A MODAL SUPERPOSITION PSEUDO-FORCE METHOD FOR DYNAMIC ANALYSIS OF NON-PROPORTIONALLY DAMPED LINEAR SYSTEMS

For non-proportionally damped linear systems the modal equations obtained from the undamped eigenvectors are coupled with the modal damping matrix. The non-proportional damping may be divided into two parts: the proportional part for dissipation of energy and the non-proportionalpart for transformation of .energy. Based on this concept, a modal superposition pseudo-force method for the dynamic analysis of non-proportionallydamped systems is presented. In this method, the coupled modal equations are solved by iteration in which the coupling terms are treated as pseudo-force and set to the right side of the equations. The method combinesthe advantages of the classical modal superposition method and the pseudo-force method. Numerical examples show good convergence of the process and good acuracy of the computed results.