Signal Analysis Applied to the Parametric Identification of Non- Linear Vibratory Systems

Nowadays the use of mechanical non-linear devices to control the dynamic behavior of vibrating structures is increasing. Modern engineering applications use materials with non-linear properties such as springs, viscous, and Coulomb dampers, to reduce the structure vibration. The main objective of this paper is to study the vibration signals generated in a simulation of a vibratory system with non-linear stiffness using a non-linear signal analysis formulation. A two input and one output MISO model is proposed to represent the non-linear system dynamics. The global measured output is considered to be the sum of two outputs produced by one linear path associated in parallel with a non-linear path. This last path has a non-linear model that represents non-linear stiffness and another linear transfer function connected in series. Since the linear path is identified by traditional signal analysis, the non-linear function can be evaluated by using the global input/output relationships, and can be used to identify physical parameters of the non-linear stiffness. The input and output probability density functions and the coherence functions are used to quantify the system non-linear behavior. Simulations are conducted on a single degree of freedom system coupled to a cubic non-linear spring, to validate the non-linear model identified by the proposed methodology.