Physical consideration of complex modal solutions of a nonproportionally damped mechanical system

Abstract

A mathematical method of complex modal analysis and an experimental identification procedure of modal parameters for nonproportionally damped mechanical systems have been established thus far. However, the physical structure of complex modes of nonproportionally damped systems has not been thoroughly understood. This paper deals with a physical and graphical interpretation of complex modes in comparison with real modes of proportionally damped systems using the complex plane and the complex vector space. It is explained why the resonance vibration of nonproportionally damped systems does not exhibit the natural mode shape which appears in the free vibration of the same system. The condition that makes the resonance vibration mode approximately coincide with the natural mode shape of the free vibration is discussed.