Wave displacement of rigid bodies and particles

The displacement of various particles and mechanical systems by waves finds wide use in technical devices, technological processes, takes place in non living and living nature. Here the system displaced by waves with four degrees of freedom is analyzed when one member of the system, while contacting with the working profile of the input member performing wave motion, provides motion to the output system. The obtained differential equations of motion of the system have been analyzed analytically and numerically. For the analytical investigation modification of the asymptotic method is used, which is based on the division of motion into the slow and quick motions. This method is justified when the frequencies of variation of slow motions are much smaller than the frequencies of quick motions. When the working surface of the input member moves according to the harmonic Rayleigh waves more detailed full investigations have been performed. The characteristics of transition to steady state and of stationary regimes of motions have been obtained, such as the conditions of existence and stability of the stationary regimes, curves of bifurcation, existing complicated motions.