Escape dynamics of a particle from a purely nonlinear truncated quartic potential well under harmonic excitation
Abstract This paper focuses on the escape problem of a harmonically forced classical particle from a purely quartic truncated potential well. The latter corresponds to various engineering systems that involve purely cubic restoring force and absence of linear stiffness even under the...
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| Format: | Article |
| Language: | English |
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Springer Netherlands
2023
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| Online Access: | https://hdl.handle.net/1721.1/147580 |
| _version_ | 1811081660213493760 |
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| author | Farid, Maor |
| author2 | Massachusetts Institute of Technology. Department of Mechanical Engineering |
| author_facet | Massachusetts Institute of Technology. Department of Mechanical Engineering Farid, Maor |
| author_sort | Farid, Maor |
| collection | MIT |
| description | Abstract
This paper focuses on the escape problem of a harmonically forced classical particle from a purely quartic truncated potential well. The latter corresponds to various engineering systems that involve purely cubic restoring force and absence of linear stiffness even under the assumption of small oscillations, such as pre-tensioned metal wires and springs, and compliant structural components made of polymer materials. This is in contrast to previous studies where the equivalent potential well could be treated as linear at first approximation under the assumption of small perturbations. Due to the strong nonlinearity of the current potential well, traditional analytical methods are inapplicable for describing the transient bounded and escape dynamics of the particle. The latter is analyzed in the framework of isolated resonance approximation by canonical transformation to action–angle variables and the corresponding reduced resonance manifold. The escape envelope is formulated analytically. Surprisingly, despite the essential nonlinearity of the well investigated, it exhibits a universal property of a sharp minimum due to the existence of multiple intersecting escape mechanisms. Unlike previous studies, three underlying mechanisms that govern the transient dynamics of the particle were identified: two maximum mechanisms and a saddle mechanism. The first two correspond to a gradual increase in the system’s response amplitude for a proportional increase in the excitation intensity, and the latter corresponds to an abrupt increase in the system’s response and therefore more potentially hazardous. The response of the particle is described in terms of energy-based response curves. The maximal transient energy is predicted analytically over the space of excitation parameters and described using iso-energy contours. All theoretical predictions are in complete agreement with numerical results. |
| first_indexed | 2024-09-23T11:50:22Z |
| format | Article |
| id | mit-1721.1/147580 |
| institution | Massachusetts Institute of Technology |
| language | English |
| last_indexed | 2024-09-23T11:50:22Z |
| publishDate | 2023 |
| publisher | Springer Netherlands |
| record_format | dspace |
| spelling | mit-1721.1/1475802024-01-11T21:06:55Z Escape dynamics of a particle from a purely nonlinear truncated quartic potential well under harmonic excitation Farid, Maor Massachusetts Institute of Technology. Department of Mechanical Engineering Abstract This paper focuses on the escape problem of a harmonically forced classical particle from a purely quartic truncated potential well. The latter corresponds to various engineering systems that involve purely cubic restoring force and absence of linear stiffness even under the assumption of small oscillations, such as pre-tensioned metal wires and springs, and compliant structural components made of polymer materials. This is in contrast to previous studies where the equivalent potential well could be treated as linear at first approximation under the assumption of small perturbations. Due to the strong nonlinearity of the current potential well, traditional analytical methods are inapplicable for describing the transient bounded and escape dynamics of the particle. The latter is analyzed in the framework of isolated resonance approximation by canonical transformation to action–angle variables and the corresponding reduced resonance manifold. The escape envelope is formulated analytically. Surprisingly, despite the essential nonlinearity of the well investigated, it exhibits a universal property of a sharp minimum due to the existence of multiple intersecting escape mechanisms. Unlike previous studies, three underlying mechanisms that govern the transient dynamics of the particle were identified: two maximum mechanisms and a saddle mechanism. The first two correspond to a gradual increase in the system’s response amplitude for a proportional increase in the excitation intensity, and the latter corresponds to an abrupt increase in the system’s response and therefore more potentially hazardous. The response of the particle is described in terms of energy-based response curves. The maximal transient energy is predicted analytically over the space of excitation parameters and described using iso-energy contours. All theoretical predictions are in complete agreement with numerical results. 2023-01-20T13:02:27Z 2023-01-20T13:02:27Z 2022-11-01 2023-01-20T04:37:52Z Article http://purl.org/eprint/type/JournalArticle https://hdl.handle.net/1721.1/147580 Farid, Maor. 2022. "Escape dynamics of a particle from a purely nonlinear truncated quartic potential well under harmonic excitation." en https://doi.org/10.1007/s11071-022-07976-5 Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use. The Author(s), under exclusive licence to Springer Nature B.V. application/pdf Springer Netherlands Springer Netherlands |
| spellingShingle | Farid, Maor Escape dynamics of a particle from a purely nonlinear truncated quartic potential well under harmonic excitation |
| title | Escape dynamics of a particle from a purely nonlinear truncated quartic potential well under harmonic excitation |
| title_full | Escape dynamics of a particle from a purely nonlinear truncated quartic potential well under harmonic excitation |
| title_fullStr | Escape dynamics of a particle from a purely nonlinear truncated quartic potential well under harmonic excitation |
| title_full_unstemmed | Escape dynamics of a particle from a purely nonlinear truncated quartic potential well under harmonic excitation |
| title_short | Escape dynamics of a particle from a purely nonlinear truncated quartic potential well under harmonic excitation |
| title_sort | escape dynamics of a particle from a purely nonlinear truncated quartic potential well under harmonic excitation |
| url | https://hdl.handle.net/1721.1/147580 |
| work_keys_str_mv | AT faridmaor escapedynamicsofaparticlefromapurelynonlineartruncatedquarticpotentialwellunderharmonicexcitation |