Receptance method for active vibration control of a nonlinear system

This paper presents the application of the receptance method to nonlinear systems for active vibration control. The method, previously established for linear systems, is extended to a class of single-degree-of-freedom nonlinear systems that can be characterised using describing functions. A significant advantage of the receptance method is that there is no requirement to know the system parameters such as mass, damping and stiffness terms, typically obtained using finite element methods. The method is particularly advantageous for nonlinear systems, since there is no requirement for nonlinear identification. A linear state feedback controller is applied to an example of a single-degree-of-freedom Duffing oscillator, to assign the peak resonance to a prescribed value using the established Sherman-Morrison receptance method. It is then demonstrated that an iterative form of the Sherman-Morrison receptance method is required for the accurate assignment of this peak resonance, in order to account for changes in the open-loop receptance. Both harmonic balance and Volterra series representations are investigated to approximate the receptance in the complex domain, and their advantages and disadvantages are discussed in a numerical example.