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

Ebrahimi, Farzad; Rastgoo, Abbas

doi:10.1007/s00419-010-0415-x

Cited by 16 publications

(3 citation statements)

References 33 publications

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“…Alipour and Shariyat [20] gave analytical stress analysis of annular FGM sandwich plates with non-uniform shear and normal tractions employing a zigzag-elasticity plate theory. More works can be seen in [21][22][23][24][25][26][27][28][29][30].…”

Section: Introductionmentioning

confidence: 99%

Nonlinear bending analysis of FGM circular plates based on physical neutral surface and higher-order shear deformation theory

Zhang

Zhou

2015

Aerospace Science and Technology

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Section: Introductionmentioning

confidence: 99%

Nonlinear bending analysis of FGM circular plates based on physical neutral surface and higher-order shear deformation theory

Zhang

Zhou

2015

Aerospace Science and Technology

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“…Based on the three-dimensional elastic theory, Nie and Zhong [8] achieved dynamic analysis of multi-directional FGM annular plates by using a semianalytical numerical method. Based on Kirchhoff'sLove hypothesis, Ebrahimi and Rastgoo [9] presented a theoretical model for geometrically nonlinear vibration analysis of FGM circular plates. By means of the differential transformation method, Shariyat and Alipour [10] developed a semi-analytical solution for free vibration and modal stress analyses of two-dimensional FGM circular plates resting on two-parameter elastic foundations.…”

Section: Introductionmentioning

confidence: 99%

Nonlinear Dynamic Analysis for FGM Circular Plates

2012

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In the paper, nonlinear dynamic analysis of a circular plate composed of functionally graded material (FGM) is presented. Considering a transverse shear deformation and geometric nonlinearity, the von Karman geometric relation of the FGM circular plate is established. Based on the theory of the first-order shear deformation, a new set of equilibrium equations is developed by the principle of minimum total energy. Applying the finite difference method and Newmark scheme, the nonlinear transient problem is solved by the iterative method. To validate the presented method, the transient problem of the FGM circular plate is compared with those of the existed literature, and good agreement is observed. The effects of the volume fraction index, boundary conditions, mechanical load and the ratio of thickness to radius on the nonlinear transient problem of the FGM circular plate are investigated.

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“…Brischetto (2013) used exact elasticity solution for study natural frequencies of functionally graded simply-supported structures. Ebrahimi and Rastgoo (2011) presented a theoretical model for geometrically nonlinear vibration analysis of thermo-piezoelectrically actuated circular plates made of FGM based on Kirchhoff's-Love hypothesis with von-Karman type geometrical large nonlinear deformations. Reddy and Cheng (2003) obtained the frequencies of functionally graded rectangular plates by using a three-dimensional asymptotic approach.…”

Section: Introductionmentioning

confidence: 99%

Deflection and vibration analysis of higher-order shear deformable compositionally graded porous plate

Ebrahimi¹,

Habibi²

2016

Steel Compos. Struct.

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In this study the finite element method is utilized to predict the deflection and vibration characteristics of rectangular plates made of saturated porous functionally graded materials (PFGM) within the framework of the third order shear deformation plate theory. Material properties of PFGM plate are supposed to vary continuously along the thickness direction according to the power-law form and the porous plate is assumed of the form where pores are saturated with fluid. Various edge conditions of the plate are analyzed. The governing equations of motion are derived through energy method, using calculus of variations while the finite element model is derived based on the constitutive equation of the porous material. According to the numerical results, it is revealed that the proposed modeling and finite element approach can provide accurate deflection and frequency results of the PFGM plates as compared to the previously published results in literature. The detailed mathematical derivations are presented and numerical investigations are performed while the emphasis is placed on investigating the effect of the several parameters such as porosity volume fraction, material distribution profile, mode number and boundary conditions on the natural frequencies and deflection of the PFGM plates in detail. It is explicitly shown that the deflection and vibration behaviour of porous FGM plates are significantly influenced by these effects. Numerical results are presented to serve as benchmarks for future analyses of FGM plates with porosity phases.

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

Cited by 16 publications

References 33 publications

Nonlinear bending analysis of FGM circular plates based on physical neutral surface and higher-order shear deformation theory

Nonlinear bending analysis of FGM circular plates based on physical neutral surface and higher-order shear deformation theory

Nonlinear Dynamic Analysis for FGM Circular Plates

Deflection and vibration analysis of higher-order shear deformable compositionally graded porous plate

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