Hierarchical unit cell employing a nonlinear energy sink for passive, low-pass amplitude filtering of acoustic waves

• Published in: Extreme Mechanics Letters 2023-09, Vol.63 (C), p.102056, Article 102056
• Main Authors: Mork, Nehemiah, Fronk, Matthew D., Biedermann, Laura B., Sinclair, Michael B., Leamy, Michael J.
• Format: Article
• Language: English
• Subjects: Amplitude-dependent transmission; Harmonic balance; Hierarchical nonlinear unit cell; Nonlinear energy sink; Passive transmission filtering
• ISSN: 2352-4316; 2352-4316
• DOI: 10.1016/j.eml.2023.102056

In this letter we present a hierarchical unit cell incorporating a nonlinear energy sink (NES) that functions as a low-pass amplitude filter. The hierarchical unit cell is composed of an outer and inner mass coupled by essentially nonlinear springs. Other than its nonlinear coupling to the outer mass, the inner mass is otherwise unconstrained and thus acts as an NES. Using numerical simulations, we show that the nonlinear unit cell passively filters incident waves as a function of their amplitude. The resonator is inactive at low amplitudes, permitting waves to pass. At high amplitudes, the NES activates and its resonant behavior reflects incident waves. Consequently, the unit cell effectively operates as an amplitude limiter for specific signal frequency and amplitude ranges. Notably, the passing of low-amplitude incident energy while bypassing the nonlinearity results in very little distortion in transmitted signals. We analytically investigate this behavior further using a harmonic balance method. The analysis supports the transmission filtering behavior as well as the activation of the nonlinear energy sink. Lastly, we design and construct the nonlinear unit cell and perform tests using incident and transmitted waveguides composed of monatomic chains. Both the nonlinear unit cell and monatomic chains are assembled using steel masses and additively-manufactured springs. We test the fabricated filter using low and high amplitude signals and observe amplitude filtering at various excitation frequencies that document strong agreement with numerical simulations and the analytical model. The ability to passively reflect high amplitude waves, and transmit low amplitude waves with minimal distortion, may inspire new devices for hearing protection, or for isolating and protecting sensitive equipment and instruments.