Geometrically nonlinear static and free vibration analysis of functionally graded piezoelectric plates

Behjat, Bashir; Khoshravan, Mohammad Reza

doi:10.1016/j.compstruct.2011.08.024

Cited by 58 publications

(20 citation statements)

References 28 publications

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“…Nonlinear results q = 0.5 The material properties, as given in Shen [30], are E m = 105 GPa, ν m = 0:3, ρ m = 4429 kg/m 3 for Ti-6Al-4V and E c = 168 GPa, ν c = 0:3, and ρ c = 3000 kg/m 3 for ZrO 2 . The nonlinear to linear frequency ratios ω NL /ω L presented in Table 2 are com-pared with Shen [30] (exact results) and Behjat and Khoshravan [31] (finite element model with mesh of 6 × 6 elements); good agreement can be seen from this table when the number of elements is large enough. Besides, it also can be observed that the mesh 14 × 14 ensures the accuracy; therefore, for all succeeding investigations, this mesh will be employed.…”

Section: Numerical Results Of Nonlinear Staticsupporting

confidence: 62%

Nonlinear Static Bending and Free Vibration Analysis of Bidirectional Functionally Graded Material Plates

Hong

2020

International Journal of Aerospace Engineering

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Bidirectional functionally graded material (2D-FGM) plates have mechanical properties that vary continuously in both the thickness and one-edge directions; these plates are more and more widely used in design and engineering applications. When these structures are subjected to strong loads, they can be largely deformed; therefore, nonlinear calculations, in this case, are necessary. In this paper, nonlinear static bending and nonlinear free vibration behaviors of 2D-FGM plates are studied by using the finite element method based on the third-order shear deformation theory; the Newton-Raphson method is used to solve this problem. The accuracy of this approach is confirmed by comparing the results with respect to other papers. The effects of some numerical aspect ratios such as volume fraction index and thickness-to-length ratio on nonlinear static bending and free vibration of the plates are explored. This study shows that there is a big difference between the numerical results obtained from the nonlinear problem and those from the linear one.

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Section: Numerical Results Of Nonlinear Staticsupporting

confidence: 62%

Nonlinear Static Bending and Free Vibration Analysis of Bidirectional Functionally Graded Material Plates

Hong

2020

International Journal of Aerospace Engineering

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“…Loja et al (2013) studied the static and free vibration behavior of functionally graded sandwich plate-type structures, using B-spline finite strip element models based on different shear deformation theories. Geometrical nonlinear static and free vibration analyses of FG piezoelectric plates using FEM were studied by Behjat and Khoshravan (2012). On their work, different sets of mechanical and electrical loadings were considered.…”

Section: Introductionmentioning

confidence: 99%

Transient bending analysis of a functionally graded circular plate with integrated surface piezoelectric layers

Jafari

Jandaghian

Rahmani

2014

Int J Mech Mater Eng

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Background: Thin and piezoelectric materials are widely used as sensors or actuators in smart structures by embedding or surface-mounted them. Methods: This paper report on the exact, explicit solution for the transient bending of a circular functionally graded (FG) plates integrated with two uniformly distributed actuator layers made of piezoelectric material based on the classical plate theory (CPT). The material properties of the FG substrate 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 and the distribution of electric potential field along the thickness direction of piezoelectric layers is simulated by a quadratic function. The form of the electric potential field in the piezoelectric layer is considered such that the Maxwell static electricity equation is satisfied. The governing equations are solved for clamped and simply supported edge boundary condition of the circular plate. The solutions are expressed by elementary Bessel functions and derived via exact inverse Laplace transform. Results and Conclusions: It is seen that the power index (g) and thickness of piezo-layer have significant effect on the deflection amplitude and natural frequency of piezo-FG plate.

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“…Loja et al (2012) studied the static and free vibration behavior of functionally graded sandwich plate type structures, using B-spline finite strip element models based on different shear deformation theories. Geometrical nonlinear static and free vibration analyses of FG piezoelectric plates using FEM were studied by Behjat and Khoshravan (2012). On their work different sets of mechanical and electrical loadings were considered.…”

Section: Introductionmentioning

confidence: 99%

Vibrational response of functionally graded circular plate integrated with piezoelectric layers: An exact solution

Jandaghian¹,

Jafari²,

Rahmani

2014

10.5267/j.esm

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In this paper, harmonic forced vibration of circular functionally graded plate integrated with two uniformly distributed actuator faces made of piezoelectric material is studied. The material properties of the functionally graded substrate layers are assumed to be graded in the thickness direction according to the power-law distribution, also the distribution of electric potential field along the thickness direction of piezoelectric layers is modeled by a quadratic function. The governing equations are solved for simply supported boundary condition of the sandwich circular plate and the solutions are presented by elementary Bessel functions. The performance of the present model is compared with that of finite element analyses as well as other available literature by the presentation of comparative results obtained for several examples encompassing different power indexes and vibration modes. The results show that thickness of piezoelectric layer and changing the power index in FG material has a significant influence on the deflection and natural frequencies of system.

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Geometrically nonlinear static and free vibration analysis of functionally graded piezoelectric plates

Cited by 58 publications

References 28 publications

Nonlinear Static Bending and Free Vibration Analysis of Bidirectional Functionally Graded Material Plates

Nonlinear Static Bending and Free Vibration Analysis of Bidirectional Functionally Graded Material Plates

Transient bending analysis of a functionally graded circular plate with integrated surface piezoelectric layers

Vibrational response of functionally graded circular plate integrated with piezoelectric layers: An exact solution

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