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Dynamics of a non-linearly damped microresonator under parametric excitation and its application in developing sensitive inertial sensors with ultra-wide dynamic ranges

S. Amir Mousavi Lajimi, Michael Friswell

International Journal of Non-Linear Mechanics, Volume: 123, Start page: 103491

Swansea University Author: Michael Friswell

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DOI (Published version): 10.1016/j.ijnonlinmec.2020.103491

Abstract

We model and investigate the response of a nonlinear cantilever beam under principal parametric excitation. The design is initially assessed, optimized, and tuned using three-dimensional finite element analysis (FEA) to ensure the presence of fundamental parametric resonance and the absence of other...

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Published in: International Journal of Non-Linear Mechanics
ISSN: 0020-7462
Published: Elsevier BV 2020
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URI: https://cronfa.swan.ac.uk/Record/cronfa54221
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spelling 2022-11-15T16:12:11.9652212 v2 54221 2020-05-14 Dynamics of a non-linearly damped microresonator under parametric excitation and its application in developing sensitive inertial sensors with ultra-wide dynamic ranges 5894777b8f9c6e64bde3568d68078d40 Michael Friswell Michael Friswell true false 2020-05-14 FGSEN We model and investigate the response of a nonlinear cantilever beam under principal parametric excitation. The design is initially assessed, optimized, and tuned using three-dimensional finite element analysis (FEA) to ensure the presence of fundamental parametric resonance and the absence of other internal and higher-order parametric resonances. The derived governing differential equation represents a modified generalized parametrically excited dynamic system under principal parametric excitation. The nonlinear dynamic system is developed and presented in the context of resonators with extensive applications in developing sensors, filters, and switches. The quadratic and cubic nonlinearities include second- and third-order deflection, velocity, acceleration terms describing stiffness, damping, and inertial nonlinearities. To explore and investigate the corresponding generalized nonlinear Mathieu equation, the method of multiple-scales along with the reconstitution method are used and modulation equations are obtained and solved to obtain closed-form amplitude and phase equations. The quadratic damping is modeled and approximated using a Fourier series and analytical models are generated in both Cartesian and Polar frames. To further explore the dynamic system and its applications, a resonator is designed to measure external acceleration and investigated for two cases. It is discussed and shown how the external acceleration modifies the dynamic system, the corresponding reduced-order model, and the modulation equations. The external acceleration affects the amplitude, phase, and frequency of oscillation providing means to estimate the input. These results indicate that the proposed resonator design (dynamic system) is able to significantly improve the dynamic range of shock/acceleration sensors. Journal Article International Journal of Non-Linear Mechanics 123 103491 Elsevier BV 0020-7462 Generalized parametric resonance, Nonlinear dynamic, Quadratic damping, Inertial and stiffness nonlinearity, Bifurcation, Sensors, FEA 1 7 2020 2020-07-01 10.1016/j.ijnonlinmec.2020.103491 COLLEGE NANME Science and Engineering - Faculty COLLEGE CODE FGSEN Swansea University 2022-11-15T16:12:11.9652212 2020-05-14T13:29:20.8982121 Faculty of Science and Engineering School of Engineering and Applied Sciences - Uncategorised S. Amir Mousavi Lajimi 1 Michael Friswell 2 54221__17235__fad7cdef323f46759174748683230339.pdf 54221.pdf 2020-05-14T16:21:27.5268174 Output 990648 application/pdf Accepted Manuscript true 2021-04-23T00:00:00.0000000 © 2020. This manuscript version is made available under the CC-BY-NC-ND 4.0 license. true English http://creativecommons.org/licenses/by-nc-nd/4.0/
title Dynamics of a non-linearly damped microresonator under parametric excitation and its application in developing sensitive inertial sensors with ultra-wide dynamic ranges
spellingShingle Dynamics of a non-linearly damped microresonator under parametric excitation and its application in developing sensitive inertial sensors with ultra-wide dynamic ranges
Michael Friswell
title_short Dynamics of a non-linearly damped microresonator under parametric excitation and its application in developing sensitive inertial sensors with ultra-wide dynamic ranges
title_full Dynamics of a non-linearly damped microresonator under parametric excitation and its application in developing sensitive inertial sensors with ultra-wide dynamic ranges
title_fullStr Dynamics of a non-linearly damped microresonator under parametric excitation and its application in developing sensitive inertial sensors with ultra-wide dynamic ranges
title_full_unstemmed Dynamics of a non-linearly damped microresonator under parametric excitation and its application in developing sensitive inertial sensors with ultra-wide dynamic ranges
title_sort Dynamics of a non-linearly damped microresonator under parametric excitation and its application in developing sensitive inertial sensors with ultra-wide dynamic ranges
author_id_str_mv 5894777b8f9c6e64bde3568d68078d40
author_id_fullname_str_mv 5894777b8f9c6e64bde3568d68078d40_***_Michael Friswell
author Michael Friswell
author2 S. Amir Mousavi Lajimi
Michael Friswell
format Journal article
container_title International Journal of Non-Linear Mechanics
container_volume 123
container_start_page 103491
publishDate 2020
institution Swansea University
issn 0020-7462
doi_str_mv 10.1016/j.ijnonlinmec.2020.103491
publisher Elsevier BV
college_str Faculty of Science and Engineering
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hierarchy_top_title Faculty of Science and Engineering
hierarchy_parent_id facultyofscienceandengineering
hierarchy_parent_title Faculty of Science and Engineering
department_str School of Engineering and Applied Sciences - Uncategorised{{{_:::_}}}Faculty of Science and Engineering{{{_:::_}}}School of Engineering and Applied Sciences - Uncategorised
document_store_str 1
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description We model and investigate the response of a nonlinear cantilever beam under principal parametric excitation. The design is initially assessed, optimized, and tuned using three-dimensional finite element analysis (FEA) to ensure the presence of fundamental parametric resonance and the absence of other internal and higher-order parametric resonances. The derived governing differential equation represents a modified generalized parametrically excited dynamic system under principal parametric excitation. The nonlinear dynamic system is developed and presented in the context of resonators with extensive applications in developing sensors, filters, and switches. The quadratic and cubic nonlinearities include second- and third-order deflection, velocity, acceleration terms describing stiffness, damping, and inertial nonlinearities. To explore and investigate the corresponding generalized nonlinear Mathieu equation, the method of multiple-scales along with the reconstitution method are used and modulation equations are obtained and solved to obtain closed-form amplitude and phase equations. The quadratic damping is modeled and approximated using a Fourier series and analytical models are generated in both Cartesian and Polar frames. To further explore the dynamic system and its applications, a resonator is designed to measure external acceleration and investigated for two cases. It is discussed and shown how the external acceleration modifies the dynamic system, the corresponding reduced-order model, and the modulation equations. The external acceleration affects the amplitude, phase, and frequency of oscillation providing means to estimate the input. These results indicate that the proposed resonator design (dynamic system) is able to significantly improve the dynamic range of shock/acceleration sensors.
published_date 2020-07-01T04:07:37Z
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