Investigation of Subcombination Internal Resonances in Cantilever Beams
Activation of subcombination internal resonances in transversely excited cantilever beams is investigated. The effect of geometric and inertia nonlinearities, which are cubic in the governing equation of motion, is considered. The method of time-averaged Lagrangian and virtual work is used to determ...
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| Format: | Article |
| Language: | English |
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Wiley
1998-01-01
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| Series: | Shock and Vibration |
| Online Access: | http://dx.doi.org/10.1155/1998/649527 |
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| _version_ | 1832565382058082304 |
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| author | Haider N. Arafat Ali H. Nayfeh |
| author_facet | Haider N. Arafat Ali H. Nayfeh |
| author_sort | Haider N. Arafat |
| collection | DOAJ |
| description | Activation of subcombination internal resonances in transversely excited cantilever beams is investigated. The effect of geometric and inertia nonlinearities, which are cubic in the governing equation of motion, is considered. The method of time-averaged Lagrangian and virtual work is used to determine six nonlinear ordinary-differential equations governing the amplitudes and phases of the three interacting modes. Frequency- and force-response curves are generated for the case ω ≈ ω4 ≈ 1/2(ω2 + ω5). There are two possible responses: single-mode and three-mode responses. The single-mode periodic response is found to undergo supercritical and subcritical pitchfork bifurcations, which result in three-mode interactions. In the case of three-mode responses, there are conditions where the low-frequency mode dominates the response, resulting in high-amplitude quasiperiodic oscillations. |
| format | Article |
| id | doaj-art-5d2be901b8234159953c5a98b1f4d92e |
| institution | Kabale University |
| issn | 1070-9622 1875-9203 |
| language | English |
| publishDate | 1998-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Shock and Vibration |
| spelling | doaj-art-5d2be901b8234159953c5a98b1f4d92e2025-02-03T01:07:51ZengWileyShock and Vibration1070-96221875-92031998-01-0155-628929610.1155/1998/649527Investigation of Subcombination Internal Resonances in Cantilever BeamsHaider N. Arafat0Ali H. Nayfeh1Department of Engineering Science and Mechanics, MC 0219, Virginia Polytechnic Institute and State University, Blacksburg, VA 24061, USADepartment of Engineering Science and Mechanics, MC 0219, Virginia Polytechnic Institute and State University, Blacksburg, VA 24061, USAActivation of subcombination internal resonances in transversely excited cantilever beams is investigated. The effect of geometric and inertia nonlinearities, which are cubic in the governing equation of motion, is considered. The method of time-averaged Lagrangian and virtual work is used to determine six nonlinear ordinary-differential equations governing the amplitudes and phases of the three interacting modes. Frequency- and force-response curves are generated for the case ω ≈ ω4 ≈ 1/2(ω2 + ω5). There are two possible responses: single-mode and three-mode responses. The single-mode periodic response is found to undergo supercritical and subcritical pitchfork bifurcations, which result in three-mode interactions. In the case of three-mode responses, there are conditions where the low-frequency mode dominates the response, resulting in high-amplitude quasiperiodic oscillations.http://dx.doi.org/10.1155/1998/649527 |
| spellingShingle | Haider N. Arafat Ali H. Nayfeh Investigation of Subcombination Internal Resonances in Cantilever Beams Shock and Vibration |
| title | Investigation of Subcombination Internal Resonances in Cantilever Beams |
| title_full | Investigation of Subcombination Internal Resonances in Cantilever Beams |
| title_fullStr | Investigation of Subcombination Internal Resonances in Cantilever Beams |
| title_full_unstemmed | Investigation of Subcombination Internal Resonances in Cantilever Beams |
| title_short | Investigation of Subcombination Internal Resonances in Cantilever Beams |
| title_sort | investigation of subcombination internal resonances in cantilever beams |
| url | http://dx.doi.org/10.1155/1998/649527 |
| work_keys_str_mv | AT haidernarafat investigationofsubcombinationinternalresonancesincantileverbeams AT alihnayfeh investigationofsubcombinationinternalresonancesincantileverbeams |