Sonic black holes (SBHs) are waveguides designed to slow down incident sound waves and dissipate their energy, leading to near-perfect absorption. While numerous studies have focused on the modeling, experimental characterization, design optimization, and comprehension of the internal wave dynamics of isolated SBHs, their interaction with other acoustic systems has received little attention. In this context, SBHs have previously been investigated numerically as a means of reducing noise inside resonant cavities. This work aims to experimentally assess the coupled cavity–SBH problem and evaluate the accuracy of the numerical patch transfer function (PTF) method in describing this interaction. To this end, experimental setups for the SBH, the resonant cavity, and the fully coupled system are presented. The PTF framework is briefly reviewed, and numerical strategies based on the finite element method (FEM) and modal expansion formulations are developed for the SBH and cavity subsystems, respectively. The response of the coupled system is then reconstructed using the PTF approach and compared against experimental measurements. Different SBH configurations are investigated, including variations in their location on the top surface of the cavity and the inclusion of melamine filling between SBH rings. The resulting mean quadratic pressure inside the cavity is then analyzed.

The objective of similitude theory is to establish scaling conditions and laws by which the response of a given system can be scaled to infer that of another, distinct system. Exact similitude laws for the structural acoustic response of thin cylindrical shells exist only in the trivial case where length, radius and thickness are scaled equally, because of the coupling between in-plane and transverse deformations. However, under the bending approximation, which applies when bending wavelengths are one order of magnitude smaller than the length and radius of the shell, thickness can be scaled differently to length and radius. This work focuses on similitude laws and conditions for the structural acoustic response of fluid-loaded cylindrical shells, under the bending approximation. The scaling parameters include the shell dimensions, material parameters and the properties of the acoustic domain. A criterion for validity of the bending approximation based on ring frequencies of the reference and scaled in vacuo shells is proposed. In the case of fluid-loaded cylindrical shells, new similitude conditions and laws are derived for exact scaling of the modal radiation impedance. When these conditions are satisfied, satisfactory re-scaling of both the spatially-averaged vibration response and the radiated sound power is obtained.

Acoustic black hole (ABH) indentations in beams and plates are known to reduce vibrations and sound radiation above their cut-on frequency, f(cut-on). However, their effect on transmission loss between cavities has not been fully explored. This study presents a two-dimensional model, representative of a three-dimensional case, that demonstrates that when the ABH cut-on frequency f(cut-on) is lower than the plate's critical frequency f(crit), an ABH beam can underperform a uniform one in the frequency range f(cut-on) < f < f(crit), leading to lower transmission loss. It is demonstrated that this counterintuitive behavior is linked to the excitation of different types of global modes in the coupled system (Source cavity - ABH beam - Receiver cavity) and to low-frequency non-resonant modes in the ABH beam, which lie in the radiation domain and inhibit the ABH effect. As a result, the acoustic pressure in the receiver cavity becomes higher compared to that for a uniform beam partition. The two-dimensional model is analyzed using a Rayleigh-Ritz formulation that couples the beam's bending displacement to the acoustic particle displacement in the cavities. Natural boundary and traction continuity conditions are imposed weakly, while essential and displacement continuity conditions are enforced using the nullspace method, thus avoiding explicit coupling matrices.

Sonic black holes (SBHs) typically consist of a waveguide with concentric rings that induce a gradual reduction of the local wave speed, resulting in high absorption. Although the black hole effect in SBHs is primarily associated with axial resonances, growing evidence indicates that, in many designs, multidirectional modal interactions and viscothermal losses play a crucial role in shaping the internal acoustic field. To date, these effects have been mainly captured using computationally expensive numerical methods, such as the finite element method (FEM) applied to the linearized Navier–Stokes (LNS) equations. In contrast, this work proposes a multimodal transfer matrix method (MM-TMM) to characterize the acoustic field in SBHs within a reduced-order framework. The MM-TMM combines a multimodal solution for the lateral cavities based on Bessel functions with viscothermal losses introduced via perturbation theory. The model is validated against impedance tube measurements and two FEM-based numerical benchmarks. After validation, the MM-TMM is used to investigate the spatial and spectral distribution of dissipated energy inside the SBH. The results show that the proposed formulation provides accurate predictions while significantly reducing computational cost and enabling direct assessment of the interplay between geometry, modal behavior, and viscothermal dissipation.

