Self-Oscillation in Active Wires with Asymmetric Willis-Type Viscosity

Wires designed to carry loads through uniaxial tensile forces are particularly useful in creating large-span, yet lightweight, structures of diverse shapes and functions. Incorporating self-oscillation capabilities within the wires could be a promising approach to enhance the autonomous dynamic functions of these structures. However, self-oscillation, which usually appears in biological organisms and active materials, requires complex feedback interactions between activity and elasticity, hindering their application in self-oscillating wires. Here, a simple self-oscillation strategy is suggested by extending Willis elasticity to Willis-type viscosity through an irreversible coupling between strain rate and body force. A class of active wires equipped with electro-magneto-mechanically coupled feedforward loops is designed to realize the irreversible coupling. Numerical experiments show that the active wire hosts biased limit-cycle self-oscillation, where oscillation amplitudes are amplified linearly along one direction. Using continuum models, the linear amplification is interpreted as the force equilibrium caused by asymmetric Willis viscosity. In the design, the oscillation mode shape can be tailored independently of frequency, and the active wire supports the standing propagating mode transition. The design and continuum model suggested can benefit the development of autonomous materials for large-span structures.