Wave non-reciprocity at a nonlinear structural interface
The principle of reciprocity is a basic feature of linear structural dynamics and acoustics. This work studies the passive break of reciprocity in two linear structural waveguides coupled by an unsymmetric nonlinear interface possessing mass, linear stiffness, and clearance nonlinearities. We show that the asymmetry and nonlinearity of the connection break reciprocity even with symmetric boundary conditions, and in some cases enable one-way transmission of propagating wavepackets in a preferential direction. A quantitative measure of non-reciprocity is introduced and applied to systematically study the effect of the clearance nonlinearities for two cases: an asymmetric system with dual identical clearance nonlinearities and an asymmetric system with dual unequal clearances. In the case of the asymmetric system with dual identical clearances, we demonstrate that the effectiveness of the non-reciprocity depends on whether incident waves at the structural interface encounter the clearance nonlinearities in series or in parallel. Finally, by considering interfaces with differing clearances, we show that it is possible to realize unidirectional propagation, i.e., preferential wave transmission in one direction and prevention of wave transmission in the reverse direction. These results demonstrate the efficacy of passively controlling the flow of energy in elastic waveguides using joints with clearance nonlinearities.
Unable to display preview. Download preview PDF.
The authors would like to thank an anonymous reviewer for pointing out an error of interpretation in the original version of the paper, which was corrected in the final version of the manuscript.
This material is based upon work supported in part by the National Science Foundation Graduate Research Fellowship under Grant No. DGE-1144245.
- 8.Tsakmakidis, K.L., Shen, L., Schulz, S.A., Zheng, X., Upham, J., Deng, X., Altug, H., Vakakis, A.F., Boyd, R.W.: Breaking Lorentz reciprocity to overcome the time-bandwidth limit in physics and engineering. Science 356, 1260–1264 (2017). https://doi.org/10.1126/science.aam6662 MathSciNetCrossRefGoogle Scholar
- 19.Bunyan, J., Moore, K.J., Mojahed, A., Fronk, M.D., Tawfick, S., Leamy, M., Vakakis, A.F.: Acoustic non-reciprocity in a lattice incorporating nonlinearity, asymmetry and internal scale hierarchy:experimental study. Phys. Rev. E. 97(5), 052211 (2018). https://doi.org/10.1103/PhysRevE.97.052211 CrossRefGoogle Scholar