Vibration Analysis of Piezoelectric Composite using Sinc and Discrete Singular Convolution Differential Quadrature Techniques

Ragb, Ola; Salah, Mohamed; Matbuly, M. S.; Amer, R. M.

doi:10.36478/jeasci.2019.6540.6553

Cited by 4 publications

(4 citation statements)

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“…e DSC algorithm can be applied using many types of kernels. ese kernels are applied as shape functions, such that the unknown ψ and its derivatives are approximated as a weighted linear sum of [33][34][35][36][37].…”

Section: Discrete Singular Convolution Differential Quadrature Methodmentioning

confidence: 99%

“…where σ is a regularization parameter and r is a computational parameter. e weighting coefficients A x ij and B x ij can be defined as follows [33][34][35][36][37][38][39][40][41][42]:…”

Section: Discrete Singular Convolution Differential Quadrature Methodmentioning

confidence: 99%

“…Additionally, there is no research in piezoelectric composite plate resting on nonlinear elastic foundations, whether analytically or numerically. e sinc differential quadrature method (SDQM) [27][28][29][30][31][32] and the discrete singular convolution differential quadrature method (DSCDQM) [33][34][35][36][37][38][39][40][41][42] are more reliable than the polynomial-based DQM.…”

Section: Introductionmentioning

confidence: 99%

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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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Section: Discrete Singular Convolution Differential Quadrature Methodmentioning

confidence: 99%

“…where σ is a regularization parameter and r is a computational parameter. e weighting coefficients A x ij and B x ij can be defined as follows [33][34][35][36][37][38][39][40][41][42]:…”

Section: Discrete Singular Convolution Differential Quadrature Methodmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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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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“…However, DQM based on different shape functions has not been utilized to solve FOPDEs like Lagrange interpolation (PDQM), cardinal sine (SDQM), and discrete singular convolution based on delta Lagrange kernel (DSCDQM‐DLK), regularized Shannon kernel (DSCDQM‐RSK), and regularized Dirichlet kernel (DSCDQM‐RDK). From Ragb et al, 36–45 we found that these techniques are accurate, reliable, and highly efficient approaches with small grid points and less CPU time for solving initial and/or boundary value problems.…”

Section: Introductionmentioning

confidence: 95%

Fractional differential quadrature techniques for fractional order Cauchy reaction‐diffusion equations

Ragb

Wazwaz

Mohamed

et al. 2023

Math Methods in App Sciences

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This paper aims to explore and apply differential quadrature based on different test functions to find an efficient numerical solution of fractional order Cauchy reaction-diffusion equations (CRDEs). The governing system is discretized through time and space via novel techniques of differential quadrature method and the fractional operator of Caputo kind. Two problems are offered to explain the accuracy of the numerical algorithms. To verify the reliability, accuracy, efficiency, and speed of these methods, computed results are compared numerically and graphically with the exact and semi-exact solutions. Then mainly, we deal with absolute errors and L ∞ errors to study the convergence of the presented methods. For each technique, MATLAB Code is designed to solve these problems with the error reaching ≤1 Â 10 À5 . In addition, a parametric analysis is presented to discuss influence of fractional order derivative on results. The achieved solutions prove the viability of the presented methods and demonstrate that these methods are easy to implement, effective, high accurate, and appropriate for studying fractional partial differential equations emerging in fields related to science and engineering.

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Fractional modelling of piezoelectric composite nanobeams via novel numerical schemes

Salah,

Civalek,

Ragb

2023

Appl. Phys. A

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Vibration Analysis of Piezoelectric Composite using Sinc and Discrete Singular Convolution Differential Quadrature Techniques

Cited by 4 publications

References 0 publications

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

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

Fractional differential quadrature techniques for fractional order Cauchy reaction‐diffusion equations

Fractional modelling of piezoelectric composite nanobeams via novel numerical schemes

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