A New Numerical Procedure for Vibration Analysis of Beam under Impulse and Multiharmonics Piezoelectric Actuators
The dynamic behavior of structures with piezoelectric patches is governed by partial differential equations with strong singularities. To directly deal with these equations, well adapted numerical procedures are required. In this work, the differential quadrature method (DQM) combined with a regular...
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| Format: | Article |
| Language: | English |
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Wiley
2020-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2020/7391848 |
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| author | Yassin Belkourchia Lahcen Azrar |
| author_facet | Yassin Belkourchia Lahcen Azrar |
| author_sort | Yassin Belkourchia |
| collection | DOAJ |
| description | The dynamic behavior of structures with piezoelectric patches is governed by partial differential equations with strong singularities. To directly deal with these equations, well adapted numerical procedures are required. In this work, the differential quadrature method (DQM) combined with a regularization procedure for space and implicit scheme for time discretization is used. The DQM is a simple method that can be implemented with few grid points and can give results with a good accuracy. However, the DQM presents some difficulties when applied to partial differential equations involving strong singularities. This is due to the fact that the subsidiaries of the singular functions cannot be straightforwardly discretized by the DQM. A methodological approach based on the regularization procedure is used here to overcome this difficulty and the derivatives of the Dirac-delta function are replaced by regularized smooth functions. Thanks to this regularization, the resulting differential equations can be directly discretized using the DQM. The efficiency and applicability of the proposed approach are demonstrated in the computation of the dynamic behavior of beams for various boundary conditions and excited by impulse and Multiharmonics piezoelectric actuators. The obtained numerical results are well compared to the developed analytical solution. |
| format | Article |
| id | doaj-art-95381006b8aa410b82f44b75db8bf299 |
| institution | Kabale University |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2020-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-95381006b8aa410b82f44b75db8bf2992025-02-03T06:05:41ZengWileyJournal of Applied Mathematics1110-757X1687-00422020-01-01202010.1155/2020/73918487391848A New Numerical Procedure for Vibration Analysis of Beam under Impulse and Multiharmonics Piezoelectric ActuatorsYassin Belkourchia0Lahcen Azrar1Research Center STIS, M2CS, Department of Applied Mathematics and Informatics, ENSET, Mohammed V University, Rabat, MoroccoResearch Center STIS, M2CS, Department of Applied Mathematics and Informatics, ENSET, Mohammed V University, Rabat, MoroccoThe dynamic behavior of structures with piezoelectric patches is governed by partial differential equations with strong singularities. To directly deal with these equations, well adapted numerical procedures are required. In this work, the differential quadrature method (DQM) combined with a regularization procedure for space and implicit scheme for time discretization is used. The DQM is a simple method that can be implemented with few grid points and can give results with a good accuracy. However, the DQM presents some difficulties when applied to partial differential equations involving strong singularities. This is due to the fact that the subsidiaries of the singular functions cannot be straightforwardly discretized by the DQM. A methodological approach based on the regularization procedure is used here to overcome this difficulty and the derivatives of the Dirac-delta function are replaced by regularized smooth functions. Thanks to this regularization, the resulting differential equations can be directly discretized using the DQM. The efficiency and applicability of the proposed approach are demonstrated in the computation of the dynamic behavior of beams for various boundary conditions and excited by impulse and Multiharmonics piezoelectric actuators. The obtained numerical results are well compared to the developed analytical solution.http://dx.doi.org/10.1155/2020/7391848 |
| spellingShingle | Yassin Belkourchia Lahcen Azrar A New Numerical Procedure for Vibration Analysis of Beam under Impulse and Multiharmonics Piezoelectric Actuators Journal of Applied Mathematics |
| title | A New Numerical Procedure for Vibration Analysis of Beam under Impulse and Multiharmonics Piezoelectric Actuators |
| title_full | A New Numerical Procedure for Vibration Analysis of Beam under Impulse and Multiharmonics Piezoelectric Actuators |
| title_fullStr | A New Numerical Procedure for Vibration Analysis of Beam under Impulse and Multiharmonics Piezoelectric Actuators |
| title_full_unstemmed | A New Numerical Procedure for Vibration Analysis of Beam under Impulse and Multiharmonics Piezoelectric Actuators |
| title_short | A New Numerical Procedure for Vibration Analysis of Beam under Impulse and Multiharmonics Piezoelectric Actuators |
| title_sort | new numerical procedure for vibration analysis of beam under impulse and multiharmonics piezoelectric actuators |
| url | http://dx.doi.org/10.1155/2020/7391848 |
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