This paper presents a dynamic analysis of vibro impacts of a slender cantilever beam carrying a lumped tip mass between two rigid stops subjected to horizontal harmonic excitation of basement. This vibro impacting s...This paper presents a dynamic analysis of vibro impacts of a slender cantilever beam carrying a lumped tip mass 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 Poincaré 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.展开更多
文摘This paper presents a dynamic analysis of vibro impacts of a slender cantilever beam carrying a lumped tip mass 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 Poincaré 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.
