A New Numerical Procedure for Vibration Analysis of Beam under Impulse and Multiharmonics Piezoelectric Actuators
Joint Authors
Belkourchia, Yassin
Azrar, Lahcen
Source
Journal of Applied Mathematics
Issue
Vol. 2020, Issue 2020 (31 Dec. 2020), pp.1-19, 19 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2020-08-28
Country of Publication
Egypt
No. of Pages
19
Main Subjects
Abstract EN
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.
American Psychological Association (APA)
Belkourchia, Yassin& Azrar, Lahcen. 2020. A New Numerical Procedure for Vibration Analysis of Beam under Impulse and Multiharmonics Piezoelectric Actuators. Journal of Applied Mathematics،Vol. 2020, no. 2020, pp.1-19.
https://search.emarefa.net/detail/BIM-1174573
Modern Language Association (MLA)
Belkourchia, Yassin& Azrar, Lahcen. A New Numerical Procedure for Vibration Analysis of Beam under Impulse and Multiharmonics Piezoelectric Actuators. Journal of Applied Mathematics No. 2020 (2020), pp.1-19.
https://search.emarefa.net/detail/BIM-1174573
American Medical Association (AMA)
Belkourchia, Yassin& Azrar, Lahcen. A New Numerical Procedure for Vibration Analysis of Beam under Impulse and Multiharmonics Piezoelectric Actuators. Journal of Applied Mathematics. 2020. Vol. 2020, no. 2020, pp.1-19.
https://search.emarefa.net/detail/BIM-1174573
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1174573