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This paper presents a mass-spring model to predict the normal incidence acoustic response of a metamaterial composed of a compact linear periodic array of dead-end resonators. The dead-end resonators considered are ring-shaped Helmholtz resonators. The model is based on a mass-spring analogy and considers the thermoviscous losses in the metamaterial following an effective fluid approach. A matrix equation of acoustic motion is derived for the finite case of N-periodic arrays. Under external excitation, its direct solution predicts the sound absorption coefficient and transmission loss. Under the homogeneous case, the solution of its associated eigenvalue problem predicts the acoustic eigenfrequencies and mode shapes. The dispersion relation is also solved to predict the beginning of the first stopband, and a low frequency approximation allows development of a formula to estimate the first eigenfrequency. The results show that the system with N degrees of freedom has three stopbands over the frequency range studied, with zero sound absorption and transmission. The model also helps to understand how the acoustic dissipation, at a given resonant frequency, is affected by the position of the acoustic velocity nodes (eigenmodes) in the geometry of the metamaterial. Prototypes are designed, manufactured, and tested in an impedance tube to validate the model.

A technique for estimating the sound absorption of materials under oblique incidence plane wave and diffuse field excitations is proposed. It requires a mobile loudspeaker and a pair of fixed microphones above a layer of absorbing material. Starting from sound pressure measurements made above the material surface for multiple source positions and by inverting Allard’s propagation model, the proposed method allows for the identification of two effective (or equivalent) parameters, namely, the complex effective density and the complex wave number. Obtaining these parameters makes it possible to estimate the sound absorption coefficient for a plane wave with any angle of incidence or under a diffuse acoustic field by summation over the angles. The results are compared to theoretical values calculated using the Johnson-Champoux-Allard model and to reference measurements obtained using an impedance tube, a small cabin, a large reverberant room, and a sound field synthesis method. One of the limitations of this method lies in the assumptions associated with the Allard model to describe the sound field above the material (assumed to be isotropic, homogeneous, of constant thickness, and to behave like an equivalent fluid). The main advantages are (1) that the sound absorption coefficient can be estimated under oblique incidence plane wave and diffuse acoustic field with values that are always in a physical range (between 0 and 1), and (2) that samples of the order of the square meter without specific preparation can be tested which reduces the constraints associated with impedance tube or reverberant room measurements

To protect workers, it is necessary to characterize the noise and vibration emissions value of nailers. Standardized characterization methods exist but require three trained human operators, which leads to a dispersion in the results and a difficult implementation. An automatic test stand (ATS) was developed to characterize those values without the participation of human operators. It is proposed here that we compare the results obtained by the two methods. Preliminary results suggest that further refinement of the ATS is needed to better mimic the biodynamics of the human hand–arm and that a larger number of operators would be required for validation.

Structure borne noise induced by vibrating systems is considered as a major contribution to the noise generated inside vehicles and can be assessed using Transfer Path Analysis (TPA) methods. Their theoretical formulation requires the mobility of either the vibrating system, the receiving structure or the assembly of the two components according to all Degrees of Freedom (DoFs). However, rotational and in-plane DoFs cannot be measured easily and their determination may result in a more complex experimental set-up or an increase in measurement uncertainties. The need for assessing the full mobility matrices thus deserves to be investigated. In this work, the robustness of multiple TPA methods dedicated to the design and validation phases of aircraft light equipment is investigated numerically according to the mobility matrices completeness and by considering several configurations of assemblies (i.e., different active source properties, different numbers of contact points). Numerical models have been developed to simulate a source with controlled vibratory behavior and the spatial averaged mean-square velocity on the receiving structure is used as an objective indicator of the method’s robustness. For proper predictions accuracy, it is shown that the required completeness should account for the terms of highest amplitude and thus depends on the (i) TPA method, (ii) active behavior of the source and (iii) coupling configuration. A completeness involving all the DoFs is generally required for TPA methods based entirely on the mobility of the decoupled components. Otherwise, the omission of rotational or in-plan DoFs could be suitable for TPA methods based on the mobility of the assembly.

Acoustic properties of the metamaterial graded absorber, also known as ``acoustic black hole'', are studied in the linear regime. The absorber consists of thin metallic circular plates, each with a central perforation, separated by annular air cavities. Radius of the perforation in each plate is gradually decreasing with the distance from the plate to the front surface, forming a central channel with a staircase radius profile. A semi-analytical equivalent fluid model accounting for the variations of both the effective density and compressibility of air inside this channel is developed, which incorporates the staircase variations of the perforation radius with distance and assumes motionless plates. The viscous and thermal losses inside the side cavities and the central channel are accounted for using a well-established Johnson-Champoux-Allard-Lafarge model. It is demonstrated that high absorption coefficient values are achieved in a wide range of frequencies starting from a few hundred Hz or less. At low frequencies, the resonances along the length of the structure, i.e. global resonances, are responsible for sound attenuation. At higher frequencies, the resonances of the lateral cavities, i.e. local resonances, play a major role. The upper boundary of the frequency range of high sound absorption is determined by the resonance frequency of the front annular plate. The model is validated against impedance tube measurements on five samples of different geometry and FEM models. FEM model predicts that the elasticity of the plates affects the absorption coefficient behaviour in the frequency range of plate resonances and at frequencies well below the plate resonances.

