In this article, a novel iterative method is introduced to dynamic analysis of multi-degree-of-freedom systems in which all characteristics of the system could be simultaneously changed with respect to time. The proposed scheme is based on the differentiation of the original equation of motion, on the contrary to the conventional approaches which are usually based on the integration of the motion equation. The numerical investigation of the present method was carried out by analyzing the three systems with one, two and three degrees of freedom. Moreover, the obtained results were comprehensively verified by two distinct approaches: a system with invariant characteristics, and a system with varying mass and stiffness, with closed-form solution. It should be noted that some closed-form solutions of multi-degree-of-freedom (MDOF) time-varying systems were derived and presented for the first time in this article.

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