Vibrational Energies of Members in Structural Networks Fitted With Tuned Vibration Absorbers

The distribution of vibrational energy in members of a complex structure with tuned absorbers attached at the joints and subjected to dynamic loading is studied. The concept of power flows through the structure is used to determine the time-averaged energy levels of each member in the structure. The power flows are calculated using the time-averaged product of force and velocity at the input and coupling points (joints) of a general structure made of axially vibrating rods. The receptance approach is used to calculate the coupling forces and velocities in the structure. By balancing the input power against the dissipated powers, the time-averaged energy levels in members are determined. The main criteria studied here is the reduction in the frequency-averaged vibrational energy level of a member when an absorber is attached, expressed as a percentage compared to the case where there are no absorbers. The concept is first illustrated with a simple model of 2 axially vibrating rods with an absorber attached to the joint. Next, a more complex structure comprising 8 rods with arbitrary orientations and several absorbers attached to junctions is studied. The effect of activating absorbers at various locations on reducing the energy levels of certain members is examined. It is possible to estimate the usefulness of the absorber with respect to any member by determining the percentage reduction of energy level for that member.