Unilateral vibration transmission in mechanical systems with bilinear coupling

TL;DR

This paper computationally investigates unilateral vibration transmission in bilinear elastic systems, revealing how asymmetry facilitates nonreciprocal transmission and complex dynamic behaviors near resonances.

Contribution

It introduces a detailed analysis of unilateral transmission in bilinear systems, highlighting the role of asymmetry and extending the study to periodic structures with diverse dynamic responses.

Findings

Unilateral transmission occurs near primary resonances in asymmetric bilinear systems.

Breaking symmetry enables nonreciprocal and nonreciprocal transmission phenomena.

Stable nonreciprocal behaviors include period-doubled and quasiperiodic responses.

Abstract

Unilateral transmission refers to the scenario in which the waves transmitted through a system remain in pure tension or pure compression. This transmission phenomenon may occur in systems that exhibit different effective elasticity in compression and tension; i.e. bilinear elasticity. We present a computational investigation of unilateral transmission in the steady-state response of harmonically driven mechanical systems with bilinear coupling. Starting with two bilinearly coupled oscillators, we find that breaking the mirror symmetry of the system, in either elastic or inertial properties, facilitates unilateral transmission by allowing it to occur near a primary resonance. This asymmetry also enables nonreciprocal transmission to occur. We then investigate the nonreciprocal dynamics of the system, including linear stability analysis, with a focus on unilateral transmission. We also extend our discussion to a bilinear periodic structure, for which we investigate the influence of the number of units and energy dissipation on unilateral transmission. We report on the existence of stable nonreciprocal unilateral transmission near primary and internal resonances of the system, as well as other nonreciprocal features such as period-doubled and quasiperiodic response characteristics.