On the Application of Mindlin’s Plate Theory to Free Vibration Analysis of Piezoelectric Coupled Circular FGM Plate

2008 ◽  
Author(s):  
Farzad Ebrahimi ◽  
Abbas Rastgoo
Keyword(s):  
Free Vibration ◽  
Vibration Analysis ◽  
Plate Theory ◽  
Equations Of Motion ◽  
Free Vibration Analysis ◽  
Functionally Graded ◽  
Mindlin Plate ◽  
Piezoelectric Layers ◽  
Mindlin Plate Theory ◽  
Clamped Edge

In this paper, a free vibration analysis of moderately thick circular functionally graded (FG) plate integrated with two thin piezoelectric (PZT4) layers is presented based on Mindlin plate theory. The material properties of the FG core plate are assumed to be graded in the thickness direction while the distribution of electric potential field along the thickness of piezoelectric layers is simulated by sinusoidal function. The differential equations of motion are solved analytically for two boundary conditions of the plate: clamped edge and simply supported edge. The analytical solution is validated by comparing the obtained resonant frequencies with those of an isotropic host plate. The emphasis is placed on investigating the effect of varying the gradient index of FG plate on the free vibration characteristics of the structure. Good agreement between the results of this paper and those of the finite element analyses validated the presented approach.

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.

A Cell-Based Smoothed Finite Element Method for Free Vibration Analysis of a Rotating Plate

2019 ◽  
Vol 16 (05) ◽  
pp. 1840003 ◽  
Author(s):  
C. F. Du ◽  
D. G. Zhang ◽  
G. R. Liu
Keyword(s):  
Free Vibration ◽  
Vibration Analysis ◽  
Natural Frequencies ◽  
Plate Theory ◽  
Free Vibration Analysis ◽  
Mindlin Plate ◽  
Smoothed Finite Element Method ◽  
A Cell ◽  
Mindlin Plate Theory ◽  
Rotating Plate

A cell-based smoothed finite element method (CS-FEM) is formulated for nonlinear free vibration analysis of a plate attached to a rigid rotating hub. The first-order shear deformation theory which is known as Mindlin plate theory is used to model the plate. In the process of formulating the system stiffness matrix, the discrete shear gap (DSG) method is used to construct the strains to overcome the shear locking issue. The effectiveness of the CS-FEM is first demonstrated in some static cases and then extended for free vibration analysis of a rotating plate considering the nonlinear effects arising from the coupling of vibration of the flexible structure with the undergoing large rotational motions. The nonlinear coupling dynamic equations of the system are derived via employing Lagrange’s equations of the second kind. The effects of different parameters including thickness ratio, aspect ratio, hub radius ratio and rotation speed on dimensionless natural frequencies are investigated. The dimensionless natural frequencies of CS-FEM are compared with those other existing method including the FEM and the assumed modes method (AMM). It is found that the CS-FEM based on Mindlin plate theory provides more accurate and “softer” solution compared with those of other methods even if using coarse meshes. In addition, the frequency loci veering phenomena associated with the mode shape interaction are examined in detail.

Free Vibration Analysis of Composite Material Plates "Case of a Typical Functionally Graded FG Plates Ceramic/Metal" with Porosities

2019 ◽  
Vol 25 ◽  
pp. 69-83 ◽  
Author(s):  
Slimane Merdaci
Keyword(s):  
Free Vibration ◽  
Shear Deformation ◽  
Vibration Analysis ◽  
Equations Of Motion ◽  
Porous Plate ◽  
Shear Deformation Theory ◽  
Free Vibration Analysis ◽  
Functionally Graded ◽  
Simply Supported ◽  
Fg Plates

This article presents the free vibration analysis of simply supported plate FG porous using a high order shear deformation theory. In is work the material properties of the porous plate FG vary across the thickness. The proposed theory contains four unknowns unlike the other theories which contain five unknowns. This theory has a parabolic shear deformation distribution across the thickness. So it is useless to use the shear correction factors. The Hamilton's principle will be used herein to determine the equations of motion. Since, the plate are simply supported the Navier procedure will be retained. To show the precision of this model, several comparisons have been made between the present results and those of existing theories in the literature for non-porous plates. Effects of the exponent graded and porosity factors are investigated.

An Extended Cell-Based Smoothed Three-Node Mindlin Plate Element (XCS-MIN3) for Free Vibration Analysis of Cracked FGM Plates

2017 ◽  
Vol 14 (02) ◽  
pp. 1750011 ◽  
Author(s):  
T. Nguyen-Thoi ◽  
T. Rabczuk ◽  
V. Ho-Huu ◽  
L. Le-Anh ◽  
H. Dang-Trung ◽  
...  
Keyword(s):  
Free Vibration ◽  
Vibration Analysis ◽  
Free Vibration Analysis ◽  
Functionally Graded ◽  
Mindlin Plate ◽  
Plate Element ◽  
Softening Effect ◽  
Strain Smoothing ◽  
Graded Material ◽  
A Cell

A cell-based smoothed three-node Mindlin plate element (CS-MIN3) was recently proposed and proven to be robust for static and free vibration analyses of Mindlin plates. The method improves significantly the accuracy of the solution due to softening effect of the cell-based strain smoothing technique. In addition, it is very flexible to apply for arbitrary complicated geometric domains due to using only three-node triangular elements which can be easily generated automatically. However so far, the CS-MIN3 has been only developed for isotropic material and for analyzing intact structures without possessing internal cracks. The paper hence tries to extend the CS-MIN3 by integrating itself with functionally graded material (FGM) and enriched functions of the extended finite element method (XFEM) to give a so-called extended cell-based smoothed three-node Mindlin plate (XCS-MIN3) for free vibration analysis of cracked FGM plates. Three numerical examples with different conditions are solved and compared with previous published results to illustrate the accuracy and reliability of the XCS-MIN3 for free vibration analysis of cracked FGM plates.

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.

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