The role of damping in vibration theory

Abstract

In many applications of vibration and wave theory the magnitudes of the damping forces are small in comparison with the elastic and inertia forces. These small forces may, however, have very great influence under certain special circumstances. Damping arises from the removal of energy by radiation or dissipation. It is generally measured under conditions of cyclic or near-cyclic motion. The nature of some important damping mechanisms is discussed and an indication is given of how the damping depends on the amplitude and frequency of the cyclic motion. The idealized models of damping which are commonly employed in theoretical analyses are described and some limitations are noted. Damping is of primary importance in controlling vibration response amplitudes under conditions of steady-state resonance and stationary random excitation. Damping also plays a crucial role in fixing the borderline between stability and instability in many dynamical systems. Some examples which illustrate this are discussed, including shaft whirl, and pipeline flutter.