Vibration isolation properties of the nonlinear X-combined structure with a high-static and low-dynamic stiffness: Theory and experiment

Abstract

A nonlinear X-combined structure is proposed and designed using an X-shaped structure (positive/negative stiffness mechanism) and two inclined springs (positive stiffness mechanism) to avoid existing negative stiffness and unstable factors and to improve vibration isolation characteristics. The mechanism possesses high-static and low-dynamic stiffness in a larger displacement range. In order to identify the coupling mechanism of the combination of two nonlinear mechanisms, its static and dynamic properties are investigated. The displacement transmissibility with multi-valued solutions is used to evaluate the vibration isolation of the combined structure. A new mathematical method is used to obtain a multi-valued analytical solution to the nonlinear equation of motion, which is then validated using the ADAMS software and the least square method (LSM). The novelty of this study is (a) the system has a very useful nonlinear stiffness with positive/quasi-zero/zero stiffness over the entire working range, and the quasi-zero stiffness (QZS) range is greater than that of an X-shaped structure; (b) compared to the existing nonlinear vibration isolator, such as three-spring systems and X-shaped structures, the proposed structure has the lower equivalent stiffness in the vibration isolation range, and the vibration isolation performance is better when each system has the same loading capacity; (c) the completed and accurate nonlinear solutions can more scientifically reflect the vibration isolation characteristics of the system; (d) the introduction of oblique springs into the X-shaped structure can make it easier to adjust the stiffness of the structure and use the tensile spring as the oblique spring, and the X-combined structure is easier to be designed and installed. This study shows that the proposed structure can provide excellent vibration isolation by combining two nonlinear mechanisms. These advantages are also confirmed by experiments and comparison with existing QZS isolators. This vibration isolation system will provide a new analytic method and innovative approach to the QZS isolator.