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Steel and Composite Structures Volume 53, Number 1, October 10 2024 , pages 1-27 DOI: https://doi.org/10.12989/scs.2024.53.1.001 |
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Nonlinear vibration of laminated piezoelectric layered plates with nonlinear viscoelastic support using different DQM techniques |
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Ola Ragb, Mohamed Abd Elkhalek, M.S. Matbuly, Mohamed Salah, Mohamed Eltaher and Tharwat Osman
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| Abstract | ||
| This work presents the effectiveness of differential quadrature shape functions (i.e., Lagrange interpolation polynomial, Cardinal sine function, Delta Lagrange kernel and Regularized Shannon kernel) in the solution of nonlinear vibration of multilayers piezoelectric plates with nonlinear elastic support. A piezoelectric composite laminated plate is rested on nonlinear Winkler and Visco-Pasternak elastic foundations problems. Based on 3D elasticity theory and piezoelectricity, the governing equations of motion are derived. Differential quadrature methods based on four shape functions are presented as numerical techniques for solving this problem. The perturbation method is implemented to solve the obtained nonlinear eigenvalue problem. A MATLAB code is written for each technique for solving this problem and extract the numerical results. To validate these methods, the computed results are we compare with the previous exact results. In addition, parametric analyses are offered to investigate the influence of length to thickness ratio, elastic foundation parameters, various boundary conditions, and piezoelectric layers thickness on the natural frequencies and mode shapes. Consequently, it is discovered that the obtained results via the proposed schemes can be applied in structural health monitoring. | ||
| Key Words | ||
| laminated plate; nonlinear viscoelastic foundation; perturbation; piezoelectric material; quadrature techniques; vibration | ||
| Address | ||
| Ola Ragb, Mohamed Abd Elkhalek, M.S. Matbuly, Mohamed Salah, and Tharwat Osman:Department of Engineering Mathematics and Physics, Faculty of Engineering, Zagazig University, P.O. 44519, Egypt Mohamed Eltaher:1)Mechanical Engineering Department, Faculty of Engineering, King Abdulaziz University, P.O. Box 80204, Jeddah, Saudi Arabia 2)Mechanical Design & Production Department, Faculty of Engineering, Zagazig University, P.O. Box 44519, Zagazig, Egypt | ||