Chaotification of quasi-zero-stiffness system with time delay control

Abstract

Since the control energy for chaotification of Duffing-type dynamics system depends on the linear stiffness of the system, a quasi-zero-stiffness (QZS) isolated system with time delay control is introduced for line spectrum reconstruction of acoustic noise of machinery vibration of underwater vehicles. To investigate the critical condition for chaotification, the stability analysis of the dynamic system with time delay is conducted by the generalized Sturm criterion, and the analytical expression for critical control parameters is obtained. By converting the time-delayed differential equations of the critical condition into discrete mappings through a finite difference scheme, the Lyapunov criterion for chaotification of the QZS system is acquired, which yields the same critical time delay control as the results obtained by the generalized Sturm criterion. Effective chaotification by setting control parameters in the unstable region is demonstrated by numerical examples, which proves the accurate guidance of the stability analysis on chaotification design.