Analysis of vibration suppression of master structure in nonlinear systems using nonlinear delayed absorber

Abstract

In this paper, a nonlinear delayed absorber is proposed by a delayed feedback loop and is utilized to absorb or suppress the vibration of a two-degree-of-freedom nonlinear system when the primary resonance and the 1:1 internal resonance occur simultaneously. To explain analytically mechanism of performance of the absorber, an integral equation method is provided to obtain the second order approximation and the amplitude equations. As a result, the feedback gain and time delay which make the amplitude of the main system equal to zero can be derived analytically. Optimal working conditions of the system are extracted from the time delay-response curves, the force-response curves and the frequency-response curves. In the illustrative example, the appropriate choice of feedback gains and time delays can reduce the amplitude of the main system by more than 98 % in comparison with the amplitude with no time delay. All analytical predictions are in excellent agreement with the numerical simulations.

Applications of the integral equation method on nonlinear multi degree of freedom vibration systems

“…In (Xu,et al (2015)), the authors used the integral equation method to analyze a flexible, geometrically nonlinear beam structure controlled by an improved saturation controller with time delay. In (Chen,et al (2014)), the amplitude equation of a two-degree-of-freedom nonlinear system with external excitation is derived by using integral equation method, and the mechanism of performance of the nonlinear delay absorber is explained. In (Chen and Xu (2013)), Chen and Xu considered three examples: a single-degree-of-freedom Van der Pol oscillator under state feedback control with a time delay, a single-degree-of-freedom Duffing oscillator under state feedback control with a time delay and a two degree-of-freedom model.…”

Periodic Response Analysis of A Jeffcott-Rotor System By The Integral Equation Method

“…In this paper, two modified saturation-based controllers and negative velocity feedbacks are applied to suppress the nonlinear vibrations of a horizontally supported Jeffcott-rotor system subjected to harmonic excitation force. The integral equation method [23][24][25][26], which was introduced by G.Schimidt, is utilized to obtain the second order approximations and the amplitude equations. The stability of the system is investigated by applying a combination of the Floquet theory and Hill's determinant.…”