Physical Space Solutions of Non-proportionally Damped Systems
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Numerical methods to obtain the responses of non-proportionally damped systems are compared in terms of accuracy and efficiency. Based on a theoretical investigation of non-proportional damping mechanisms, a new class of iterative schemes are proposed, followed by an analysis of their convergence and optimal convergent speed. It is found that such iterative schemes possess faster convergent speed than many currently available numerical methods and require less computer memory space. The new schemes converge unconditionally for both classically and non-classically damped systems.