Control of reflected waves that meet surfaces from oblique directions is crucial, for instance, in closed spaces. Metasurfaces composed of Helmholtz resonators can be efficient and compact absorbers but have limited ability to achieve high absorption over a wide incidence angle range, especially when designed for high performance in the region approaching grazing incidence. In turn, sonic crystals can be used to manipulate wave propagation direction at low frequencies. We propose a type of absorber that combines a surface of 2D Helmholtz resonators and a 2D sonic crystal with cylindrical scatterers arranged in a hexagonal lattice. The combined effect of both structures yields a metasurface that can achieve high absorption over a broad range of incidence angles. Here, an analytic model to estimate the behavior of the absorbers for wavelengths that are much longer than the unit cell dimensions is presented. The model is used in combination with an optimization strategy to realize designs for single frequency and octave-band performance. The test cases show that surfaces with absorption coefficient values above 0.9 for the range of incidence angle extending from 0∘ until 83∘ can be realized. The performance of the absorbers is verified with a finite element model and experimentally.

When modeling sound waves in fluids it can be important to include the viscous and thermal losses originating from the fluids’ interaction with boundaries. In the audible frequency range, the thickness of the boundary layers is between a micrometer and a millimeter. As such the viscous and thermal losses are important when simulating the properties of small acoustical devices such as e.g. hearing aids or transducers. However, the inclusion of viscous and thermal losses is a computationally demanding task as it requires a fine discretization of the boundary layer in order to fully capture the complicated physical phenomena happening on the microscale. Recently, there has been developments to ease the computational demands using both the Finite Element Method and the Boundary Element Method, by approximating the losses using the Boundary Layer Impedance (BLI) boundary condition. In this paper, we extend previous developments for multi-frequency analysis using the Reduced Order Series Expansion Boundary Element Method to handle the BLI condition. This model follows a two-step procedure: Using a series expansion to decrease the assembly time of the BEM matrices and a projection to reduce the overall memory consumption of the model. Results from two acoustic interior problems show that the model decreases the total computational time by around 96% while using less than 15% of the memory. For both test setups the limiting factor of the accuracy was the reduction and not the series expansion.

The shift to virtual meetings, online classes, and remote work has established a new norm, leading to a surge in the use of virtual communication platforms such as Zoom and Microsoft Teams. This shift has increased the demand for high-quality headsets and speakerphones, emphasizing the need for clear, superior audio quality. The process of calibrating material properties typically relies on repetitive simulations guided by experts' intuition, presenting challenges in establishing new Finite Element Models (FEMs) of loudspeakers, as it requires the repeated identification of material property values. We present a systematic framework for calibrating the mechanical material properties of loudspeaker drivers, a crucial prerequisite for developing accurate FEMs of loudspeakers. Specifically, we propose a statistically-driven approach to replace the conventional manual calibration process, which typically relies on multiple simulations guided by expert intuition. Efficient Global Optimization (EGO) is applied to address the expensive optimization problems of loudspeaker simulation. To tackle the curse of dimensionality, the objective function is decomposed into several functions based on effective parameter groups using Global Sensitivity Analysis (GSA) results. The parameters of the FEM are then calibrated to the reference data from the Lumped Parameter Model (LPM) using the decomposed-reduced objective function, providing the calibrated parameters for the loudspeaker simulation. By implementing this novel approach, even individuals without prior knowledge or experience in loudspeaker material properties can effectively and reliably obtain the necessary data for finite element modeling.

This work presents the shape optimization and subsequent experimental validation of an acoustic lens with application to a compact loudspeaker, such as found in commercial speakerphones. The shape optimization framework is based on a combined lumped parameter and boundary element method model using free form deformation geometry parameterization. To test the optimized design, the loudspeaker lens is three-dimensionally printed and experimentally characterized under anechoic conditions on a finite baffle with respect to its off-axis frequency response. The overall tendencies of the frequency responses agree well between measurement and simulations within the optimization frequency range and at low frequencies. The optimization process is applied to a model including acoustic lumped parameter approximations. The shortcomings of the assumptions made in the model are revealed by laser Doppler vibrometer measurements of the loudspeaker driver and modelling of the mechanical vibrations of the lens.

