Free vibration of a piezoelectric nanobeam resting on nonlinear Winkler-Pasternak foundation by quadrature methods

Ragb, Ola; Mohamed, Mokhtar; Matbuly, M. S.

doi:10.1016/j.heliyon.2019.e01856

Cited by 22 publications

(16 citation statements)

References 59 publications

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“…One of the numerical methods that achieve accurate results with lower mesh sizes and without employing high effort is differential quadrature method (DQM) 37 . There are many forms of DQM, each form with different shape function and effect domain for all points.…”

Section: Introductionmentioning

confidence: 99%

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An accurate numerical approach for studying perovskite solar cells

et al. 2021

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Summary This work presents different numerical methods that are used for the first time in solving Perovskite solar cells (PSCs). Classical differential quadrature, sinc, and discrete singular convolution (Regularized Shannon and Delta Lagrange kernels) methods are employed for studying this problem. The governing equations are derived based on Poisson's and continuity equations. The different quadrature techniques are introduced to convert the system of nonlinear partial differential equations to nonlinear algebraic system. Then, an iterative method is used to solve this system. Convergence and efficiency of the obtained results with error ≤10−8 depend on various computational characteristics for each technique. The computed results match with previous experiment, exact, finite difference, SCAPS 1‐D simulation software, and finite element scheme. Then, the comprehensive parametric study is explored to show the effects of density states, gap energy, thickness, temperatures, lifetimes, wavelength, absorption coefficient, recombination prefactor, and recombination mechanisms whether direct or indirect on power conversion efficiency (PCE) and charge transport of solar cells with and without interface material. After all that have been studied on PSCs, it was found that the best value of PCEs was 32%. Thus, the computed results of the present schemes may be useful for improving the performance level of PSCs.

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Section: Introductionmentioning

confidence: 99%

“…Then, the governing equations can be reduced into a nonlinear algebraic system with discretizing the spatial derivatives by DQM. Also, iterative quadrature technique was used to solve this system 37‐46 . For each method, we ensure the efficiency and convergence by design a MATLAB code to get a numerical solution for this problem.…”

Section: Introductionmentioning

confidence: 99%

An accurate numerical approach for studying perovskite solar cells

et al. 2021

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“…Given the various beam theories mentioned above, numerous researchers have achieved remarkable results in the analysis of piezoelectric beams. From the perspective of their shape, beams can be divided into bimorph beams [11][12][13], functionally graded piezoelectric beams (FGPM) and sandwich beams [14][15][16][17][18][19][20][21][22], nano-microbeams [23][24][25][26][27], and curved beams [28,29]. e above literature shows that the transition from the traditional composite material lamination theory to the piezoelectric material lamination structure has been relatively complete.…”

Section: Introductionmentioning

confidence: 99%

“…c ij is the elastic constants; e ij and s ij are piezoelectric and dielectric constants, respectively. Notably, e ij and s ij are equal to zero when the kth layer is a general metal material; these constants can be specifically expressed as follows[23]:…”

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confidence: 99%

A Unified Analysis for the Free Vibration of the Sandwich Piezoelectric Laminated Beam with General Boundary Conditions under the Thermal Environment

Gao

Sun

Shao

et al. 2021

Shock and Vibration

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This article mainly analyzes the free vibration characteristic of the sandwich piezoelectric beam under elastic boundary conditions and thermal environment. According to the first-order shear deformation theory and Hamilton’s principle, the thermo-electro-elastic coupling equations of the sandwich piezoelectric beam are obtained. Meanwhile, elastic boundary conditions composed of an array of springs are introduced, and the displacement variables and external potential energy of the beam are expressed as wave functions. By using the method of reverberation-ray matrix to integrate and solve the governing equations, a search algorithm based on golden-section search is introduced to calculate the required frequency parameters. A series of numerical results are compared with those reported in literature studies and obtained by simulation software to verify the correctness and versatility of the search algorithm. In addition, three parametric research cases are proposed to investigate the frequency parameters of sandwich piezoelectric beams with elastic restraint conditions, material parameters, thickness ratio, different temperature rises, and external electric potential.

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“…Previous DQ techniques are then employed to reduce the problem to the eigenvalue or bending problem. e same schemes are used for free vibration analysis of piezoelectric nanobeams [45,46]. Recent studies have investigated the vibration analysis of composite plate resting on elastic foundations, using DSCDQM [47][48][49][50][51][52][53][54][55][56][57][58].…”

Section: Introductionmentioning

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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Free vibration of a piezoelectric nanobeam resting on nonlinear Winkler-Pasternak foundation by quadrature methods

Cited by 22 publications

References 59 publications

An accurate numerical approach for studying perovskite solar cells

An accurate numerical approach for studying perovskite solar cells

A Unified Analysis for the Free Vibration of the Sandwich Piezoelectric Laminated Beam with General Boundary Conditions under the Thermal Environment

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

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