Complex Modal Analysis for Vibration of Damped Continua

This paper presents the complex modal analysis procedure for vibration of damped continua. The governing equation in the state vector form, defined by two symmetric matrix differential operators, is decoupled by use of orthogonal complex eigenfuctions. The explicit expression is obtained for the responses to arbitrary initial conditions and external excitation. The complex modal analysis is applied to transverse vibration of a viscoelastic beam constituted by the Kelvin model. The natural frequencies, the decrement coefficients, and the modal functions are determined under the simple supported boundary conditions. The responses of the beam to two typical external excitations are also calculated.