Acoustic metamaterials have emerged as alternative solutions to achieve useful physical effects that differ from the ones obtained with traditional materials. In terms of sound absorption, previous works have addressed their potential as compact surfaces with high performance. Nevertheless, studies on their angle-dependent behavior are scarce. In this work, an analytic model and a numerical model to estimate the performance of periodic surfaces with unit cells composed of 2D Helmholtz resonators are presented. By making use of these modeling tools, the absorption of surfaces with one and three different resonators is studied as a function of both incidence angle and frequency. Changes in the incidence angle can cause variation of the maximum absorption coefficient, the frequencies at which the maximum performance is observed, and the frequency range of significant absorption. Furthermore, the rate at which the performance changes as a function of the incidence angle is larger as the angle increases. Given the angle dependency of these absorbers, a strategy to optimize the dimensions of the surface elements to maximize the absorption performance for predefined ranges of incidence angles and frequencies is presented.

The increasing interest in miniaturizing acoustic devices has made accurate and efficient models of acoustic viscous and thermal losses progressively more important. This is especially the case in micro-acoustic devices such as hearing aids, condenser microphones and MEMS devices. Using the full linearized Navier Stokes equations to numerically model losses comes at a high computational cost. An approximate boundary layer impedance boundary condition representing acoustic losses has therefore become popular due to its high computational efficiency. This is especially true in the context of optimization where an efficient numerical method is required due to the many repeated analyses needed. However, the boundary layer impedance is only valid in the computational region where boundary layers are non-overlapping. Applying the boundary layer impedance can therefore lead to poor optimization results or limit the possible design space if the optimization violates this limitation. Therefore, the benefit of losses in narrow regions cannot be exploited if the boundary layer impedance is used. This work investigates two shape optimization test cases for maximizing the absorption properties of Helmholtz-like geometries based on the Boundary Element Method. The test cases are used to compare and validate the boundary layer impedance against a full viscothermal implementation revealing the benefits of the boundary layer impedance but also its limitations in a structural optimization setting. Based on the numerical experiments it is recommend to avoid the use of the boundary layer impedance in cases where any theoretical boundary layer overlap exists or at least verify simulation and optimization results with a full-losses implementation.

This paper presents a method to perform gradient-based shape optimization to minimize the root mean square deviation of the exterior acoustic sound pressure level distribution in front of an initially spherically shaped loudspeaker. The work includes several examples of how different multi-frequency optimization strategies can affect the final optimized design performance. This includes testing, averaging, and weighting of multi-frequency cost functions or using a minimax formulation. The shape optimization technique is based on an acoustic Boundary Element Method coupled to a Lumped Parameter loudspeaker model. To control and alter the deformation of the loudspeaker cabinet the optimization method adapts a spherical free-form deformation approach based on Bernstein polynomials. For the particular optimization problems presented, it is shown that improvements in the root mean square deviation of the sound pressure level in front of the loudspeaker can be achieved between 1 and 5 kHz. In the best-case scenario, less than a 1 dB sound pressure level (SPL) variation is observed between on-axis and a 70° off-axis response in the range 2 to 5 kHz. The widest frequency bandwidth and smoothest response of the root mean square deviation is found by utilizing the minimax formulation.

Improving the performance of loudspeaker units and cabinet designs traditionally relies on a combination of trial and error, sometimes based on a lumped parameter modelling approach. During the last decades, however, large-scale numerical simulations are playing a growing role as a means of improving performance of complex engineering devices such as loudspeakers. However, a numerical model still relies on the experience of the operating engineer to make the appropriate design changes. This can be a difficult task. The use of numerical simulations combined with optimization has a huge potential for further guiding the design process of advanced industrial products where intuition alone is not sufficient. Nevertheless, broadband acoustic simulations are still very time consuming. In this work, we explore the efficiency of a newly proposed semi-analytical adjoint sensitivity approach based on the boundary element method in combination with a lumped parameter model. The sensitivity analysis is used to shape optimize the cabinet of a loudspeaker using free form deformation. The objective of the optimization is to improve frequency responses and directivity patterns.

