Periodic solutions of a graphene based model in micro-electro-mechanical pull-in device
Phase plane analysis of the nonlinear spring-mass equation arising in modeling vibrations of a lumped mass attached to a graphene sheet with a fixed end is presented. The nonlinear lumped-mass model takes into account the nonlinear behavior of the graphene by including the third-order elastic stiffn...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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University of West Bohemia
2017-06-01
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| Series: | Applied and Computational Mechanics |
| Subjects: | |
| Online Access: | https://www.kme.zcu.cz/acm/acm/article/view/322/412 |
| _version_ | 1818723930072940544 |
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| author | Wei D. Kadyrov S. Kazbek Z. |
| author_facet | Wei D. Kadyrov S. Kazbek Z. |
| author_sort | Wei D. |
| collection | DOAJ |
| description | Phase plane analysis of the nonlinear spring-mass equation arising in modeling vibrations of a lumped mass attached to a graphene sheet with a fixed end is presented. The nonlinear lumped-mass model takes into account the nonlinear behavior of the graphene by including the third-order elastic stiffness constant and the nonlinear electrostatic force. Standard pull-in voltages are computed. Graphic phase diagrams are used to demonstrate the conclusions. The nonlinear wave forms and the associated resonance frequencies are computed and presented graphically to demonstrate the effects of the nonlinear stiffness constant comparing with the corresponding linear model. The existence of periodic solutions of the model is proved analytically for physically admissible periodic solutions, and conditions for bifurcation points on a parameter associated with the third-order elastic stiffness constant are determined. |
| first_indexed | 2024-12-17T21:18:20Z |
| format | Article |
| id | doaj.art-54d5b771865f4f80b7d83f8dfb124bbe |
| institution | Directory Open Access Journal |
| issn | 1802-680X 2336-1182 |
| language | English |
| last_indexed | 2024-12-17T21:18:20Z |
| publishDate | 2017-06-01 |
| publisher | University of West Bohemia |
| record_format | Article |
| series | Applied and Computational Mechanics |
| spelling | doaj.art-54d5b771865f4f80b7d83f8dfb124bbe2022-12-21T21:32:16ZengUniversity of West BohemiaApplied and Computational Mechanics1802-680X2336-11822017-06-01111819010.24132/acm.2017.322Periodic solutions of a graphene based model in micro-electro-mechanical pull-in deviceWei D.0Kadyrov S.1Kazbek Z.2Nazarbayev University, School of Science and Technology, Department of Mathematics, Astana, KazakhstanNazarbayev University, School of Science and Technology, Department of Mathematics, Astana, KazakhstanNazarbayev University, School of Science and Technology, Department of Mathematics, Astana, KazakhstanPhase plane analysis of the nonlinear spring-mass equation arising in modeling vibrations of a lumped mass attached to a graphene sheet with a fixed end is presented. The nonlinear lumped-mass model takes into account the nonlinear behavior of the graphene by including the third-order elastic stiffness constant and the nonlinear electrostatic force. Standard pull-in voltages are computed. Graphic phase diagrams are used to demonstrate the conclusions. The nonlinear wave forms and the associated resonance frequencies are computed and presented graphically to demonstrate the effects of the nonlinear stiffness constant comparing with the corresponding linear model. The existence of periodic solutions of the model is proved analytically for physically admissible periodic solutions, and conditions for bifurcation points on a parameter associated with the third-order elastic stiffness constant are determined.https://www.kme.zcu.cz/acm/acm/article/view/322/412lumped-mass modelnonlinear springgrapheneelectrostatic pull-in stabilityperiodic solutions |
| spellingShingle | Wei D. Kadyrov S. Kazbek Z. Periodic solutions of a graphene based model in micro-electro-mechanical pull-in device Applied and Computational Mechanics lumped-mass model nonlinear spring graphene electrostatic pull-in stability periodic solutions |
| title | Periodic solutions of a graphene based model in micro-electro-mechanical pull-in device |
| title_full | Periodic solutions of a graphene based model in micro-electro-mechanical pull-in device |
| title_fullStr | Periodic solutions of a graphene based model in micro-electro-mechanical pull-in device |
| title_full_unstemmed | Periodic solutions of a graphene based model in micro-electro-mechanical pull-in device |
| title_short | Periodic solutions of a graphene based model in micro-electro-mechanical pull-in device |
| title_sort | periodic solutions of a graphene based model in micro electro mechanical pull in device |
| topic | lumped-mass model nonlinear spring graphene electrostatic pull-in stability periodic solutions |
| url | https://www.kme.zcu.cz/acm/acm/article/view/322/412 |
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