Analytical description of the effects of system nonlinearities on output frequency responses: A case study

The output spectrum of a linear dynamic system can be expressed as the input spectrum multiplied by the system frequency response function. This well-known relationship analytically exposes the effects of the system parameters on the output frequency response. In this paper, the extension of this relationship to the nonlinear case is investigated via a case study where an analytical relationship between the output frequency response and the nonlinear damping characteristic parameters is derived for a sdof spring damper system. The analysis is based on the frequency domain analysis of nonlinear systems, and the basic idea can be extended to general situations. Simulation studies are included to verify the theoretical analysis and demonstrate the effectiveness of the new relationship. The results provide an important basis for the analytical study and the design of nonlinear engineering systems and structures in the frequency domain.