An archetypal zero- or quasi-zero-stiffness model with three degrees of freedom based upon an inverse method

Abstract

In this paper, a three degrees of freedom archetypal model with arbitrary designable features and its inverse construction method based upon the target restoring force functions are proposed. The construction conditions of the zero-stiffness and quasi-zero-stiffness systems with 3-DOF have been studied in detail, by introducing the definitions of the zero-stiffness and the quasi-zero-stiffness system, based upon the archetypal model. The static characteristic and the low-frequency vibration isolation performance of the zero-stiffness and quasi-zero-stiffness systems with 3-DOF in multiple direction have been analyzed, by comparing with the linear system with the same support stiffness. The conclusion shows that there are finite solutions for the construction of 3-DOF zero-stiffness characteristic, and infinite solutions for the construction of 3-DOF quasi-zero-stiffness characteristic, based on 3-DOF archetypal model and its dimensionless parameters. The feasibility of constructing the zero-stiffness system with 3-DOF will lead to a new inspiration for the design of the passive zero-stiffness support structures; and the low-frequency vibration isolation performance of the 3-DOF quasi-zero-stiffness system in multiple direction is significantly improved compared with the linear system, which expresses a great potential in the multi-DOF design of the low-frequency, ultra-low-frequency vibration isolation.