Supercritical Nonlinear Vibration of a Fluid-Conveying Pipe Subjected to a Strong External Excitation
Nonlinear vibration of a fluid-conveying pipe subjected to a transverse external harmonic excitation is investigated in the case with two-to-one internal resonance. The excitation amplitude is in the same magnitude of the transverse displacement. The fluid in the pipes flows in the speed larger than...
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| Format: | Article |
| Language: | English |
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Wiley
2016-01-01
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| Series: | Shock and Vibration |
| Online Access: | http://dx.doi.org/10.1155/2016/3907498 |
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| _version_ | 1832559401869770752 |
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| author | Yan-Lei Zhang Hui-Rong Feng Li-Qun Chen |
| author_facet | Yan-Lei Zhang Hui-Rong Feng Li-Qun Chen |
| author_sort | Yan-Lei Zhang |
| collection | DOAJ |
| description | Nonlinear vibration of a fluid-conveying pipe subjected to a transverse external harmonic excitation is investigated in the case with two-to-one internal resonance. The excitation amplitude is in the same magnitude of the transverse displacement. The fluid in the pipes flows in the speed larger than the critical speed so that the straight configuration becomes an unstable equilibrium and two curved configurations bifurcate as stable equilibriums. The motion measured from each of curved equilibrium configurations is governed by a nonlinear integro-partial-differential equation with variable coefficients. The Galerkin method is employed to discretize the governing equation into a gyroscopic system consisting of a set of coupled nonlinear ordinary differential equations. The method of multiple scales is applied to analyze approximately the gyroscopic system. A set of first-order ordinary differential equations governing the modulations of the amplitude and the phase are derived via the method. In the supercritical regime, the subharmonic, superharmonic, and combination resonances are examined in the presence of the 2 : 1 internal resonance. The steady-state responses and their stabilities are determined. The various jump phenomena in the amplitude-frequency response curves are demonstrated. The effects of the viscosity, the excitation amplitude, the nonlinearity, and the flow speed are observed. The analytical results are supported by the numerical integration. |
| format | Article |
| id | doaj-art-2621907d7eec4a6cb0885a4f1f490f5b |
| institution | Kabale University |
| issn | 1070-9622 1875-9203 |
| language | English |
| publishDate | 2016-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Shock and Vibration |
| spelling | doaj-art-2621907d7eec4a6cb0885a4f1f490f5b2025-02-03T01:30:10ZengWileyShock and Vibration1070-96221875-92032016-01-01201610.1155/2016/39074983907498Supercritical Nonlinear Vibration of a Fluid-Conveying Pipe Subjected to a Strong External ExcitationYan-Lei Zhang0Hui-Rong Feng1Li-Qun Chen2College of Engineering, Shanghai Second Polytechnic University, Shanghai 201209, ChinaCollege of Transportation and Civil Engineering, Fujian Agriculture and Forestry University, Fuzhou, Fujian 350002, ChinaDepartment of Mechanics, Shanghai University, Shanghai 200444, ChinaNonlinear vibration of a fluid-conveying pipe subjected to a transverse external harmonic excitation is investigated in the case with two-to-one internal resonance. The excitation amplitude is in the same magnitude of the transverse displacement. The fluid in the pipes flows in the speed larger than the critical speed so that the straight configuration becomes an unstable equilibrium and two curved configurations bifurcate as stable equilibriums. The motion measured from each of curved equilibrium configurations is governed by a nonlinear integro-partial-differential equation with variable coefficients. The Galerkin method is employed to discretize the governing equation into a gyroscopic system consisting of a set of coupled nonlinear ordinary differential equations. The method of multiple scales is applied to analyze approximately the gyroscopic system. A set of first-order ordinary differential equations governing the modulations of the amplitude and the phase are derived via the method. In the supercritical regime, the subharmonic, superharmonic, and combination resonances are examined in the presence of the 2 : 1 internal resonance. The steady-state responses and their stabilities are determined. The various jump phenomena in the amplitude-frequency response curves are demonstrated. The effects of the viscosity, the excitation amplitude, the nonlinearity, and the flow speed are observed. The analytical results are supported by the numerical integration.http://dx.doi.org/10.1155/2016/3907498 |
| spellingShingle | Yan-Lei Zhang Hui-Rong Feng Li-Qun Chen Supercritical Nonlinear Vibration of a Fluid-Conveying Pipe Subjected to a Strong External Excitation Shock and Vibration |
| title | Supercritical Nonlinear Vibration of a Fluid-Conveying Pipe Subjected to a Strong External Excitation |
| title_full | Supercritical Nonlinear Vibration of a Fluid-Conveying Pipe Subjected to a Strong External Excitation |
| title_fullStr | Supercritical Nonlinear Vibration of a Fluid-Conveying Pipe Subjected to a Strong External Excitation |
| title_full_unstemmed | Supercritical Nonlinear Vibration of a Fluid-Conveying Pipe Subjected to a Strong External Excitation |
| title_short | Supercritical Nonlinear Vibration of a Fluid-Conveying Pipe Subjected to a Strong External Excitation |
| title_sort | supercritical nonlinear vibration of a fluid conveying pipe subjected to a strong external excitation |
| url | http://dx.doi.org/10.1155/2016/3907498 |
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