Unilateral transmission in bilinearly coupled systems

This work investigates the steady-state vibration transmission characteristics of phononic lattices featuring bilinear coupling forces. We focus specifically on the phenomenon of unilateral transmission, which occurs when the transmitted vibrations maintain either complete compression or tension; i.e., the transmitted displacement does not change signs and remains either positive or negative. We consider bilinearly coupled oscillators as the unit cell for a bilinear phononic lattice. We conduct a parametric study for the unit cell and determine the boundary for the onset of unilateral transmission. We then extend the analysis to a bilinear phononic lattice. In both cases, we compute the steady-state response and linear stability of the system, considering bilinear forces with both amplitude-dependent and amplitude-independent properties. We identify regimes of nonreciprocal unilateral transmission when the mirror symmetry of the unit cell is broken. Our findings contribute to a better understanding of unilateral transmission in systems with bilinear elasticity.