Stiffened panels are featured in a wide range of engineering applications to provide structural integrity. However, periodic stiffeners can promote Bloch-Floquet wave propagation, which results in increased far-field noise. Moreover, many stiffened structures, such as the hull of a ship or an underwater vehicle and an aircraft fuselage, are subjected to flow-induced vibrations due to the surrounding fluid motion, resulting in additional vibration and noise. This work aims to control the vibroacoustic response of an infinite fluid-loaded stiffened plate under turbulent boundary layer excitation by embedding acoustic black holes into the stiffeners. An efficient hybrid method whereby the impedances of an acoustic black hole stiffener are extracted numerically and coupled to an analytical model of a stochastically-excited plate is proposed. This extends a previous two-dimensional formulation to now incorporate the bidirectional variation of a turbulent boundary layer excitation. The vibroacoustic response of the three-dimensional stiffened plate obtained by the semi-analytical method is first verified against a full finite element model. The flow-induced vibroacoustic behavior of the plate with acoustic black hole stiffeners is then compared against an equivalent case involving rectangular stiffeners as well as with the results from an unstiffened plate.

Non-negative intensity (NNI) has been previously proposed for identifying the surface areas of a vibrating structure that most significantly contributes to the sound power. Formulations of finite radiating structures under a deterministic load using the boundary element method and infinite radiating structures excited by a stochastic excitation have been developed in the literature. However, these formulations cannot permit the calculation of the NNI of a finite structure excited by a stochastic excitation, which has engineering applications for structures exposed to flow-induced vibrations or machinery noise, typically represented by a turbulent boundary layer excitation or diffuse acoustic field. To fill this gap, two formulations are proposed: one that is an analytical approach based on the wavenumber space formulation and another that is useful for numerical approaches using the realizations of deterministic wall pressure fields. Numerical results for both baffled and unbaffled finite panels under a turbulent boundary layer excitation are presented and compared against a relevant previous investigation.

Two-way fluid-structure interaction (FSI) problems, in the sense that a flow induces the motion of a solid, which in turn modifies the flow boundary conditions, have been approached with very different strategies, the most common of which is probably the finite element method (FEM). In the case of elastoacoustics, the flow consists of an acoustic field interacting with a vibrating structure. When the problem is discretized with the FEM, an algebraic block matrix system is obtained and the coupling between the acoustic field and the structure takes place through a coupling matrix with off-diagonal terms. Usually the structure is characterized by its displacement field, while for the acoustics several options are available, ranging from pressure to acoustic displacement or velocity/displacement acoustic potentials. Depending on the formulation, symmetric or asymmetric systems are obtained and different types of numerical stability problems have to be faced. In this work, a monolithic strategy based on the Rayleigh- Ritz method is proposed. The displacement is used as the primary variable for both the structure and the acoustic field and is expanded in terms of Gaussians as basis functions. This provides an algebraic block matrix system for the global uncoupled problem. However, instead of resorting to a coupling matrix, the essential continuity conditions at the acoustic-structure interface are imposed by the nullspace method (NSM). That is, the solution of the uncoupled system is expanded in terms of a basis of the nullspace generated by the essential conditions of the problem, including the displacement continuity constraints at the interface, thus giving the solution of the coupled problem. As for natural conditions, they are imposed in a weak sense. For ease of explanation, a one-dimensional (1D) case is first introduced, followed by the coupling of a 2D acoustic cavity with a beam and a 3D one with a plate. The proposed method is validated with FEM simulations on fine meshes and the advantage of using Gaussian basis functions over trigonometric ones is also demonstrated.

Stiffened structures are commonly used in engineering applications such as aerospace, marine, automotive and civil engineering. Vibration control of these structures is a critical area of research that aims to enhance their reliability and durability by effectively mitigating vibrations. This work aims to demonstrate the potential of integrating acoustic black holes (ABHs) into stiffened structures by altering only the shape of the stiffeners without adding mass to the host structure or compromising structural integrity. Towards this aim, experimental and numerical analyses are conducted on finite beams coupled with ABH or rectangular pillars. The ABH design has the same mass and moment of inertia at the contact point as the rectangular pillars to establish a comparison. Three configurations are tested for both cases: without damping layers, with viscoelastic damping layers, and constrained viscoelastic damping layers. Experimental results revealed that the beam with ABH pillars, particularly when paired with constrained viscoelastic damping layers, exhibited higher vibration mitigation (up to 33 dB) compared to the vibrational response of a beam with the rectangular pillar with the same constrained viscoelastic damping layers. Numerical simulations using finite element models supported the experimental findings, and provided insight into the vibration mitigation mechanism by examining the mode shapes of the two considered beams. The combined experimental and numeral results highlight the potential of ABH stiffeners as an innovative solution for vibration control in stiffened structures.

