Non-linear dynamic response of a rotating thin-walled composite beam
The nonlinear planar response of a cantilever rota ting slender beam to a principal parametric resonance of its first bending mode is analyzed. The equation of motion is obtained in the form of an integro-partial differential equation, taking into account mid-plane stretching, a rotation speed and m...
| Autores: | , |
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| Tipo de recurso: | artículo |
| Estado: | Versión publicada |
| Fecha de publicación: | 2010 |
| País: | Argentina |
| Institución: | Consejo Nacional de Investigaciones Científicas y Técnicas |
| Repositorio: | CONICET Digital (CONICET) |
| Idioma: | inglés |
| OAI Identifier: | oai:ri.conicet.gov.ar:11336/68294 |
| Acceso en línea: | http://hdl.handle.net/11336/68294 |
| Access Level: | acceso abierto |
| Palabra clave: | COMPOSITE MATERIAL THIN-WALLED ROTATING BEAM NON-LINEAR DYNAMIC https://purl.org/becyt/ford/2.3 https://purl.org/becyt/ford/2 |
| Sumario: | The nonlinear planar response of a cantilever rota ting slender beam to a principal parametric resonance of its first bending mode is analyzed. The equation of motion is obtained in the form of an integro-partial differential equation, taking into account mid-plane stretching, a rotation speed and modal damping. A composite linear elastic material is considered and the cross-section properties are assumed to be constant given the assumption of sma ll strains. The beam is subjected to a harmonic transverse load in the presence of in ternal resonance. The internal resonance can be activated for a range of the beam rotating speed, where the second natural frequency is approximately three times the first natural frequency. The method of multiple scales method is used to derive four-first ordinary differential equations that govern the evolution of the amplitude and phase of the response. These equations are used to determine the steady stat e responses and their stability. Amplitude and phase modulation equations as well as external force–r esponse and frequency–response curves are obtained. Numerical simulations show a complex dynamic scenario and detect chaos and unbounded motions in the instability regions of the periodic solutions. |
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