参激屈曲梁非线性现象的数值模拟

Numerical Simulations on the Nonlinear Phenomena of a Parametrically Excited Buckled Beam

研究了一端固定一端滑动承受轴向简谐载荷的屈曲梁的非线性振动现象,建立了系统的非线性偏微分控制方程,利用Galerkin法,得到微分动力系统,采用数值模拟研究了系统基本参数共振和主参数共振的两种情况,得到了响应的时间历程及相图,揭示了系统的倍周期分岔、暂态混沌和混沌运动等复杂动力学行为.

Nonlinear vibration responses of a cantilevered sliding buckled beam to a harmonic axial excitation are studied and nonlinear partial differential governing equations of the system are built. Galerkin method is employed to set up the differential dynamic system. By use of numerical simulations, fundamental parametric resonance and principle parametric resonance are studied. Some typical time histories, phase diagrams are obtained and the system＇s complicated dynamic behaviors, such as period doubling bifurcations, transient chaos and chaos are observed.