Nonlinear stochastic dynamics of an array of coupled micromechanical oscillators
Abstract The stochastic response of a multi‐degree‐of‐freedom nonlinear dynamical system is determined based on the recently developed Wiener path integral (WPI) technique. The system can be construed as a representative model of electrostatically coupled arrays of micromechanical oscillators, and r...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Wiley
2023-03-01
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| Series: | International Journal of Mechanical System Dynamics |
| Subjects: | |
| Online Access: | https://doi.org/10.1002/msd2.12066 |
| _version_ | 1797858995667468288 |
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| author | Maria I. Katsidoniotaki Ioannis Petromichelakis Ioannis A. Kougioumtzoglou |
| author_facet | Maria I. Katsidoniotaki Ioannis Petromichelakis Ioannis A. Kougioumtzoglou |
| author_sort | Maria I. Katsidoniotaki |
| collection | DOAJ |
| description | Abstract The stochastic response of a multi‐degree‐of‐freedom nonlinear dynamical system is determined based on the recently developed Wiener path integral (WPI) technique. The system can be construed as a representative model of electrostatically coupled arrays of micromechanical oscillators, and relates to an experiment performed by Buks and Roukes. Compared to alternative modeling and solution treatments in the literature, the paper exhibits the following novelties. First, typically adopted linear, or higher‐order polynomial, approximations of the nonlinear electrostatic forces are circumvented. Second, for the first time, stochastic modeling is employed by considering a random excitation component representing the effect of diverse noise sources on the system dynamics. Third, the resulting high‐dimensional, nonlinear system of coupled stochastic differential equations governing the dynamics of the micromechanical array is solved based on the WPI technique for determining the response joint probability density function. Comparisons with pertinent Monte Carlo simulation data demonstrate a quite high degree of accuracy and computational efficiency exhibited by the WPI technique. Further, it is shown that the proposed model can capture, at least in a qualitative manner, the salient aspects of the frequency domain response of the associated experimental setup. |
| first_indexed | 2024-04-09T21:23:27Z |
| format | Article |
| id | doaj.art-163b4dca7e9743849906f33056bc04aa |
| institution | Directory Open Access Journal |
| issn | 2767-1402 |
| language | English |
| last_indexed | 2024-04-09T21:23:27Z |
| publishDate | 2023-03-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mechanical System Dynamics |
| spelling | doaj.art-163b4dca7e9743849906f33056bc04aa2023-03-28T02:41:26ZengWileyInternational Journal of Mechanical System Dynamics2767-14022023-03-013131110.1002/msd2.12066Nonlinear stochastic dynamics of an array of coupled micromechanical oscillatorsMaria I. Katsidoniotaki0Ioannis Petromichelakis1Ioannis A. Kougioumtzoglou2Department of Civil Engineering and Engineering Mechanics Columbia University New York New York USADepartment of Civil Engineering and Engineering Mechanics Columbia University New York New York USADepartment of Civil Engineering and Engineering Mechanics Columbia University New York New York USAAbstract The stochastic response of a multi‐degree‐of‐freedom nonlinear dynamical system is determined based on the recently developed Wiener path integral (WPI) technique. The system can be construed as a representative model of electrostatically coupled arrays of micromechanical oscillators, and relates to an experiment performed by Buks and Roukes. Compared to alternative modeling and solution treatments in the literature, the paper exhibits the following novelties. First, typically adopted linear, or higher‐order polynomial, approximations of the nonlinear electrostatic forces are circumvented. Second, for the first time, stochastic modeling is employed by considering a random excitation component representing the effect of diverse noise sources on the system dynamics. Third, the resulting high‐dimensional, nonlinear system of coupled stochastic differential equations governing the dynamics of the micromechanical array is solved based on the WPI technique for determining the response joint probability density function. Comparisons with pertinent Monte Carlo simulation data demonstrate a quite high degree of accuracy and computational efficiency exhibited by the WPI technique. Further, it is shown that the proposed model can capture, at least in a qualitative manner, the salient aspects of the frequency domain response of the associated experimental setup.https://doi.org/10.1002/msd2.12066Wiener path integralnonlinear systemstochastic dynamicsnanomechanics |
| spellingShingle | Maria I. Katsidoniotaki Ioannis Petromichelakis Ioannis A. Kougioumtzoglou Nonlinear stochastic dynamics of an array of coupled micromechanical oscillators International Journal of Mechanical System Dynamics Wiener path integral nonlinear system stochastic dynamics nanomechanics |
| title | Nonlinear stochastic dynamics of an array of coupled micromechanical oscillators |
| title_full | Nonlinear stochastic dynamics of an array of coupled micromechanical oscillators |
| title_fullStr | Nonlinear stochastic dynamics of an array of coupled micromechanical oscillators |
| title_full_unstemmed | Nonlinear stochastic dynamics of an array of coupled micromechanical oscillators |
| title_short | Nonlinear stochastic dynamics of an array of coupled micromechanical oscillators |
| title_sort | nonlinear stochastic dynamics of an array of coupled micromechanical oscillators |
| topic | Wiener path integral nonlinear system stochastic dynamics nanomechanics |
| url | https://doi.org/10.1002/msd2.12066 |
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