Complex modes and frequencies in damped structural vibrations

It is demonstrated that a state space formulation of the equation of motion of damped structural elements like cables and beams leads to a symmetric eigenvalue problem if the stiffness and damping operators are self-adjoint, and that this is typically the case in the absence of gyroscopic forces. The corresponding theory of complex modal analysis of continuous systems is developed and illustrated in relation to optimal damping and impulse response of cables and beams with discrete viscous dampers.