Rocking Vibration of Rigid Block Under Horizontal Harmonic Excitation With Noise

Abstract

This study deals with the rocking behavior of a rigid block subjected to horizontal harmonic excitations with minute fluctuation. Nonlinear rocking behaviors may be often accompanied by minute changes of rocking system parameters, such as friction and restitution coefficients, depending on contact conditions between the block and the base. In this paper, the minute fluctuation of excitation amplitude is imitated by random numbers with normal probability distribution and the fluctuation range is adjusted by their standard deviation. Analytical results in our previous studies have shown that rocking responses are very sensitive to small changes of friction coefficients and noise included in the excitation and the distribution of rocking response is greatly affected by the effects. Nonrecurring rocking responses observed in our previous experimental works have been reproduced by simulation considering minute fluctuation of excitation amplitude. Minute changes of excitation amplitude make the rocking response unstable and aperiodic, and distribution of rocking responses is also massively changed by adding the excitation noise.