Classical Normal Modes in Damped Linear Dynamic Systems

An analysis of the conditions under which a damped linear system possesses classical normal modes is presented. It is shown that a necessary and sufficient condition for the existence of classical normal modes is that the damping matrix be diagonalized by the same transformation that uncouples the undamped systems. Sufficient though not necessary conditions on the damping matrix are developed, and it is shown that Rayleigh’s solution is a special case of the present theory.