Modeling the sound radiated from underwater structures immersed in various environments is necessary in ocean acoustics and naval engineering. Typically, an underwater vibroacoustic system is composed of an elastic cylindrical shell that is radiated into an unbounded fluid domain. However, in contrast to deep oceans, for a shallow water environment, the influence of the sea surface and seabed can no longer by ignored. The significant fluid-structure interaction arising from the coupling at the boundary of the structure and surrounding fluid complicates the prediction of vibroacoustic behaviour. A sub-structuring technique based on the condensed transfer function (CTF) approach and reverse condensed transfer function (rCTF) approach has been proposed recently to tackle complex vibroacoustic problems by coupling/decoupling the necessary subsystems. Its potential is demonstrated in the present study through a two-dimensional case study to predict the sound radiation from an elastic structure of a cylindrical shell excited by a harmonic line force and immersed in a fluid domain of a perfect underwater acoustic waveguide, that is composed of an upper free surface and a lower rigid floor. The targeted model is obtained from a perfect underwater waveguide in which a water disk is subtracted from, and an excited shell is added in place of the water disk. The predictions of the proposed CTF-rCTF process are verified against analytical solutions for two different partitions of the global system and two types of condensation functions.

Sonic black holes (SBHs) typically consist of a waveguide with concentric rings of decreasing radius separated by cavities that slow down incident sound waves, dissipate their energy, and cause minimal reflection. Although there are many works on SBH simulation methods, performance analysis, and design optimization, no one has considered the interaction of SBHs with other systems. The purpose of this paper is to begin to explore this point by considering the connection of an SBH to a resonant cavity and determining the effects the SBH has on the internal acoustic pressure field of the cavity. Since this is a complex problem, it is first proposed to resort to the patch transfer function (PTF) substructuring method to simulate the behavior of the coupled system. After validating the PTF with finite element simulations (FEM) of the entire coupled system, the PTF is used to perform parametric analyses to evaluate the influence of the position and the number of SBHs on the cavity mean quadratic pressure. Although SBHs are typically intended for medium and high frequency pressure reduction in ducts, it is shown that with proper design they can be very effective in dissipating low frequency pressure peaks within the cavity, with potential for room acoustics applications, among others.

The Laboratoire Vibrations Acoustique is a research unit of INSA Lyon, founded in the late 1960s to study vibrations and their consequences on noise emitted by machines and structures. The aim of this article is to review the historical contributions and main developments of the laboratory over the last fifty years. After examining the early years of the laboratory, the authors retrace the developments and key scientific contributions that have enabled it to gain renown at national and international levels in the field of vibration and acoustical engineering.

The theory of similitudes provides simple laws by which the response of one system (usually of small size) can be used to predict the response of another system (usually larger). This paper establishes the exact conditions and laws of similitude for the vibrations and acoustic radiation of a panel immersed in a heavy fluid and excited by a turbulent boundary layer. Previous work on vibroacoustic similitude had not considered the problem of a panel radiating in heavy fluid, for which the radiation impedance of the structure must be scaled. The scaling parameters studied here are the dimensions and thickness of the structure, its material properties, the properties of the acoustic domain, and the convective velocity of the turbulent boundary layer. The corresponding scaling laws are derived analytically and verified numerically; in particular, material properties of scaled panels can be determined with simple geometrical constructions on the diagram of Ashby.

An analytical method for predicting the forced vibroacoustic response of a fluid-filled baffled cylindrical shell submerged in a shallow-water waveguide is presented. The structural equations are governed by a thin shell theory that is decomposed into circumferential modes with a Fourier series and axial modes using a beam function. Heavy fluid fills the exterior and interior domains of the shell. The exterior fluid domain is further constrained by acoustic boundaries of an upper free surface and lower rigid bottom, which together form an ideal shallow-water waveguide. The acoustic boundaries are enforced by employing the image source method and Graf’s addition theorem which reconciles the differing coordinate systems of the many image sources that appear in the analytical expressions for the fluid–structure coupling. Vibroacoustic characteristics due to a mechanical point excitation on the surface of the shell or acoustic excitation from an internal monopole source and influence of different waveguide depths are investigated.

