Nonlinear dynamics of 1D meta-structure with inertia amplification

Considering the low-frequency vibration isolation properties of the inertial amplification mechanism (IAM) and the band gap of the periodic structure, this paper is concerned with the dynamic characteristics of the nonlinear inertial amplification mechanism (NIAM), theoretically. This study focused on the influence of nonlinearity on vibration isolation characteristics. Both analytical and numerical methods are adopted. Through the analysis of a basic NIAM element, nonlinear modes and complex phase motions are observed. The bifurcation property shows that complex motions (periodic, quasi-periodic, and chaotic) can be obtained by altering the exciting frequency for some intended goals, especially for vibration reduction. Analysis of the dispersion relation and the vibration transmissibility of the 1D periodic meta-structure composed of multiple NIAMS (NIAMMS) demonstrates its superiority with a decrease of 18.4% in the lower bound of the band gap, compared with a common 1D nonlinear periodic meta-structures. Furthermore, it is possible to obtain an ultra-low and ultra-wide nonlinear band gap by properly adjusting the parameters such as nonlinear stiffness, mass ratio, assembly angle, and damping.