This is the first part of a paper on an innovative approach of studying general nonlinear structural dynamic systems. In this part, the theoretical background and some numerical simulations are presented. Firstly, a frequency domain nonlinear compensation method is proposed. It can be used to recover the linear path of a general non-linear system as long as the Volterra expansion is held between the input and the output. Secondly, a new nonlinear element location scheme is developed based on the system linear path identification. Lastly, as a natural extension in the development of the contents of this paper, an in-situ nonlinear restoring force state mapping technique is proposed. The use of these new methods is demonstrated through several numerical examples of either single or multiple DOF systems incorporating some typical types of nonlinearities.

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