Vibration Analysis of Magneto-Electro-Thermo NanoBeam Resting on Nonlinear Elastic Foundation Using Sinc and Discrete Singular Convolution Differential Quadrature Method

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

doi:10.5539/mas.v13n7p49

Cited by 12 publications

(20 citation statements)

References 37 publications

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“…Different differential quadrature schemes such as classical DQ or PDQM, SDQM, DSCDQM‐DLK, and DSCDQM‐RSK are presented to formulate and solve PSCs such as follows 37‐39,47‐51 …”

Section: Methods Of Solutionmentioning

confidence: 99%

“…Based on Lagrange interpolation polynomial, we suppose that the unknown W and its derivatives are the approximation weighted linear sum of nodal values, W i as 37‐39 :

W ((), z_{i}) = \sum_{j = 1}^{N} ([], \frac{1}{z_{i} - z_{j}} ((), \frac{{false\prod}_{k = 1}^{N} (z_{i} - z_{k})}{{false\prod}_{j = 1, j \neq k}^{N} (z_{j} - z_{k})})) W ((), z_{j}), italicwhere i = 1, 2, 3, \dots N,

\frac{\partial^{r} W}{\partial z^{r}} (|, \begin{array}{c} z = z_{i} \end{array}) = \sum_{j = 1}^{N} a_{ij}^{(r)} W ((), z_{j}), italicwhere i = 1, 2, 3, \dots N, W ((), n, h, J_{h}, J_{n}, E)

where N is mesh point numbers.

a_{ij}^{(1)}

is the first‐order derivative weighting coefficients and can be evaluated as 39 :

a_{ij}^{(1)} = ({, \begin{array}{c} \frac{1}{(z_{i} - z_{j})} \prod_{k = 1, k \neq i, j}^{N} (z_{i} -) \end{array})

…”

Section: Methods Of Solutionmentioning

confidence: 99%

“…Each shape function has convergence and stability different from the other. The common investigated shape functions are Lagrange interpolation polynomials, 38,39 Cardinal sine, 40 Delta Lagrange, and Regularized Shannon kernels (RSKs) 41‐46 …”

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%

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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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“…Different differential quadrature schemes such as classical DQ or PDQM, SDQM, DSCDQM‐DLK, and DSCDQM‐RSK are presented to formulate and solve PSCs such as follows 37‐39,47‐51 …”

Section: Methods Of Solutionmentioning

confidence: 99%

“…Based on Lagrange interpolation polynomial, we suppose that the unknown W and its derivatives are the approximation weighted linear sum of nodal values, W i as 37‐39 :

W ((), z_{i}) = \sum_{j = 1}^{N} ([], \frac{1}{z_{i} - z_{j}} ((), \frac{{false\prod}_{k = 1}^{N} (z_{i} - z_{k})}{{false\prod}_{j = 1, j \neq k}^{N} (z_{j} - z_{k})})) W ((), z_{j}), italicwhere i = 1, 2, 3, \dots N,

\frac{\partial^{r} W}{\partial z^{r}} (|, \begin{array}{c} z = z_{i} \end{array}) = \sum_{j = 1}^{N} a_{ij}^{(r)} W ((), z_{j}), italicwhere i = 1, 2, 3, \dots N, W ((), n, h, J_{h}, J_{n}, E)

where N is mesh point numbers.

a_{ij}^{(1)}

is the first‐order derivative weighting coefficients and can be evaluated as 39 :

a_{ij}^{(1)} = ({, \begin{array}{c} \frac{1}{(z_{i} - z_{j})} \prod_{k = 1, k \neq i, j}^{N} (z_{i} -) \end{array})

…”

Section: Methods Of Solutionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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An accurate numerical approach for studying perovskite solar cells

et al. 2021

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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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Sinc and discrete singular convolution for analysis of three‐layer composite of perovskite solar cell

Ragb

Mohamed

Matbuly

et al. 2021

Intl J of Energy Research

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This work studies the performance of composite solar cell model consisting of perovskite absorber layer (CH 3 NH 3 PbI 3 ), electron transport layer (TiO 2 or PCBM), and hole transport layer (Spiro-OMeTAD or CuI) via sinc and discrete singular convolution quadrature techniques. The governing equations for hole transport layer, electron transport layer, and absorber layer (perovskite) are derived depending on the equations of continuity and Poisson. Different quadrature and block-marching techniques convert these equations to the nonlinear algebraic system. Then, we apply the iterative method to solve the problem of nonlinearity. For each scheme, a programmed code is designed to get a numerical solution for composite perovskite solar cells by MATLAB. To ensure the efficiency and convergence of these schemes, the obtained results match with previous experiments and other numerical schemes. From these comparisons, the discrete singular convolution quadrature technique gives high accuracy, speed of convergence, and more reliability than other methods with error up to 10 À8 . Consequently, the effects of different thicknesses, mobilities, band gaps, temperatures, absorption factors, wavelengths, and doping concentrations on current density, open-circuit voltage, and efficiency of solar cells are investigated in a full parametric study. Hence, the obtained effects of the current schemes increase the efficiency of perovskite solar cells. Novelty StatementSinc and discrete singular convolution quadrature techniques are applied to reach high performance for perovskite absorber layer sandwiched between electron transport layer (ETL) and hole transport layer (HTL). The study demonstrates that the discrete singular convolution quadrature method gives high efficiency and accurate results at different parameters. It is obtained that the power conversion efficiency is approximately 35% at specific parameters.

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Vibration Analysis of Magneto-Electro-Thermo NanoBeam Resting on Nonlinear Elastic Foundation Using Sinc and Discrete Singular Convolution Differential Quadrature Method

Cited by 12 publications

References 37 publications

An accurate numerical approach for studying perovskite solar cells

An accurate numerical approach for studying perovskite solar cells

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

Sinc and discrete singular convolution for analysis of three‐layer composite of perovskite solar cell

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