Investigation of unidirectional vibration isolation and nonreciprocal design of axial elastic waves based on topological pumping theory

Abstract

In this work, a spiral structure (SS) based on the nonreciprocal waveguide theory of adiabatic evolution principle is designed, which can generate dynamic boundaries on a rotation shaft. The spatiotemporal topological pumping formed by SS can achieve nonreciprocal transmission of elastic waves in shaft, and the transmission can achieve unidirectional isolation of shaft vibration. Firstly, transfer matrix method (TMM) is used to theoretically derive the continuity at two-phase spiral periodic shaft structure (SPSS) medium. Then, finite element method (FEM) is utilized to calculate energy bands and frequency response functions of SPSS. Next, the calculations results obtained by FEM are used to analyze the influence of material parameters, geometric dimensions and other factors on band gap, and SPSS of rotation is used to confirm the variation of topological edge modes produced by spatiotemporal pumping. Finally, realistic shaft model and analytical parameters are combined to determine the dimensional parameters and materials of unidirectional vibration isolation shaft, vibration transmission characteristics of spiral shaft are obtained by numerical simulation, and its unidirectional vibration isolation performance is verified through experiment. The results show that SS can achieve spatiotemporal topological pumping function at a certain modulation speed, when the band gap is deflected in a specific frequency range, elastic waves can be transmitted unidirectional in deflected frequency range, the dynamic spiral shaft has a good unidirectional vibration isolation effect when the shaft is modulated in the reverse direction, and changing helical angular velocity can tune frequency range of nonreciprocal transmission of elastic waves. The design can provide a theoretical basis for engineering application of unidirectional vibration isolation bushing in wide frequency range.