SUBHARMONIC RESPONSE OF A QUASI-ISOCHRONOUS VIBROIMPACT SYSTEM TO A RANDOMLY DISORDERED PERIODIC EXCITATION

A quasi-isochronous vibroimpact system is considered, i.e. a linear sy stem with a rigid one-sided barrier, which is slightly offset from the system's static equilibrium position. The system is excited by a sinu soidal force with disorder, or random phase modulation. The mean excit ation frequency corresponds to a simple or subharmonic resonance, i.e. the value of its ratio to the natural frequency of the system without a barrier is close to some even integer. Influence of white-noise flu ctuations of the instantaneous excitation frequency around its mean on the response is studied in this paper. The analysis is based on a spe cial Zhuravlev transformation, which reduces the system to one without impacts, or velocity jumps, thereby permitting the application of asy mptotic averaging over the period for slowly varying inphase and quadr ature responses. The averaged stochastic equations are solved exactly by the method of moments for the mean square response amplitude for th e case of zero offset. A perturbation-based moment closure scheme is p roposed for the case of nonzero offset and small random variations of amplitude. Therefore, the analytical results may be expected to be ade quate for small values of excitation/system bandwidth ratio or for sma ll intensities of the excitation frequency variations. However, at ver y large values of the parameter the results are approaching those pred icted by a stochastic averaging method. Moreover, Monte-Carlo simulati on has shown the moment closure results to be sufficiently accurate in general for any arbitrary bandwidth ratio. The basic conclusion, both of analytical and numerical simulation studies, is a sort of 'smearin g' of the amplitude frequency response curves owing to disorder, or ra ndom phase modulation: peak amplitudes may be strongly reduced, wherea s somewhat increased response may be expected at large detunings, wher e response amplitudes to perfectly periodic excitation are relatively small.