Sound induced by a simple impact oscillator

Acoustic radiation due to vibration and impact of a spring-mass-damper oscillator whose motion is constrained by a barrier is analyzed at a field point in a free field. Impact between the mass and the barrier is modeled using a coefficient of restitution model. Non-linear behavior of the oscillator is observed due to motion constraint. Steady state response is studied using a bifurcation diagram. For small amplitudes of oscillation, the pressure perturbation by a vibrating mass in a compressible fluid is modeled as an acoustic dipole with its center at the equilibrium position of the mass and its axis aligned with the motion of the oscillator. The boundary condition for the acoustic domain is an acoustic free-field condition. It is observed that the unsteady acoustic pressure resulting from the impact force is a few orders of magnitude greater relative to the pressure field resulting from vibration alone before or after impact. We also analyzed the influence of coefficient of restitution, damping ratio, the ration of base excitation frequency to the natural frequency, and the ratio of the distance of the barrier to the base excitation amplitude on the acoustic radiation. Damping ratio and coefficient of restituion are shown to be the most significant paramters that affect the acoustic radiation from the vibro-impact oscillator.