This paper presents an experimental and theoretical study of the nonlinear behavior of imperfect interfaces in multilayer structures using an equivalent vibro-acoustic approach. The multilayer system is modeled through a Zig-Zag formulation, in which interfacial coupling conditions, stress continuity and displacement discontinuity, relate the kinematics of adjacent layers while preserving an independent description of each layer. This framework significantly reduces the number of kinematic unknowns without compromising the model accuracy. An equivalent Kirchhoff-Love plate formulation is then introduced to derive a frequency-dependent bending stiffness representative of the global structural response. Experimental measurements of the transverse displacement field are performed using laser vibrometry and processed via the Corrected Force Analysis Technique (CFAT).The results demonstrate that the dynamic response of a three-layer beam with imperfect interfaces depends on the excitation level. In particular, variations in the equivalent bending stiffness are observed, revealing the nonlinear nature of the interfacial behavior. The proposed methodology is applied to a glass-epoxy-glass multilayer beam under various excitation levels.

Vegetal wools are highly porous materials made of vegetal fibres and bicomponent polymer fibres. Despite their high-level multifunctional properties, they suffer from poor low-frequency acoustic absorption for thin panels. In order to lay the foundations for optimisation, it is essential to use models with the porosity, an effective radius, and the mass ratio between fibre types as inputs. However, unlike more conventional materials, vegetal wools don't have calibrated fibres. Not only are these fibres not cylindrical, but they also exhibit high radius polydispersity, which can be described through a probability distribution. This work aims to determine the best way to measure these radius probability distributions and to calculate the most suitable effective radii to use in these models. A measurement protocol is established to obtain these distributions for six vegetal wools, by observing them transversally through a scanning electron microscope and approximating their profile to ellipses. Four averaging methods are investigated to determine an effective radius. Three analytical models simulate the visco-inertial and thermal effects of the wools: Tarnow-Brinkman, Umnova-Johnson-Champoux-Allard-Lafarge and Pi & eacute;gay models. To calculate the sound absorption, a direct approach using one effective radius and a composite approach using two effective radii discriminating fibre types in a wool are compared. In total, 18 different methods to simulate the sound absorption and other parameters are evaluated and compared to acoustic measurements of the wools, giving us the most precise analytical estimations. This analysis concludes that, to calculate the resistivity, using Tarnow's model in direct or composite approach with an arithmetic or quadratic average as effective radius is best. The two characteristic lengths are best estimated with Umnova's model and an inverse volume weighted average radius. For sound absorption, the best approaches are Umnova-Johnson-Champoux-Allard-Lafarge in direct or composite approach, and Pi & eacute;gay in composite approach with an arithmetic average radius.

This paper presents an experimental and theoretical study of the nonlinear behavior of imperfect interfaces in multilayer structures using an equivalent vibro-acoustic approach. The multilayer system is modeled through a Zig-Zag formulation, in which interfacial coupling conditions, stress continuity and displacement discontinuity, relate the kinematics of adjacent layers while preserving an independent description of each layer. This framework significantly reduces the number of kinematic unknowns without compromising the model accuracy.An equivalent Kirchhoff–Love plate formulation is then introduced to derive a frequency-dependent bending stiffness representative of the global structural response. Experimental measurements of the transverse displacement field are performed using laser vibrometry and processed via the Corrected Force Analysis Technique (CFAT). The results demonstrate the excitation level dependency of the dynamic response of a three-layer beam. In particular, variations in the equivalent bending stiffness are observed, revealing the nonlinear nature of the interfacial behavior. The proposed methodology is applied to a glass/epoxy/glass multilayer beam under various excitation levels.

The initial conditions of a deterministic nonlinear system affects the attained asymptotic solutions. This is a problem when the nonlinear behaviour is achieved by active control synthesis, and the initial conditions are not accessible for pre-constraining. Meanwhile, the generalized impedance control is recently gaining increasing attention in acoustics, and has been enlarged to achieve nonlinear mechanical responses of Electroacoustic Resonators at low excitation levels. Nevertheless, as the initial conditions of Electroacoustic Resonators are hardly accessible, the equilibrium points actually showcased by the synthetic nonlinear dynamics are not advantageous for noise attenuation in cavities excited by realistic noise sources. In this paper, we propose a control strategy being able to attain the desired equilibrium points, due to the definition of an exosystem characterized by a desired nonlinear impedance and a synthetic external excitation. The exosystem dynamics is integrated in real time and its response is enforced in the actual system (in our case, the Electroacoustic Resonator), by a model-inversion feedforward strategy. The proposed algorithm is implemented in the Electroacoustic Resonator, and is validated both numerically and experimentally. In particular, the experimental testing is conducted both in a quasi-open acoustic environment, and in enclosed cavities for acoustic mode attenuation.

