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Period-doubling cascade route to chaos in an initially curved microbeam resonator exposed to fringing-field electrostatic actuation
Nonlinear Dynamics, Volume: 112, Issue: 12, Pages: 9915 - 9932
Swansea University Author: Saber Azizi Azizishirvanshahi
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DOI (Published version): 10.1007/s11071-024-09575-y
Abstract
This paper explores the chaotic dynamics of a piezoelectrically laminated initially curved microbeam resonator subjected to fringing-field electrostatic actuation, for the first time. The resonator is fully clamped at both ends and is coated with two piezoelectric layers, encompassing both the top a...
| Published in: | Nonlinear Dynamics |
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| ISSN: | 0924-090X 1573-269X |
| Published: |
Springer Science and Business Media LLC
2024
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| Online Access: |
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| URI: | https://cronfa.swan.ac.uk/Record/cronfa66206 |
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| Abstract: |
This paper explores the chaotic dynamics of a piezoelectrically laminated initially curved microbeam resonator subjected to fringing-field electrostatic actuation, for the first time. The resonator is fully clamped at both ends and is coated with two piezoelectric layers, encompassing both the top and bottom surfaces. The nonlinear motion equation which is obtained by considering the nonlinear fringing-field electrostatic force, includes geometric nonlinearities due to the mid-plane stretching and initial curvature. The motion equation is discretized using Galerkin method and the reduced order system is numerically integrated over the time for the time response. The variation of the first three natural frequencies with respect to the applied electrostatic voltage is determined and the frequency response curve is obtained using the combination of shooting and continuation methods. The bifurcation points have been examined and their types have been clarified based on the loci of the Floquet exponents on the complex plane. The period-doubled branches of the frequency response curves originating from the period doubling (PD) bifurcation points are stablished. It's demonstrated that the succession PD cascades leads to chaotic behavior. The chaotic behavior is identified qualitatively by constructing the corresponding Poincaré section and analyzing the response's associated frequency components. The bifurcation diagram is obtained for a wide range of excitation frequency and thus the exact range in which chaotic behavior occurs for the system is determined. The chaotic response of the system is regularized and controlled by applying an appropriate piezoelectric voltage which shifts the frequency response curve along the frequency axis. |
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| Keywords: |
Chaotic dynamics; Period-doubling bifurcation; MEMS resonators; Initially curved;microbeam; Piezoelectric actuation; Fringing-field; electrostatic actuation |
| College: |
Faculty of Science and Engineering |
| Funders: |
Swansea University |
| Issue: |
12 |
| Start Page: |
9915 |
| End Page: |
9932 |