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Passive acoustic foams have limitations in efficiently reducing low-frequency noise below 800 Hz due to the associated wavelengths for reasonable material thickness. To address this challenge, passive or semi-active resonators are commonly employed solutions. Linear resonators are very efficient within a narrow frequency bandwidth. However, nonlinear oscillators can broaden this bandwidth, but activation of their nonlinear responses typically requires high excitation amplitudes, beyond human hearing tolerance amplitudes. Furthermore, the specific type of nonlinearity in such devices is often predetermined by the inherent properties of the resonator. In this study, we employ a novel digital control algorithm, allowing to activate the nonlinear response of the electroacoustic resonator at low excitation amplitudes. This algorithm, which relies on real-time integration, facilitates the creation of nonlinear resonators featuring polynomial or diverse non-polynomial nonlinearities within the range of low amplitudes. The nonlinear control is carried out on a loudspeaker equipped with a microphone. Our research highlights the potential to create nonlinear resonators with different, versatile and programmable behaviors. Unprecedented non-polynomial nonlinear behaviors are experimentally exhibited, we consider cubic, piece-wise linear, and logarithmic nonlinearities. These behaviors are implemented and compared to a semi-analytic model to control an acoustic mode of a tube under conditions of low excitation amplitudes and frequencies. • We exploit advantages of nonlinearities in vibro-acoustical control. • The exploited nonlinearities are polynomial and non-polynomial. • We digitally program nonlinearities of an electroacoustic resonator. • The nonlinear behaviors are activated at low excitation amplitudes. • The programmed resonator is used for control of an acoustic mode. [ABSTRACT FROM AUTHOR]

The electroacoustic resonator is an efficient electro-active device for noise attenuation in enclosed cavities or acoustic waveguides. It is made of a loudspeaker (the actuator) and one or more microphones (the sensors). So far, the desired acoustic behaviour, expressed in terms of a linear-time-invariant relationship between sound pressure and vibrational motion (the acoustical impedance), has been more efficiently achieved by a model-inversion strategy which is implemented by driving the electrical current in the loudspeaker coil, based upon the measured pressure. The corrector transfer function is defined in the Laplace domain and digitally executed by the classical infinite-impulse-response technique, though a state–space representation could be employed. In this work, we are interested in enforcing a nonlinear behaviour at low sound excitation levels, where the electroacoustic resonator would normally behave as a linear-time-invariant system. Hence, in order to transform its acoustical response from linear to nonlinear, the model-inversion technique must be reformulated in time domain. The state–space representation of the relationship between the input measured pressure and the output electrical current gives the right perspective and the solution to this problem. We provide the conception of this model-inversion control algorithm capable of transforming a linear-time-invariant acoustical response to potentially any causal acoustical response of the electroacoustic resonator. Such control strategy is tested by targeting a Duffing acoustical response with tunable parameters. Both numerical simulations and experimental tests in quasi-open field validate the approach. The results provided in this contribution open the doors for conceiving non-conventional absorbers which can exploit nonlinear phenomena for noise mitigation even at low excitation amplitudes. [ABSTRACT FROM AUTHOR]