Non-trivial effect of fast vibration on the dynamics of a class of non-linearly damped mechanical systems

The effect of very high-frequency excitation on the slow dynamics of a class of non-linearly damped mechanical oscillators is considered. Two different models of damping namely, piecewise linear and pth power damping are considered. Fast excitation is modelled as triangular, sinusoidal and random base excitation. The effect of fast excitation is theoretically analyzed using the method of direct partition of motion (MDPM) and direct simulation. The method of numerical averaging is also used, where damping characteristics or excitations are not amenable to analytical techniques. Fast excitation has the non-trivial effect of increasing and decreasing the low-velocity damping of hard and soft dampers, respectively. The effect of fast excitation on the transient and steady state slow dynamics of the system is investigated by direct numerical integration of the equation of motion.