Three dimensional static and free vibration analysis of cross-ply laminated plate bonded with piezoelectric layers using differential quadrature method

The three-dimensional bending behavior of a viscoelastic functionally graded material (FGM) layer embedded between piezoelectric layers and subjected to an electric field as well as a uniform transverse pressure is studied. An analytical solution is computed for a simply supported viscoelastic smart FGM plate using the state space technique along the thickness direction and a Fourier expansion along the in-plane coordinates. The governing differential equations in the time domain are transformed to the Laplace domain, solved in the Laplace domain, and transformed back to the time domain using the inverse Laplace transform. In the present study, the relaxation modulus of the FGM layer is assumed in the form of a Prony series, and it varies according to the power law in the thickness direction. The validity of the proposed approach is assessed by comparison of the numerical results of the approach with those of published works in the literature. The effects of geometric dimensions, electromechanical loads, and relaxation time constant on the behavior of the smart plate are investigated.

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“…Based on Eq. (27a), at the lower surface of the actuator layer, electric displacement is (Feri, Alibeigloo, and Pasha Zanoosi, 2016):…”

Section: Piezoelectric Layermentioning

confidence: 99%

Three-dimensional static analysis of a viscoelastic rectangular functionally graded material plate embedded between piezoelectric sensor and actuator layers

Feri

Krommer

Alibeigloo

2021

Mechanics Based Design of Structures and Machines

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“…Based on the theory of elasticity and piezoelectricity, the equations of motion and the charge equation of electrostatic can be written as follows [59,[65][66][67][68][69]:…”

Section: Formulation Of the Problemmentioning

confidence: 99%

Vibration Analysis of Piezoelectric Composite Plate Resting on Nonlinear Elastic Foundations Using Sinc and Discrete Singular Convolution Differential Quadrature Techniques

Ragb

Salah

Matbuly

et al. 2020

Mathematical Problems in Engineering

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In this work, free vibration of the piezoelectric composite plate resting on nonlinear elastic foundations is examined. The three-dimensionality of elasticity theory and piezoelectricity is used to derive the governing equation of motion. By implementing two differential quadrature schemes and applying different boundary conditions, the problem is converted to a nonlinear eigenvalue problem. The perturbation method and iterative quadrature formula are used to solve the obtained equation. Numerical analysis of the proposed schemes is introduced to demonstrate the accuracy and efficiency of the obtained results. The obtained results are compared with available results in the literature, showing excellent agreement. Additionally, the proposed schemes have higher efficiency than previous schemes. Furthermore, a parametric study is introduced to investigate the effect of elastic foundation parameters, different materials of sensors and actuators, and elastic and geometric characteristics of the composite plate on the natural frequencies and mode shapes.

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“…Navy-type analytical solutions are available for the three-dimensional vibrations of such rectangular plates [9][10][11][12][13][14]. However, the majority of studies on the free vibrations of such rectangular plates with general boundary conditions have been based on various plate theories and different assumptions regarding the distribution of electric potential in the thickness direction or have relied on various numerical approaches, such as the Ritz method [15], the differential quadrature method [16,17], the finite element method (FEM) [18][19][20][21], the finite strip method [22], or isogeometric analysis [23]. Notably, the vibrations of magneto-electro-thermo-elastic rectangular nanoplates have been extensively studied over the past decade [24][25][26][27][28], employing various nonlocal continuum mechanicsbased plate theories.…”

Section: Introductionmentioning

confidence: 99%

Levy-type analytical series solution for the three-dimensional free vibrations of functionally graded material rectangular plates with piezoelectric layers

Huang,

Chen,

2023

Smart Mater. Struct.

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Analytical solutions founded on three-dimensional theories play a crucial role in evaluating the credibility and precision of different plate theories and numerical methodologies. While Levy-type analytical solutions are widely recognized, they have been primarily confined to purely elastic plates. This study introduces a Levy-type analytical series solution for three-dimensional vibrations in a sandwich rectangular plate featuring a functionally graded material (FGM) core, along with piezoelectric material (PM) layers on the top and bottom surfaces. The behaviors of the FGM and PM layers were described using three-dimensional elasticity and piezoelasticity theories, respectively. In this study, the displacement functions and electric potential of each layer were expanded by Fourier series and polynomial auxiliary functions. An analytical series solution was then established by satisfying the governing equations of each layer, the mechanical and electric boundary conditions on the six faces of the plate, and the continuity conditions on the interfaces between the PM and FGM layers. To validate the proposed solutions, in-depth convergence studies were conducted for the vibration frequencies of the first six modes of sandwich square plates with various boundary conditions on the other pair of side faces. The well-converged results were then compared with published data based on various plate theories to verify the accuracy of these published data. Finally, accurate nondimensional frequencies were tabulated for the first six modes of sandwich rectangular plates with various aspect ratios, thickness-to-width ratios, PM-to-FGM layer thickness ratios, power law indices for the FGM layer, and six combinations of boundary conditions. These new numerical results when piezoelectric coupling is considered should be very useful to future analytical and numerical studies.

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Three dimensional static and free vibration analysis of cross-ply laminated plate bonded with piezoelectric layers using differential quadrature method

Cited by 11 publications

References 28 publications

Three-dimensional static analysis of a viscoelastic rectangular functionally graded material plate embedded between piezoelectric sensor and actuator layers

Three-dimensional static analysis of a viscoelastic rectangular functionally graded material plate embedded between piezoelectric sensor and actuator layers

Vibration Analysis of Piezoelectric Composite Plate Resting on Nonlinear Elastic Foundations Using Sinc and Discrete Singular Convolution Differential Quadrature Techniques

Levy-type analytical series solution for the three-dimensional free vibrations of functionally graded material rectangular plates with piezoelectric layers

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