AbstractNon‐classically damped structural systems do not easily lend themselves to the modal superposition method because these systems yield coupled second‐order differential equations. In this paper, a variety of new computationally efficient iterative methods for determining the response of such systems are developed. The iterative approaches presented here differ from those presented earlier in that they are computationally superior and/or are applicable to the determination of the responses of broader classes of structural systems. Numerical examples, which are designed to evaluate the efficacy of these schemes, show the vastly improved rates of convergence when compared to earlier iterative sche
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