Free vibration analysis of functionally graded coupled circular plate with piezoelectric layers

2009 ◽  
Vol 23 (8) ◽  
pp. 2008-2021 ◽  
Author(s):  
Saeed Jafari Mehrabadi ◽  
M. H. Kargarnovin ◽  
M. M. Najafizadeh
Keyword(s):  
Free Vibration ◽  
Circular Plate ◽  
Vibration Analysis ◽  
Free Vibration Analysis ◽  
Functionally Graded ◽  
Piezoelectric Layers

Two-Dimensional Free Vibration Analysis of Axially Functionally Graded Beams Integrated with Piezoelectric Layers: An Piezoelasticity Approach

2020 ◽  
Vol 12 (04) ◽  
pp. 2050037
Author(s):  
Agyapal Singh ◽  
Poonam Kumari
Keyword(s):  
Free Vibration ◽  
Boundary Conditions ◽  
Vibration Analysis ◽  
Free Vibration Analysis ◽  
Variable Coefficients ◽  
Functionally Graded ◽  
Numerical Results ◽  
Two Dimensional ◽  
Kantorovich Method ◽  
Piezoelectric Layers

For the first time, a two-dimensional (2D) piezoelasticity-based analytical solution is developed for free vibration analysis of axially functionally graded (AFG) beams integrated with piezoelectric layers and subjected to arbitrary supported boundary conditions. The material properties of the elastic layers are considered to vary linearly along the axial ([Formula: see text]) direction of the beam. Modified Hamiltons principle is applied to derive the weak form of coupled governing equations in which, stresses, displacements and electric field variables acting as primary variables. Further, the extended Kantorovich method is employed to reduce the governing equation into sets of ordinary differential equations (ODEs) along the axial ([Formula: see text]) and thickness ([Formula: see text]) directions. The ODEs along the [Formula: see text]-direction have constant coefficients, where the ODEs along [Formula: see text]-direction have variable coefficients. These sets of ODEs are solved analytically, which ensures the same order of accuracy for all the variables by satisfying the boundary and continuity conditions in exact pointwise manner. New benchmark numerical results are presented for a single layer AFG beam and AFG beams integrated with piezoelectric layers. The influence of the axial gradation, aspect ratio and boundary conditions on the natural frequencies of the beam are also investigated. These numerical results can be used for assessing 1D beam theories and numerical techniques.

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.

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