An Approximate Normal Mode Method for Damped Lumped Parameter Systems

Abstract

An approximate normal mode method is introduced which permits any linear non-conservative system to be solved by super position of uncoupled coordinates. Accuracy of the method was found to be good when checked by digital computer for dynamic damper systems subjected to sinusoidal and white noise random excitation. A technique is presented which permits a mathematical model for a damped multimass system to be constructed entirely from experimentally obtained sinusoidal frequency response data. An expression is derived for optimum damping ratio and natural frequency ratio that will minimize the response of a two-mass system to white noise random excitation.