Two Degree Of Freedom Vibro-impact System Of Random Response

The response of a two-degree-of-freedom vibro-impact system under stochastic excitation can be obtained by using stochastically excited and dissipated Hamiltonian system theory. First of all, the vibro-impact system is formulated as a stochastically excited and dissipated Hamiltonian system. Then the exact stationary solution of the system under certain conditions is obtained by using the exact stationary solution for stochastically excited and dissipated Hamiltonian system. After that, the approximate stationary solution of the system is obtained by using the stochastic averaging method for quasi-non-integrable Hamiltonian system when the response of the system is strongly affected by the barrier of system, or by using the stochastic averaging method for quasi-integrable Hamiltonian system when the response of the system is not strongly affected by the barrier of the system. Later on, the approximate stationary solution of the system is obtained based on the combination of the stochastic averaging methods for quasi-integrable or quasi-non-integrable Hamiltonian system and the least-square-method when the parameters of the system located between the two extreme cases. Finally, all the results obtained by using the stochastic averaging method for quasi-Hamiltonian system agree well with those obtained from digital simulation.