Modeling the vibroacoustic behavior of structures excited by random pressure fields, such as turbulent boundary layers (TBL), is of interest for naval applications. Most works in the literature address the problem by considering periodically stiffened plates or shells. These studies have highlighted the role of Bloch–Floquet waves in increasing radiated pressure in certain frequency bands. However, in industrial applications, the stiffened structure excited by the TBL is generally coupled with internal structures such as bulkheads, floor partitions and engine foundations. To understand how these internal structures can modify the propagation of Bloch–Floquet waves and, consequently, the pressure radiated in the far field, it is necessary to have an efficient simulation tool. We propose developing a dedicated numerical process to estimate the radiated pressure from a cylindrical shell stiffened by axisymmetric/non-axisymmetric internal frames and excited by a homogeneous TBL. The process is based on the wavenumber-point reciprocity principle, which states that the sensitivity functions at a given point M correspond to the spectral responses of the system when excited by a monopole located at M. The condensed transfer functions approach is employed to derive these responses, thereby partitioning the problem: The immersed cylindrical shell is represented by an analytical model, whereas the internal frames are described using finite element models. Numerical results highlight a significant influence of the internal structure on the acoustic radiation of the stiffened shell in far field, induced by the coupling of the circumferential modes.

The acoustic radiation from an immersed cylindrical shell, periodically stiffened by internal axisymmetric frames, has been studied in the past due to its interest in underwater applications. Particularly, it has been shown that Bloch–Floquet waves induced by the periodic arrangement of stiffeners can lead to significant radiation of the shell in the far field. However, the fluid domain in these studies was generally unbounded, which is not representative of practical applications when the submerged structure is close to the sea surface. This work, therefore, investigates the influence on radiated pressure of a free surface close to a periodically stiffened cylindrical shell immersed in water. The shell is excited by a harmonic point force. The free surface corresponds to a pressure released boundary condition. A semi-analytical model is developed based on a frequency–wavenumber decomposition. The cylindrical shell and stiffeners are represented, respectively, by Flügge's analytical model and finite element models. The radiation impedance of the fluid domain including the free surface is evaluated using the image source method. Radiated pressure results are presented as a function of angle and frequency to study the effects of the free surface, specifically on Bloch–Floquet waves.

In engineering, during the design stage of a new product, experiments can be used to verify the prototype’s performances against specifications. However, they can be complex, costly, time-consuming and difficult to implement. Experiments on reduced scale models permit to attenuate these issues, but it is necessary to know the relationship between the responses of the full scale structure and the scaled structure. The aim of similitude theory is to estimate the response of a structure from the response of another one. In this paper, we propose to study similitude laws for the vibration and the acoustic response of a simply supported panel immersed in a light fluid and excited by a turbulent boundary layer. In a first part, a review on the work proposed in the literature on vibration similitude for panels under a turbulent flow is made, whereas in a second part, new acoustic similitude laws are established. These analytical developments show that exact similitude laws exist for the vibration and the acoustic responses if certain conditions are respected. The implication of these conditions for applying the similitude laws in practice is discussed. Furthermore, it is deduced that perfect similitude can be achieved for systems with different dimensions, material properties and surrounding fluid properties. Three numerical examples are proposed to verify and illustrate the proposed scaling procedure.

This study addresses the experimental estimation of the radiated sound power from a panel excited by a homogeneous and fully developed turbulent boundary layer. Two approaches are investigated, one based on vibration measurements and the other on near-field sound pressure measurements. The first method estimates the radiated sound power from the vibration cross-spectral density matrix measured for a regular grid on the panel and the theoretical radiation resistance matrix. To reduce the number of sensors on the panel, a formulation is proposed to estimate the vibration cross-spectral density between two points not measured simultaneously, using additional reference sensors. The second method estimates the radiated sound power from measuring the near-field sound pressure. The far-field sound pressure is extrapolated from the near-field measurements using the Planar Nearfield Acoustical Holography principle. The radiated sound power is then deduced from the far-field pressure. The two methods are first studied numerically to verify their validity and to highlight their limits before being evaluated experimentally in an anechoic wind tunnel.

The reverse Condensed Transfer Function (rCTF) method is a substructuring approach based on the concept of condensed mechanical receptance and acoustical impedance. Its objective is to predict the vibroacoustic response of a subsystem which was initially part of a global system, from information taken from the global system and the subtracted subsystem which must be removed. This paper proposes an extended formulation to improve the convergence of the rCTF method for subtractive modelling. The fundamentals of the rCTF method have been proposed recently considering only the decoupling interface between the global system and the subtracted subsystem. This approach of decoupling, called the local approach, exhibits some numerical issues. In order to circumvent them, the decoupling interface is extended in this study to account for a second interface, internal to the subtracted subsystem. The numerical performances of this extension, called the global approach, are firstly studied on an academic rod decoupling case which allows parametric studies. Then, a comparison between the local and global approaches is proposed for the scattering problem of an acoustic plane wave by a rigid sphere in an infinite water medium.