Design and vibration isolation analysis of locally resonant metamaterial structures considering collision and stick-slip

Abstract

Metamaterials play a significant role in controlling wave propagation, and locally resonant metamaterial structures are widely used for vibration isolation. Therefore, this study considers discontinuous external environmental resistance and internal non-smooth collisions, and adopts a physical-to-mathematical modeling approach to build the physical model from a single-unit system to a multi-unit system. A locally resonant metamaterial structure consisting of a mass-spring-mass system with collisions and stick-slip effects is designed. Under a three-unit system, the switching mechanism is incorporated to validate and demonstrate the rationality and effectiveness of the motion behavior of the system. The wave transmission rate in the chain is obtained to reveal the wave propagation effects under different inter-unit parameter ratios. After optimizing the parameters, the number of units is varied to investigate the influence of unit quantity on wave transmission and vibration isolation performance. The research shows that increasing the inter-unit damping ratio, decreasing the inter-unit stiffness ratio, increasing the base mass ratio, decreasing the intra-unit stiffness ratio, and higher friction contribute to broadening the vibration isolation region and maintaining stable isolation. Parameter optimization and an increase in the number of units help achieve effective vibration isolation at lower frequencies, expand the isolation range, and promote wave attenuation. The research results provide a feasible approach for wave attenuation by adjusting inter-unit parameter ratios and the number of units.