Analytical jump-avoidance criteria of Duffing-type vibration isolation systems under base and force excitations based on concave-convex property

As a representative nonlinear system, Duffing oscillator has wide applications in the field of vibration control. This paper concentrates on the analytical jump criteria problem for a class of Duffing systems based on the concave-convex property. The mechanical model of Duffing-type isolators subjected to various excitations is firstly presented. The defined single critical jump point (SCJP) is proved to be an inflection point based on the concave-convex property of the dynamic response. Moreover, the analytical jump-avoidance criteria under base and force excitations are established. The sensitivities of dynamic parameters are discussed in detail, and several jump characteristics are revealed and explained. It turned out that the SCJP is inherent for Duffing systems. The key advantage is that the proposed jump-avoidance scheme can be used directly and independent of the solved dynamic response. In other words, this scheme provides a pure algebraic method for determining jumps and an accurate range of the adjustable parameters for practical applications. A series of numerical simulations and comparisons are conducted to demonstrate the effectiveness of the proposed analytical judgment method.