Free vibration of a piezoelectric nanobeam resting on nonlinear Winkler-Pasternak foundation by quadrature methods
This work introduces a numerical scheme for free vibration analysis of elastically supported piezoelectric nanobeam. Based on Hamilton principle, governing equations of the problem are derived. The problem is formulated for linear and nonlinear Winkler–Pasternak foundation type. Three differential q...
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Elsevier
2019-06-01
|
| Series: | Heliyon |
| Subjects: | |
| Online Access: | http://www.sciencedirect.com/science/article/pii/S2405844018390005 |
| _version_ | 1830481871989899264 |
|---|---|
| author | Ola Ragb Mokhtar Mohamed M.S. Matbuly |
| author_facet | Ola Ragb Mokhtar Mohamed M.S. Matbuly |
| author_sort | Ola Ragb |
| collection | DOAJ |
| description | This work introduces a numerical scheme for free vibration analysis of elastically supported piezoelectric nanobeam. Based on Hamilton principle, governing equations of the problem are derived. The problem is formulated for linear and nonlinear Winkler–Pasternak foundation type. Three differential quadrature techniques are employed to reduce the problem to an Eigen-value problem. The reduced system is solved iteratively. The natural frequencies of the beam are obtained. Numerical analysis is implemented to investigate computational characteristics affecting convergence, accuracy and efficiency of the proposed scheme. The obtained results agreed with the previous analytical and numerical ones. Furthermore, a parametric study is introduced to show influence of supporting conditions, two different electrical boundary conditions, material characteristics, foundation parameters, temperature change, external electric voltage, nonlocal parameter and beam length-to-thickness ratio on the values of natural frequencies and mode shapes of the problem. |
| first_indexed | 2024-12-21T17:25:16Z |
| format | Article |
| id | doaj.art-b93ede18e7264cb997cbd480df50817a |
| institution | Directory Open Access Journal |
| issn | 2405-8440 |
| language | English |
| last_indexed | 2024-12-21T17:25:16Z |
| publishDate | 2019-06-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Heliyon |
| spelling | doaj.art-b93ede18e7264cb997cbd480df50817a2022-12-21T18:56:04ZengElsevierHeliyon2405-84402019-06-0156e01856Free vibration of a piezoelectric nanobeam resting on nonlinear Winkler-Pasternak foundation by quadrature methodsOla Ragb0Mokhtar Mohamed1M.S. Matbuly2Department of Engineering Mathematics and Physics, Faculty of Engineering, Zagazig University, P.O. 44519, EgyptBasic Science Departement, Faculty of Engineering, Delta University for Science and Technology, P.O.2770141, Egypt; Corresponding author.Department of Engineering Mathematics and Physics, Faculty of Engineering, Zagazig University, P.O. 44519, EgyptThis work introduces a numerical scheme for free vibration analysis of elastically supported piezoelectric nanobeam. Based on Hamilton principle, governing equations of the problem are derived. The problem is formulated for linear and nonlinear Winkler–Pasternak foundation type. Three differential quadrature techniques are employed to reduce the problem to an Eigen-value problem. The reduced system is solved iteratively. The natural frequencies of the beam are obtained. Numerical analysis is implemented to investigate computational characteristics affecting convergence, accuracy and efficiency of the proposed scheme. The obtained results agreed with the previous analytical and numerical ones. Furthermore, a parametric study is introduced to show influence of supporting conditions, two different electrical boundary conditions, material characteristics, foundation parameters, temperature change, external electric voltage, nonlocal parameter and beam length-to-thickness ratio on the values of natural frequencies and mode shapes of the problem.http://www.sciencedirect.com/science/article/pii/S2405844018390005Applied mathematicsNonlocal elasticity theoryVibrationPiezoelectricNonlinear elastic foundationSINC |
| spellingShingle | Ola Ragb Mokhtar Mohamed M.S. Matbuly Free vibration of a piezoelectric nanobeam resting on nonlinear Winkler-Pasternak foundation by quadrature methods Heliyon Applied mathematics Nonlocal elasticity theory Vibration Piezoelectric Nonlinear elastic foundation SINC |
| title | Free vibration of a piezoelectric nanobeam resting on nonlinear Winkler-Pasternak foundation by quadrature methods |
| title_full | Free vibration of a piezoelectric nanobeam resting on nonlinear Winkler-Pasternak foundation by quadrature methods |
| title_fullStr | Free vibration of a piezoelectric nanobeam resting on nonlinear Winkler-Pasternak foundation by quadrature methods |
| title_full_unstemmed | Free vibration of a piezoelectric nanobeam resting on nonlinear Winkler-Pasternak foundation by quadrature methods |
| title_short | Free vibration of a piezoelectric nanobeam resting on nonlinear Winkler-Pasternak foundation by quadrature methods |
| title_sort | free vibration of a piezoelectric nanobeam resting on nonlinear winkler pasternak foundation by quadrature methods |
| topic | Applied mathematics Nonlocal elasticity theory Vibration Piezoelectric Nonlinear elastic foundation SINC |
| url | http://www.sciencedirect.com/science/article/pii/S2405844018390005 |
| work_keys_str_mv | AT olaragb freevibrationofapiezoelectricnanobeamrestingonnonlinearwinklerpasternakfoundationbyquadraturemethods AT mokhtarmohamed freevibrationofapiezoelectricnanobeamrestingonnonlinearwinklerpasternakfoundationbyquadraturemethods AT msmatbuly freevibrationofapiezoelectricnanobeamrestingonnonlinearwinklerpasternakfoundationbyquadraturemethods |