Multi-point inerter array and rotation invariance of regular polygon inerter array

Abstract

Inerter is a pure inertia two-terminal dynamic element. Physical implementations of inerters have made progress in control engineering, mechanical engineering, energy engineering and civil engineering. In this research, an interesting physical phenomenon, rotation invariance of regular polygon inerter array, is revealed. Dynamic model of a system with an inerter array composed of multiple inerters is established and analyzed. And the dynamic model is transformed into complex plane. Rotation invariance of regular polygon inerter array with more than two equidistant and equiangular equal inertance inerters is derived and the special circumstances of the dynamic models are explained. A novel special modular ball-screw inerter is designed and modeled to form inerter array. Experimental systems are built. Zero-input response experiments are carried out to obtain three natural frequencies of single layer systems with a regular triangle inerter array and a regular quadrangle inerter array, in cases of different initial angles. In conclusion, the experimental results are independent of the initial angles. And regular polygon inerter array is successfully formed by the designed inerter. Dynamic models of rotation invariance of regular polygon inerter array are verified by zero-input experiments of regular triangle inerter array and regular quadrangle inerter array.

Keywords

• Inerter
• Inerter array
• Regular polygon
• Rotation invariance