This paper transfers the concept of moment matching to nonlinear structural systems and further provides a simulation-free reduction scheme for such nonlinear second-order models. After first presenting the steady-state interpretation of linear moment matching, we then extend this reduction concept to the nonlinear second-order case based on Astolfi [2010]. Then, similar simplifications as in Cruz Varona et al. [2019] are proposed to achieve a simulation-free nonlinear moment matching algorithm. A discussion on the simplifications and their limitations is presented, as well as a numerical example which illustrates the efficiency of the algorithm.

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