On Complex Modal Inverse Analysis: The Cautionary Tale of the Single Surviving Mode

The number of modes of a mechanical system is generally assumed to equal its number of degrees of freedom. In this technical brief, a simple non-classically damped system is shown to possess fewer modes than degrees of freedom unless a restrictive condition is met. When this condition is met, while there is a full set of modes, they are not orthogonal. These results hold for vanishingly small non-classical damping, can evade detection by the modal phase collinearity metric, and are relevant to system identification of mechanical systems in which non-classical damping is present.