Heterogeneous porous materials are widely used in building and transportation sectors. The heterogeneities arise due to recycling processes or are designed to include non-conventional phenomena (pressure diffusion, acoustic resonances, multiple-scattering, Bragg-interferences, sorption, etc.) involved in acoustical metamaterials. Detailed Finite Element Models (FEM) of such materials prove prohibitively expensive, especially when embedded in large structures. Although heterogeneous analytical methods address this issue, they exist only for specific, idealized scenarios; consequently a more robust generalization is achieved by generating a condensed transfer matrix (TMM) from a single unit cell FEM computation. The coupled TMM-FEM approach is further augmented by incorporating periodicity. However, the condensed TMM is useful but dependent on the excitation incident angle, i.e., it must be recomputed for each incidence. This work combines the condensed-TMM approach with a numerical characterization of equivalent intrinsic parameters. These equivalent parameters enable to analyse the involved physical phenomena at the macroscopic scale and to condense such heterogeneous material as a single layer in more complex structures. It is further showed, when dealing with FEM, that the proposed condensation has a high computational gain over the conventional full threedimensional finite element approach, especially when dealing with excitations like diffuse field excitation. The accuracy and efficiency of the method, along with relevant examples will be discussed.

This article investigates the optimization under uncertainty of a mass-in-mass meta-cell for its potential use within a metamaterial. The specificity of the proposed mass-in-mass system stems from the hybrid nonlinear-linear stiffness at the inner level. It is well known that these systems are highly sensitivity to small perturbations in loading conditions or design parameters. In fact, the sensitivity is such that the system can exhibit discontinuous behaviors. Therefore the proposed optimization approach not only accounts for sources of uncertainties but also can handle discontinuous responses. The objective of the stochastic optimization is to find the stiffness properties of the mass-in-mass system which minimize the expected value of a specific efficiency metric. In order to better understand the system's dynamic behavior and the origins of the discontinuities, slow invariant manifolds and frequency response curves are provided. The efficiency of the optimized system with hybrid stiffness is compared with that of a similar optimized system featuring pure cubic nonlinearity.

In this article, we investigate an electroacoustic resonator with a programmed cubic nonlinearity with constant and time-dependent coefficients. We design an experiment coupling an acoustic mode of a tube with a digitally programmable nonlinear resonator. Both simulations and experiments are carried out to compare optimized points for the resonator with programmed cubic nonlinearity with constant and time-dependent coefficients. We show that the frequency bandwidth of efficiency and the noise reduction are greater with varying nonlinearity than with constant nonlinearity.

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. Despite the several assumptions of the model, the analytical modelling is validated by the experiment, showing that the model is able to predict the two-degree-of-freedom system.

Vegetal wools are highly porous materials made of vegetal and polymeric bicomponent fibers. They feature high-level multifunctional properties, such as sound absorption and hygrothermal regulation. However, despite their attractive properties, they suffer from poor low-frequency sound absorption for thin panels (less than 5 cm thick). A solution to this problem can be found in meta-material methods. Unfortunately, very little research has been done on this subject with applications for bio-based materials. Moreover, it seems relevant to use the specificities of vegetal wools, such as the polydispersity of their fiber radii, for these acoustic optimization approaches involving meta-material methods. To meet this challenge, a state-of-the-art has been carried out to identify suitable analytical modeling methods to simulate their acoustical behavior, and to optimize it. A first optimization consisted in implementing the meta-material concept of double porosity into a resistive hemp wool layer. Combined with a multiple layers configuration, this approach significantly improved the acoustic absorption of hemp wool panels. To go further, this work aims at comparing different analytical approaches to account for fiber radius polydispersity. Vegetal wools present a large range of fiber radii, and most studies consider a mean radius for simulations, with arithmetic or quadratic averaging methods. However, these approaches may overestimate the role of fibers with larger radii, which, for the example of static airflow resistivity relying on the thinner fibers, can inaccurately represent the physics. This work investigates different ways of averaging the radius probability distribution of vegetal fibers to improve the accuracy of analytical estimations.

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.

