ON THE POWER INPUT TO POINT LOADED HYSTERETICALLY DAMPED STRUCTURES

The power input to point loaded hysteretically damped one- and two-dimensional structures is investigated. Both uniform and periodic structures are considered, and in each case the input power is expressed in terms of the solutions of the damped dispersion relation. In the case of a one-dimensional periodic structure, for example, it is found that the input power is directly proportional to the rate of change of the phase constant with frequency. An established approximate formula states that the power input to a structure is independent of damping and proportional to the modal density. By considering the specific cases of a beam on multiple supports and a cylindrical shell, it is shown here that the damping can significantly affect the input power.