以基础受简谐激励的含端部集中质量柔性梁与双侧刚性约束边界的碰撞振动系统为研究对象,利用Galerkin方法和Lagrange方法建立含三次非线性项的系统自由运动微分方程,采用Newton碰撞定律建立碰撞方程,用数值方法分析了不同的激励频率或幅值,不同的约束间隔等参数对系统碰撞振动长期响应的影响,并通过Poincaré截面揭示了系统动力学行为的演变过程.结果表明,系统长期响应的性质取决于上述参数的联合作用.在所分析的激励参数边界范围内,系统存在一系列的周期运动经多次倍周期分叉直至混沌的演化过程及其逆过程.%This paper presents a dynamic analysis of vibro-impacts of a slender cantilever beam carrying a lumped tipmass between two rigid stops subjected to horizontal harmonic excitation of basement. This vibro-impacting system is a simplified model for the vibro-impacts between the shell of a flying vehicle and its interior components.The dynamic equation of vibro-impacting system is established on the basis of the Galerkin method, the Lagrange method and the Newton rule of collision. The effects of excitation frequency, excitation amplitude and the clearance between the tip mass and a stop on system dynamics are numerically investigated. The nonlinear dynamics, especially various chaotic motions, are observed by using the Poincare section. Numerical results show that the longterm behavior of system mainly depends on the above three parameters, and there exist a series of processes and corresponding reverse processes, during which a periodic motion undergoes period-doubling bifurcation and then becomes chaotic motion, or vice versa.
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机译：以基础受简谐激励的含端部集中质量柔性梁与双侧刚性约束边界的碰撞振动系统为研究对象,利用Galerkin方法和Lagrange方法建立含三次非线性项的系统自由运动微分方程,采用Newton碰撞定律建立碰撞方程,用数值方法分析了不同的激励频率或幅值,不同的约束间隔等参数对系统碰撞振动长期响应的影响,并通过Poincaré截面揭示了系统动力学行为的演变过程.结果表明,系统长期响应的性质取决于上述参数的联合作用.在所分析的激励参数边界范围内,系统存在一系列的周期运动经多次倍周期分叉直至混沌的演化过程及其逆过程.%This paper presents a dynamic analysis of vibro-impacts of a slender cantilever beam carrying a lumped tipmass between two rigid stops subjected to horizontal harmonic excitation of basement. This vibro-impacting system is a simplified model for the vibro-impacts between the shell of a flying vehicle and its interior components.The dynamic equation of vibro-impacting system is established on the basis of the Galerkin method, the Lagrange method and the Newton rule of collision. The effects of excitation frequency, excitation amplitude and the clearance between the tip mass and a stop on system dynamics are numerically investigated. The nonlinear dynamics, especially various chaotic motions, are observed by using the Poincare section. Numerical results show that the longterm behavior of system mainly depends on the above three parameters, and there exist a series of processes and corresponding reverse processes, during which a periodic motion undergoes period-doubling bifurcation and then becomes chaotic motion, or vice versa.
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