Dynamic Response Characteristics of a Nonviscously Damped Oscillator

The characteristics of the frequency response function of a nonviscously damped linear oscillator are considered in this paper. It is assumed that the nonviscous damping force depends on the past history of velocity via a convolution integral over an exponentially decaying kernel function. The classical dynamic response properties, known for viscously damped oscillators, have been generalized to such nonviscously damped oscillators. The following questions of fundamental interest have been addressed: (a) Under what conditions can the amplitude of the frequency response function reach a maximum value?, (b) At what frequency will it occur?, and (c) What will be the value of the maximum amplitude of the frequency response function? Introducing two nondimensional factors, namely, the viscous damping factor and the nonviscous damping factor, we have provided exact answers to these questions. Wherever possible, attempts have been made to relate the new results with equivalent classical results for a viscously damped oscillator. It is shown that the classical concepts based on viscously damped systems can be extended to a nonviscously damped system only under certain conditions.