An acoustic metasurface carpet cloak based on membrane-capped cavities is proposed and investigated numerically. This design has been chosen for allowing ultrathin geometries, although adapted to airborne sound frequencies in the range of 1 kHz (λ ≈ 30 cm), surpassing the designs reported in the literature in terms of thinness. A formulation of generalized Snell's laws is first proposed, mapping the directions of the incident and reflected waves to the metasurface phase function. This relation is then applied to achieve a prescribed wavefront reflection direction, for a given incident direction, by controlling the acoustic impedance grading along the metasurface. The carpet cloak performance of the proposed acoustic metasurface is then assessed on a triangular bump obstacle, generally considered as a baseline configuration in the literature.

Abstract-This paper proposes a hybrid impedance control architecture for an electroacoustic absorber, that combines an improved microphone-based feedforward control with a currentdriven electrodynamic loudspeaker system. Feedforward control architecture enables stable control to be achieved, and current driving method discards the effect of the voice coil inductance. A method is given for designing the transfer function to be implemented in the controller, according to a target specific acoustic impedance and mechanical parameters of the transducer. Numerical simulations present the expected acoustic performance, introducing global performance indicators such as the bandwidth of efficient absorption. Experimental assessments in a waveguide confirmed the accuracy of the model and the efficiency of the hybrid control technique for achieving broadband, stable lowfrequency electroacoustic absorbers. An application to damping of resonances in a duct is also presented, and the application to the modal equalization in actual listening rooms is finally discussed.

International audienceIn this paper, we extend the method proposed by Cochelin and Vergez [A high order purely frequency-based harmonic balance formulation for continuation of periodic solutions, Journal of Sound and Vibration, 324 (2009) 243-262] to the case of non-polynomial nonlinearities. This extension allows for the computation of branches of periodic solutions of a broader class of nonlinear dynamical systems. The principle remains to transform the original ODE system into an extended polynomial quadratic system for an easy application of the harmonic balance method (HBM). The transformation of non-polynomial terms is based on the differentiation of state variables with respect to the time variable, shifting the nonlinear non-polynomial nonlinearity to a time-independent initial condition equation, not concerned with the HBM. The continuation of the resulting algebraic system is here performed by the asymptotic numerical method (high order Taylor series representation of the solution branch) using a further differentiation of the non-polynomial algebraic equation with respect to the path parameter. A one dof vibro-impact system is used to illustrate how an exponential nonlinearity is handled, showing that the method works at very high order, 1000 in that case. Various kinds of nonlinear functions are also treated, and finally the nonlinear free pendulum is addressed, showing that very accurate periodic solutions can be computed with the proposed method