Convergence of Iterative Methods for Nonclassically Damped Dynamic Systems

This paper deals with two computationally efficient iterative methods for determining the response of nonclassically damped dynamic systems. Rigorous analytical convergence results related to these iterative methods are provided. Sufficient conditions under which these two iterative schemes are convergent are derived. Three different kinds of damping matrices, namely, (i) strongly diagonally dominant, (ii) irreducible and weakly diagonally dominant, and (iii) symmetric and positive definite damping matrices, are considered. Asymptotic rates of convergence are discussed. Theoretical results are illustrated with numerical examples that show vastly improved rates of convergence when compared to earlier iterative schemes.