Nonstationary Random Vibration of a Nonlinear System with Collision

抄録

This paper deals with the response of a nonlinear system with collision subjected to a nonstationary Gaussian shot noise which is a simple model of earthquake ground accelerations. The system considered consists of an oscillator and two reflectors at both sides of it, and the oscillator collides with each reflector. The response of the system is analyzed based on Markov-vector approach. A distribution based on the Maxwell-Boltzmann distribution is proposed as an approximate solution for the unsteady Fokker-Plank equation which gives the time-dependent joint probability density function for the response displacement and the velocity. The approximate solution contains three unknown functions of time, which are determined by employing the method of weighted residuals (the method of moment). Various stochastic properties of the response are derived from the approximate joint probability density function, including the probability density functions and the second moments of the displacement and the velocity, the average number of collisions, and the probability density functions, the mean values and the probability density functions, the mean values and the standard deviations of impact velocity, impulse and impact acceleration due to collision. Experiments are also carried out to examine the analytical results, and good agreement between the analytical and the experimental results is obtained.