Wave non-reciprocity at a nonlinear structural interface

Abstract

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.