We investigate the energetics of a freely vibrating circular membrane subjected to a sudden eccentric circular areal constraint. The membrane is assumed to be fixed at its outer boundary and the constraint is assumed to be applied at an arbitrary time during the motion of the membrane. The constraint is applied instantaneously such that immediately after application of the constraint, the geometry of the membrane outside the area of the constraint remains unchanged and the constrained area comes to rest. The change in total energy after constraint application is investigated for different sizes and locations of the constraint and time of application of the constraint. The results show that the energy can decrease or increase depending on the time of application of the constraint. The condition for maximum energy reduction is presented and simulation results based on this condition show that sequential application and removal of the constraint reduces the total energy rapidly. This provides the opportunity for active control of membrane vibration through direct physical interaction with a small area of the membrane.

This content is only available via PDF.
You do not currently have access to this content.