Free vibration analysis of FG plate with piezoelectric layers using four-variable refined plate theory

2015 ◽  
Vol 89 ◽  
pp. 76-83 ◽  
Author(s):  
Jafar Rouzegar ◽  
Farhad Abad
Keyword(s):  
Free Vibration ◽  
Vibration Analysis ◽  
Plate Theory ◽  
Free Vibration Analysis ◽  
Refined Plate Theory ◽  
Piezoelectric Layers

scholarly journals Free Vibration Analysis of Smart Laminated Functionally Graded CNT Reinforced Composite Plates via New Four-Variable Refined Plate Theory

Materials ◽  
2019 ◽  
Vol 12 (22) ◽  
pp. 3675 ◽  
Author(s):  
Tran Huu Quoc ◽  
Tran Minh Tu ◽  
Vu Van Tham
Keyword(s):  
Free Vibration ◽  
Boundary Conditions ◽  
Vibration Analysis ◽  
Plate Theory ◽  
Free Vibration Analysis ◽  
Composite Plates ◽  
Functionally Graded ◽  
Transverse Shear Strain ◽  
Refined Plate Theory ◽  
Reinforced Composite

This paper presents a new four-variable refined plate theory for free vibration analysis of laminated piezoelectric functionally graded carbon nanotube-reinforced composite plates (PFG-CNTRC). The present theory includes a parabolic distribution of transverse shear strain through the thickness and satisfies zero traction boundary conditions at both free surfaces of the plates. Thus, no shear correction factor is required. The distribution of carbon nanotubes across the thickness of each FG-CNT layer can be functionally graded or uniformly distributed. Additionally, the electric potential in piezoelectric layers is assumed to be quadratically distributed across the thickness. Equations of motion for PFG-CNTRC rectangular plates are derived using both Maxwell’s equation and Hamilton’s principle. Using the Navier technique, natural frequencies of the simply supported hybrid plate with closed circuit and open circuit of electrical boundary conditions are calculated. New parametric studies regarding the effect of the volume fraction, the CNTs distribution, the number of layers, CNT fiber orientation and thickness of the piezoelectric layer on the free vibration response of hybrid plates are performed.

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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