Road to entire insulation for resonances from a forced mechanical system

Abstract

The effective solution to avoid machinery damage caused by resonance has been perplexing the field of engineering as a core research direction since the resonance phenomenon was discovered by Euler in 1750. Numerous attempts have been performed to reduce the influence of resonance since the earlier of last century, by introducing a nonlinear structure or a closed-loop control system. However, the existed methodologies cannot eliminate resonance completely even extra problems were introduced inevitably, which means the technical choke-point of resonance-free remains unsolved. Here we propose a designable archetype model, which establishes a mapping between the mechanical properties and its structure. A general inverse method for structure construction is proposed based upon the required property for the system with quasi-zero stiffness of any designed finite order and the zero-stiffness properties. It is shown that an ellipse trajectory tracking of the designed model is the sufficient and necessary condition to satisfy the zero-stiffness property. Theoretical analysis shows that no resonant response happens in a zero-stiffness system to the full-band frequency excitation, or equivalently, the system can completely isolate the energy transfer between the load and environment, when the damping ratio approaches zero. Finally, an experimental rig for the prototype structure is built up according to the sufficient and necessary condition of the zero-stiffness system, for which the special dynamic behaviours are verified through experiments of frequency-sweep and random-vibration as well. Experimental results show that the prototype of the initial vibration isolation frequency of zero-stiffness system is much lower than 0.37 Hz, and the vibration attenuation of the proposed model is about 16.86 dB, 45.63 dB, and 112.37 dB at frequencies of 0.37 Hz, 1 Hz, and 10 Hz, respectively. The distinguished geometric structure of the zero-stiffness system leads to a new inspiration for the design of resonance-free in metamaterial unit and the inverse method can even adapt the design for a more targeted applications based on an arbitrary complex dynamic requirement.