Analytical investigation on axisymmetric free vibrations of moderately thick circular functionally graded plate integrated with piezoelectric layers

Ebrahimi, Farzad; Rastgoo, Abbas; Kargarnovin, M. H.

doi:10.1007/s12206-008-0303-2

Cited by 47 publications

(12 citation statements)

References 30 publications

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“…However, to the authors' best knowledge, no research dealing with the nonlinear vibration characteristics of the circular functionally graded plate integrated with the piezoelectric layers has been reported in literature except the author's recent works in presenting an analytical solution for the free axisymmetric vibration of piezoelectric coupled circular and annular FGM plates [29][30][31][32][33]. In conjunction with these works, in this paper, nonlinear static and dynamic behaviors of a piezoelectric coupled circular functionally graded plate structure with initial large nonlinear deformations (the von-Karman type geometrical nonlinear deformations) are studied.…”

Section: Introductionmentioning

confidence: 99%

Geometrically nonlinear vibration analysis of piezoelectrically actuated FGM plate with an initial large deformation

2009

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A theoretical model for geometrically nonlinear vibration analysis of piezoelectrically actuated circular plates made of functionally grade material (FGM) is presented based on Kirchhoff's-Love hypothesis with von-Karman type geometrical large nonlinear deformations. To determine the initial stress state and pre-vibration deformations of the smart plate a nonlinear static problem is solved followed by adding an incremental dynamic state to the pre-vibration state. The derived governing equations of the structure are solved by exact series expansion method combined with perturbation approach. The material properties of the FGM core plate are assumed to be graded in the thickness direction according to the power-law distribution in terms of the volume fractions of the constituents. Control of the FGM plate's nonlinear deflections and natural frequencies using high control voltages is studied and their nonlinear effects are evaluated. Numerical results for FG plates with various mixture of ceramic and metal are presented in dimensionless forms. In a parametric study the emphasis is placed on investigating the effect of varying the applied actuator voltage as well as gradient index of FGM plate on vibration characteristics of the smart structure.

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Section: Introductionmentioning

confidence: 99%

Geometrically nonlinear vibration analysis of piezoelectrically actuated FGM plate with an initial large deformation

2009

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“…However, to the authors' best knowledge, no researches dealing with the nonlinear vibration characteristics of the circular functionally graded plate integrated with the piezoelectric layers has been reported in literature except the author's recent works in presenting an analytical solution for the free axisymmetric linear vibration of piezoelectric coupled circular and annular FGM plates [25][26][27][28] and investigating the applied control voltage effect on piezoelectrically actuated FG circular plate [29] in which the thermal environment effects are not taken in to account. Though there are considerable papers dealing with FGM circular plates, most of these works neglect the implications of thermal effects on piezoelectric behavior of the coupled structure.…”

Section: List Of Symbolsmentioning

confidence: 99%

Nonlinear vibration analysis of piezo-thermo-electrically actuated functionally graded circular plates

Ebrahimi

Rastgoo

2010

Arch Appl Mech

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A theoretical model for geometrically nonlinear vibration analysis of thermo-piezoelectrically actuated circular plates made of functionally grade material (FGM) is presented based on Kirchhoff's-Love hypothesis with von-Karman type geometrical large nonlinear deformations. The material properties of the FG core plate are assumed to be graded in the thickness direction according to the power-law distribution in terms of the volume fractions of the constituents. Dynamic equations and boundary conditions including thermal, elastic and piezoelectric couplings are formulated and solutions are derived. An exact series expansion method combined with perturbation approach is used to model the nonlinear thermo-electro-mechanical vibration behavior of the structure. Control of the FG plate's nonlinear deflections and natural frequencies using high control voltages is studied and their nonlinear effects are evaluated. Numerical results for FG plates with various mixtures of ceramic and metal are presented in dimensionless forms. A parametric study is also undertaken to highlight the effects of the thermal environment, applied actuator voltage and material composition of the FG core plate on the nonlinear vibration characteristics of the composite structure.

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“…All the aforementioned studies focused on the rectangular-shaped plate structures. To the authors' best knowledge, no researches dealing with the nonlinear vibration characteristics of the circular functionally graded plate integrated with the piezoelectric layers have been reported in the literature except the author's recent works in presenting an analytical solution for the free axisymmetric linear vibration of piezoelectric coupled circular and annular FGM plates [16][17][18][19][20] and investigating the applied control voltage effect on piezoelectrically actuated nonlinear FG circular plate [21] in which the thermal environment effects are not taken in to account.…”

Section: Introductionmentioning

confidence: 99%

Investigating the thermal environment effects on geometrically nonlinear vibration of smart functionally graded plates

2010

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An analytical solution for a sandwich circular FGM plate coupled with piezoelectric layers under one-dimensional heat conduction is presented. All materials of the device may be of any functional gradients in the direction of thickness. The solution exactly satisfies all the equilibrium conditions and continuity conditions for the stress, displacement and electric displacement as well as electric potential on the interfaces between adjacency layers. A nonlinear static problem is solved first to determine the initial stress state and pre-vibration deformations of the FG plate that is subjected to in-plane forces and applied actuator voltage in thermal environment in the case of simply supported boundary conditions. By adding an incremental dynamic state to the pre-vibration state, the differential equations that govern the nonlinear vibration behavior of pre-stressed piezoelectric coupled FGM plates are derived. The role of thermal environment as well as control effects on nonlinear static deflections and natural frequencies imposed by the piezoelectric actuators using high input voltages are investigated. Numerical examples are provided and simulation results are discussed. Numerical results for FGM plates with a mixture of metal and ceramic are presented in dimensionless forms. The good agreement between the results of this paper and those of the finite element (FE) analyses validated the presented approach. In a parametric study the emphasis is placed on investigating the effect of varying the applied actuator voltage and thermal environment as well as gradient index of FG plate on the dynamics and control characteristics of the structure.

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Analytical investigation on axisymmetric free vibrations of moderately thick circular functionally graded plate integrated with piezoelectric layers

Cited by 47 publications

References 30 publications

Geometrically nonlinear vibration analysis of piezoelectrically actuated FGM plate with an initial large deformation

Geometrically nonlinear vibration analysis of piezoelectrically actuated FGM plate with an initial large deformation

Nonlinear vibration analysis of piezo-thermo-electrically actuated functionally graded circular plates

Investigating the thermal environment effects on geometrically nonlinear vibration of smart functionally graded plates

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