Analytical and experimental results: creation of a duffing acoustic nonlinear oscillator at low amplitudes

TL;DR

This paper presents an analytical and experimental investigation into creating a low-amplitude Duffing nonlinear acoustic oscillator, demonstrating how nonlinear dynamics can be harnessed for sound absorption and noise reduction.

Contribution

It introduces a method to design nonlinear acoustic resonators at low amplitudes using the Duffing equation, supported by experimental validation with real-time control algorithms.

Findings

Successful analytical modeling of a Duffing nonlinear acoustic oscillator.

Experimental validation aligning with analytical predictions.

Potential for nonlinear acoustic devices in noise control applications.

Abstract

Nonlinear dynamics have long been exploited in order to damp vibrations in solid mechanics. The phenomenon of irreversible energy transfer from a linear primary system to a nonlinear absorber has driven great attention to the optimal design of vibration absorbers both for stationary and transient regimes. Recently, the same principle has also been targeted in acoustics for the absorption of sound waves at high excitation amplitudes. Meanwhile, acoustic absorption by electro-active means has found great success for noise reduction in the linear regime. This study uses a method allowing the design of nonlinear resonators at amplitudes that typically induce linear behaviors. This research proposes an analytical study of the implementation of the duffing equation as a nonlinear electroacoustic resonator coupled to an acoustic mode of a tube. Experiments are carried out and compared to the analytical results. The experimental implementation is done using a real-time-based algorithm retrieving the measured pressure from a microphone and giving the electrical current to send to a loudspeaker as an output thanks to a Runge-Kutta-like algorithm.