Developing innovative noise policies that build on international best practices is difficult when policies around the world differ along many dimensions, ranging from different sources covered to different levels of governance involved. This is particularly critical in the context of road traffic, identified as one of the main culprits leading to noise-associated complaints and health issues. In this article, we document the wide range of specifications observed in road traffic policies and propose a methodology to compare noise limits across noise policies. First, we present the responsibilities of administrative governments according to the scope (e.g., emission vs. exposure). Second, we compare noise limits by scope and geographic areas by separating acoustic indicators (overall and event indicators). Third, we convert overall outdoor noise limits into a common basis using the method described by Brink and his associates (2018) and compare them with the World Health Organization (WHO)’s recommendations (2018). Finally, measurement protocols are also compared across outdoor noise policies. This paper shows that road noise is managed at several administrative levels using approaches that are either centralized or decentralized. We also observed disparities in the associated noise limits across geographic areas. The converted outdoor noise limits generally exceeded the WHO’s recommendations (2018). Finally, this paper outlines how outdoor measurement protocols vary across geographic areas. However, similarities were identified between state and provincial noise policies within the same country.

This article proposes a hybrid numerical-analytical approach to effectively predict the sound absorption coefficient of complex periodic metamaterials with a reasonably low computation time. A variation of an existing metamaterial, consisting of a periodic succession of necks and cavities, is also proposed. The design variation was intended to decrease the frequencies of the absorption coefficient resonant peaks and consists in adding eccentricity in the neck position. The hybrid approach combines a thermoviscous-acoustic (TVA) approach with the transfer matrix (TM) method. The TVA approach estimates the thermoviscous losses of acoustic waves in a periodic unit cell (PUC) of the metamaterial. The TM method is used to simulate the acoustic behaviour of the complete metamaterial from the TM of the PUC calculated numerically. The approach is compared to impedance tube measurements on prototypes of the metamaterial. The comparison shows that the proposed approach is in good agreement with the measured sound absorption coefficient. In addition, numerical simulations and experiments demonstrate that the proposed variation of the existing metamaterial results in a shift of the absorption peaks down in frequency without deteriorating their sound absorption performance.

Structure borne noise is considered a major contribution to the noise generated inside aircrafts. In order to analyze it, engineering methods have been developed such as Transfer Path Analysis (TPA) and Source Characterisation (SC). These methods are based on active and passive properties of the source and the receiving structure being coupled or decoupled. The theoretical formulation requires mobility according to all Degrees Of Freedom (DOFs) and rotational DOFs represent a challenge for experimental application. To fulfill the mobility matrix, indirect method have been developed and specific sensors have been proposed, resulting in a more complex experimental set-up and an increase in measurement uncertainties. The necessity of assessing the full matrix completeness is thus still questionable. The robustness of these methods with respect to the matrix completeness and the source behavior is investigated numerically in this work. A numerical model has been developed to simulate vibrating sources with simple or complex vibratory behavior and to assess the mobility matrices for any completenesses. Velocity on the receiving structure is used as a target indicator. The influence of source behavior and completeness are discussed and the results show that the required mobility completeness depends on the source behavior.

The noise control at multiple tonal frequencies simultaneously, in the low frequency range, is a challenge for aerospace, ground transportation and building industries. In the past few decades, various low frequency noise control solutions based on acoustic metamaterial designs have been presented in the literature. These solutions showed promising performance and are considered a better alternative to conventional sound insulation materials. In the present investigation, it was noticed that subdividing the cavity of a Helmholtz resonator allowed the control of multi-tonal noise at several resonance frequencies simultaneously and a shift of the resonance peaks towards the low frequencies. This paper proposes concepts of Helmholtz resonators with subdivided cavities to improve the sound transmission loss (STL) performance and simultaneously control the noise at several tonal frequencies. HRs with cylindrical shaped cavities were embedded in a layer of porous material. The STL of the metamaterial noise insulation configuration was predicted using serial and parallel assemblies of transfer matrices (TMM) incorporating a thermo-viscous-acoustic approach to accurately account for the viscous and thermal losses of acoustic wave propagation within the metamaterial. The STL calculated using the proposed TMM approach were observed to be in excellent agreement with the finite element method (FEM) numerical results.

As standard ASTM E2611 reveals, the normal incidence sound transmission loss measured on a small sample in an acoustic tube is not only a property of the material but also strongly dependent on boundary conditions (generally unknown) and on the way the material is mounted. This article proposes an experimental method to control the effects of the lateral boundary conditions in an acoustic tube. The main objective is to deduce the properties of a “client element” (material sample) from the measured global acoustic properties of a patchwork composed by the “client material” and a known “host support.” Three patchwork configurations have to be distinguished: patchworks with and without an impervious and rigid interface between the elements and patchworks composed by elements that cannot be identified as equivalent fluids. For each of these configurations, the use of a specific method based on the Mixing Rule Method (MRM) or on the Parallel Transfer Matrix Methods (P-TMM or dP-TMM) used in reverse way is proposed. Numerical and experimental validations are proposed in acoustic tubes on a convenient configuration: a material sample surrounded by an air ring. This configuration allows reducing the material elastic-frame behavior to leave a limp-frame behavior. The proposed methods allow removing the effect of the lateral air ring host surrounding the material. For homogeneous materials, the two methods based on MRM and dP-TMM give similar good results. For non-homogeneous materials or for materials that cannot be modeled as equivalent fluids, only the method based on dP-TMM gives good results.