An iterative approach for nonproportionally damped systems

Modal analysis of nonproportionally damped linear dynamic systems is considered. Dynamic response of such systems can be expressed by a modal series in terms of complex modes. Normally state-space based methods or approximate perturbation methods are necessary for the computation of complex modes. In this paper, an iterative method to calculate complex modes from classical normal modes for general linear systems is proposed. A simple numerical algorithm is developed to implement the iterative method. The new method is illustrated using a numerical example.

► We proposed a new iterative approach to obtain dynamic response of nonproportionally damped linear dynamic systems using complex modal analysis.
► A sufficient condition for the convergence of the proposed iterative method is established.
► We have provided a simple numerical algorithm to implement this method in the context of general finite element method.
► Our method is computationally more efficient compared to the classical state-space method.