Different works have shown the interest of psychoacoustic indices to account for annoying auditory sensations evoked by environmental noises.Short-term noise annoyance experiments have shown the relevance of these indices, leading to the proposal of annoyance models based on noise sensitivity and psychoacoustic indices.As these indices have to be calculated from audio recordings, their use is too time-consuming for field studies.For aircraft noise annoyance models based on noise sensitivity and psychoacoustic indices, the current work proposed to build relationships that allow an estimation of these indices from Lden index given by noise maps.The study presents the construction of these relationships, their testing using a new data set, and the testing of annoyance models based on noise sensitivity and these indices using Lden and data from a socio-acoustic survey.The testing of the relationships indicated their relevance for a future use in field studies dealing with environmental noise assessment.Thanks to the proposed relationships, the testing of noise annoyance models using field data was possible.It revealed that the models based on noise sensitivity and psychoacoustic indices estimated from Lden performed better than existing annoyance models based on Lden or on the day-night level Ldn and noise sensitivity.

The research presented in this paper aims to demonstrate how imperfect interfaces influence the behavior of a multilayered structure. To achieve this, a dynamic equivalent model for multilayered panels is used, enabling the characterization of these interfaces using experimental data. This model, known as the Layer Wise (LW) model, incorporates imperfections in the interfaces through sliding displacement. To effectively validate the model against experimental measurements, an equivalence with a thin beam is established. Then the experimental methodology used for characterization is outlined, including the setup, considered samples, and data processing techniques. Specifically, the Corrected Force Analysis Technique (CFAT) is used, which is a robust method based on the equations of motion for thin plates or beams. This method, for the first time, allows obtaining broadband frequency results, facilitating dynamic monitoring of interface states in multilayers. The concurrently developed model enables the quantification of an interface parameter through experimental measurements. Finally, a detailed analysis of the results obtained through this methodology is provided, emphasizing the significant influence of imperfect interfaces on the dynamics of multilayered structures.

The stochastic optimization of a nonlinear energy sink (NES) with a time-dependent stiffness is considered. The NES is linearly coupled to a main system. The optimization aims to find the stiffness properties of the NES that minimize the expected value of the velocity of the main system while accounting for the statistical distributions of the excitation amplitude and frequency. It is shown that the system’s responses are highly sensitive to uncertainty and can even exhibit a discontinuous behavior. This represents a major hurdle for the optimization, which is already hampered by the potentially large computational cost associated with the time integrations. To tackle the high-sensitivity to uncertainties and reduce the computational burden, a dedicated surrogate-based stochastic optimization algorithm is used. Specifically, the approach uses Kriging surrogates built from the unsupervised identification of clusters resulting from response discontinuities. Comparisons between efficiencies of optimal nonlinear absorbers with and without time-dependent stiffness are performed and discussed.

Earth construction benefits of a renewed interest particularly for environmental reasons. However, due to its mainly artisanal construction process, acoustic characterization data of earthen walls are quite rare which can limit their use for projects involving acoustic requirements. Moreover, the great diversity in materials as well as in related construction techniques could result in a large spread in terms of acoustical performances. In this context, acoustic characterizations and modelings are necessary to provide a better understanding on earth materials behaviors. In this study, the results from different modeling approaches are compared to few earth walls sound transmission loss data publicly available. The modeling tools including simplified formulas or more elaborated softwares present different levels of complexities and assumptions sometimes highlighting the specificities of this material. Depending on the construction techniques used (earth blocks, light earth, earth panels etc ...), different assumptions can be appropriate. Extrapolations of performances on several walls for both sound transmission loss and sound absorption provide information regarding tendencies and potentially achievable performances for future earth construction projects. Nevertheless, the comparison between the modeling approaches allows gaining insight on the limits of some approaches and the necessary critical analysis before a possible generalization to other earth walls.

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.

In this study, an acoustic mode of a tube is controlled by a digitally created nonlinear electroacoustic absorber (NEA) at low excitation levels, where the nonlinearity cannot be normally activated in passive vibro-acoustic absorbers. A comparison is carried out between a linear electroacoustic absorber, similar to a tuned mass damper (TMD) in mechanics, and a digital NEA. The innovative method for creating a NEA lies on real-time integration of the dynamics of the device. It permits to choose any behavior of the system by digitally programming the corresponding targeted dynamics. Here, a loudspeaker impedance control law with a cubic stiffness is considered, as this system is well-known in mechanics and provides nonlinear phenomena that are highlighted at low and moderate excitation levels in our study.

A time-dependent periodic chain of coupled nonlinear oscillators including local and global potentials is studied. The continuous form of system equations is projected on an arbitrary mode. Detection of different dynamics are highlighted leading to clarification of equilibrium and singular points of the reduced system. The analytical studies permit prediction/design of periodic and quasi-periodic regimes of the system validated by results obtained through direction numerical integrations.