Nonlinear hierarchical unit cell for passive, amplitude-dependent filtering of acoustic waves

Abstract

In this letter we propose a nonlinear hierarchical unit cell for use in passive, amplitude-dependent filtering of acoustic energy transmission. Analogous to unit cell designs which filter on frequency using bandgaps, the nonlinear hierarchical unit cell filters on amplitude with minimal waveform distortion. Numerical simulations of wave propagation in a mechanical chain employing the proposed unit cell predict nearly zero transmission of energy at low amplitudes, and nearly perfect energy transmission at large amplitudes. We hypothesize that the amplitude-dependent transmission behavior results from the nonlinear unit cell locking at high amplitudes, and thus acting as a single mass. When this single mass has the same weight as the other masses in the chain, near-perfect transmission is possible. We investigate this behavior further through a nonlinear analysis using a harmonic balance method to predict wave transmission through the nonlinear unit cell. The analysis confirms the transmission behavior and the rigid body hypothesis at large amplitudes. To validate the simulated and analysis results, we design and construct a monatomic chain using steel masses and additively-manufactured serpentine springs, to include a specially-designed nonlinear spring in the hierarchical unit cell. We then document amplitude-dependent filtering in the experiment for multiple frequencies, with strong agreement documented between measured results and simulation. In addition, high-speed camera images of the hierarchical cell verify the hypothesized locking behavior at large amplitudes. We believe the ability to passively select transmission based on a signal’s amplitude, with minimal resulting distortion, may open new opportunities in wave control and filtering, and new approaches for conceiving wave-based devices.