
pp. 43-53 ◽  
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.

scholarly journals Application of the Modified Vlasov Model to the Free Vibration Analysis of Thick Plates Resting on Elastic Foundations

2009 ◽  
Vol 16 (5) ◽  
pp. 439-454 ◽  
Author(s):  
Korhan Ozgan ◽  
Ayse T. Daloglu
Keyword(s):  
Free Vibration ◽  
Vibration Analysis ◽  
Degrees Of Freedom ◽  
Plate Theory ◽  
Free Vibration Analysis ◽  
Mindlin Plate ◽  
Thick Plates ◽  
Elastic Foundations ◽  
Plates On Elastic Foundation ◽  
Quadrilateral Finite Element

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.

Sharp Corner Functions for Mindlin Plates

2005 ◽  
Vol 72 (1) ◽  
pp. 1-9 ◽  
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.

Free Bending Vibrations of Adhesively Bonded Orthotropic Plates With a Single Lap Joint

1996 ◽  
Vol 118 (1) ◽  
pp. 122-134 ◽  
Author(s):  
U. Yuceoglu ◽  
F. Toghi ◽  
O. Tekinalp
Keyword(s):  
Boundary Conditions ◽  
Natural Frequencies ◽  
Plate Theory ◽  
Mode Shapes ◽  
Mindlin Plate ◽  
Lap Joint ◽  
Orthotropic Plates ◽  
Adhesively Bonded ◽  
Bending Vibrations ◽  
Free Bending

This study is concerned with the free bending vibrations of two rectangular, orthotropic plates connected by an adhesively bonded lap joint. The influence of shear deformation and rotatory inertia in plates are taken into account in the equations according to the Mindlin plate theory. The effects of both thickness and shear deformations in the thin adhesive layer are included in the formulation. Plates are assumed to have simply supported boundary conditions at two opposite edges. However, any boundary conditions can be prescribed at the other two edges. First, equations of motion at the overlap region are derived. Then, a Levy-type solution for displacements and stress resultants are used to formulate the problem in terms of a system of first order ordinary differential equations. A revised version of the Transfer Matrix Method together with the boundary and continuity conditions are used to obtain the frequency equation of the system. The natural frequencies and corresponding mode shapes are obtained for identical and dissimilar adherends with different boundary conditions. The effects of some parameters on the natural frequencies are studied and plotted.

Comparison of Free Flexural Vibrations of Composite Plates or Panels Stiffened by a Central and a Non-Central Plate Strip

1999 ◽  
Author(s):  
U. Yuceoglu ◽  
V. Özerciyes
Keyword(s):  
Natural Frequencies ◽  
Plate Theory ◽  
Composite Plates ◽  
Mode Shapes ◽  
Mindlin Plate ◽  
Solution Technique ◽  
Orthotropic Plates ◽  
Bending Vibration ◽  
Central Plate ◽  
Plate Strip

Abstract The natural frequencies and the corresponding mode shapes of two classes of composite base plate or panel stiffened by a central or a non-central plate strip are analyzed and compared with each other. In each case, the base plates and the single, stiffening plate strips are assumed to be dissimilar orthotropic plates connected by a very thin, yet deformable adhesive layer. The free bending vibration problems for the two cases are formulated in terms of the Mindlin Plate Theory for orthotropic plates. The governing equations are reduced to a system of first order equations. The solution technique is the “Modified Version of the Transfer Matrix Method”. The effects of the bonded central and non-central stiffening strip on the mode shapes and the natural frequencies of the composite plate or panel system are investigated. Some important conclusions are drawn from the numerical and parametric studies presented.

A Mindlin–Reissner Variational Principle to Analyze the Behavior of Moderately Thick Plates

1989 ◽  
Vol 42 (11S) ◽  
pp. S32-S38
Author(s):  
Roberto S. Carnicer ◽  
Stefano Alliney
Keyword(s):  
Finite Element ◽  
Variational Principle ◽  
Plate Theory ◽  
Mindlin Plate ◽  
General Boundary Conditions ◽  
Thick Plates ◽  
Numerical Examples ◽  
Simple Support ◽  
Mindlin Plate Theory ◽  
Moderately Thick Plates

In the present work a method to solve the plate behavior under the assumption of the Mindlin plate theory is analyzed by means of finite element techniques, avoiding the tendency of the thin element to lock when the thickness of the plates becomes very small. A different formulation is developed from the Mindlin–Reissner principle for general boundary conditions. Numerical examples to evaluate the noninfluence of locking on clamped and simple support plates are calculated.

Free Vibration Analysis for Elastic Plate Resting on Two-Parameter Foundation by Coupling FEM and BEM

2011 ◽  
Vol 368-373 ◽  
pp. 1332-1337
Author(s):  
Hong Yang Xie ◽  
Huan Yang ◽  
Jin Quan Yin
Keyword(s):  
Free Vibration ◽  
Vibration Analysis ◽  
Plate Theory ◽  
Free Vibration Analysis ◽  
Mindlin Plate ◽  
Variation Principle ◽  
Elastic Plates ◽  
Foundation Model ◽  
Mindlin Plate Theory ◽  
Two Parameter

Based on two-parameter foundation model and Mindlin plate theory, the FEM equation for free vibration analysis of elastic plates resting on elastic foundation is derived by Hamilton variation principle. The effect of foundation beneath the plate is combined in the stiffness matrix of the plate element, and the effect of the foundation outside the plate domain is taken into account by boundary element method. By coupling FEM and BEM, numerical analyses for the free vibration of foundation plates are carried out. Calculated frequencies are in good agreement with measured results, which proves the accuracy and efficiency of the present approach.

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