An Evaluation of the Fixed Point Method of Vibration Analysis for a Particular System With Initial Damping

Abstract

The maximum steady-state response of a particular linear damped two-degree-of-freedom vibratory system is minimized by determining the optimum damping constant for a single damper. This is accomplished by both a well-known approximate method and by an exact numerical method. Since the approximate method does not take into account the damping which is initially in the system, attention in this analysis is directed to determining the influence of the initial damping on the optimum value for the single damper. In order to make direct comparison of the methods, a system was chosen in which an exact numerical determination of the optimum damping was possible. The results of the investigation show for the particular case considered that, although the value of the damping constant for the optimum damper increases considerably as initial damping is included in the system, use of the value obtained for the initially undamped case would give values of the maximum steady-state response within 10 percent of the optimized value for the range of initial damping commonly encountered.