Energy Dissipation Through Modal Energy Redistribution

A vibration suppression strategy based on passive damping is presented. Modal energy is shifted from low to high frequency modes where it will be rapidly dissipated. This is achieved through the repeated application and removal of constraints. Upon application of the constraint, part of the energy is transferred to the system modes in its new configuration while the remaining energy goes into the unmodeled, high frequency, flexible body modes where it is dissipated. When the constraint is removed, the remaining energy is transferred back to the modes of the unconstrained system. Removal of the constraint allows it to be applied again and the cycle to be repeated until the energy drains away completely. It is shown that the amount of energy lost during one cycle depends on the timing of the constraint application. Special cases where energy is conserved are considered. In one such case, energy is trapped in modes which are unaffected by the application of the constraint. These modes span an invariant subspace where energy remains trapped. Examples of linear systems are presented to illustrate this strategy.