Multi-pulse chaotic dynamics with energy phase method in motion of viscoelastic moving beam

作者：Yao Ming Hui^*; Zhang Wei; Cao Dong Xing; Fan Jin Hong

来源：Journal of Beijing University of Technology, 2009, 35(SUPPL.): 32-37.

• Chaotic dynamics
• Chaotic motions
• Constitutive law
• Explicit formula
• Galerkin
• Global bifurcations
• Hamilton principle
• Internal resonance
• Jumping orbits
• Method of multiple scale
• Moving beam
• Multi-pulse orbit
• Multi-pulse orbits
• Multipulse
• Normal form
• Numerical simulation
• Parametric excitations
• Parametric resonance
• Partial differential
• Phase methods
• Planar motion
• Qualitative analysis
• Smale horseshoe
• The energy phase method
• Viscoelastic moving beam

The purpose of this paper is the multi-pulse orbits and chaotic dynamics of a parametrically excited viscoelastic moving beam studied in detail. Viscoelastic moving beam is widely used in engineering. Linear external damping and inner damping of materials are considered. Using integral viscoelastic constitutive law and Hamilton principle, the equation of planar motion for viscoelastic moving beam with the external damping and parametric excitation are determined. The four-dimensional averaged equation under the case of 1:2 internal resonance and primary parametric resonance is obtained by directly using the method of multiple scales and Galerkin';s approach to the partial differential governing equation of motion for viscoelastic moving beam. The system is transformed to the averaged equation. From the averaged equation, the theory of normal form is used to find the explicit formulas of normal form. Based on normal form obtained, the energy phase method is utilized to analyze the multi-pulse global bifurcations and chaotic dynamics for a parametrically excited viscoelastic moving beam. The results of theoretically qualitative analysis indicate the existence of the chaos for the Smale horseshoe sense for a parametrically excited viscoelastic moving beam. From the averaged equations obtained, the chaotic motions and the Shilnikov type multi-pulse orbits of viscoelastic moving beam are found by using numerical simulation. Through theoretical analysis and numerical simulation, we have drawn conclusions that there exist the different Shilnikov type multi-pulse jumping orbits in the motion of a parametrically excited viscoelastic moving beam.

• 出版日期2009
• 单位北京大学