It has been shown in several recent publications that acoustic materials consisting of a combination of resonators tuned to different frequencies can render high absorption coefficient values over an extended frequency range while maintaining compactness. This makes them attractive solutions for applications in which low frequency sound control is needed, and/or when there are significant space constraints. Nevertheless, the acoustic performance of these surfaces varies with the angle at which a wave impinges on the surface. The changes in the absorption characteristics with the incidence angle occur both on the maximum absorption coefficient, and on the effective frequency bandwidth. Numerical optimization is a tool that can help realize designs with a large degree of geometrical freedom, and using this framework we have demonstrated an array of coupled 2D Helmholtz resonators that is less sensitive to changes in the incidence angle.

Finite element methods are progressively being utilized to assist in the continuous development of loudspeakers. The core of this paper is the method of lumping certain parts of the finite element model, creating a significant reduction in the model complexity that allows for e.g. faster structural optimization. This is illustrated in the paper with a loudspeaker example where the electromagnetic parts are lumped as well as the spider. It is shown that the simplified model still matches the complex response of the full FE model at very high frequencies.

Inverse design is currently applied to obtain unusual acoustical devices based on ordered and non-ordered scatterers. Recently, flat and lenticular acoustic lenses, de-multiplexors, directional sound sources and acoustic cloaks have been designed using a variety of optimization methods like genetic algorithms, simulated annealing and shape or topology optimizations among others. For example, feasible one-directional cloaks were first designed in two- and three-dimensions using high symmetry objects like cylinders [Appl. Phys. Lett. 99, 074102 (2011)] and toroidal scatterers [Phys. Rev. Lett. 110, 124301 (2013)], respectively. Recently, an extraordinary simple one-directional acoustic cloak has been reported using a technique that combines the method of fundamental solutions with arbitrary shape scatterers [Sci. Rep. 8, 12924 (2018)]. Here, we report a further improvement of the method by combining the Boundary Element Method (BEM) with shape optimization to obtain quasi-omnidirectional cloaks in two-dimensions. The shapes of the scatterers are optimized for the cloaking of the whole setup with waves impinging on the stealth object (a cylinder) from many different directions. An important feature of the method is the possibility of including visco-thermal acoustic losses in the optimization process [J. Sound Vib. 447, 120–136 (2019)].

Acoustic cloaking is a technique that seeks hiding objects in a sound field by reducing or cancelling their scattered sound pressure. Incident waves are restored to as close as possible their original undisturbed form after hitting the cloaked object. One technique for achieving this goal is the design of additional scatterers around the object, which, properly distributed and shaped, can create cloaking at the design frequency. A newly developed numerical technique combining the Boundary Element Method (BEM) with shape optimization is applied in this work for two-dimensional cloaking of a cylinder. The shapes of the scatterers are optimized for the cloaking of the whole setup with waves impinging on the cylinder from several different directions. The results show a measure of the amount of cloaking depending on the direction at the range around the design frequency. The optimization results are compared with existing one-directional cloaks. The impact of visco-thermal acoustic losses in the cloaking design is also evaluated by means of a BEM implementation with losses.

Since the late 1980s, numerical shape optimization has been applied successfully to improve the design and development of novel acoustic devices. Most often, viscous and thermal dissipation effects are neglected in the optimization process, as this is an acceptable assumption in e.g. room acoustics, etc. However, in many acoustic devices, ranging from hearing aids to metamaterials, dissipation can significantly influence the acoustic wave behaviour. In this paper, we propose a numerical acoustic shape optimization technique and we demonstrate it using two-dimensional quarter-wave and Helmholtz resonators including accurate modelling of viscous and thermal dissipation. By combining a dissipative boundary element method with shape optimization, the sound absorption capability of the resonators located at an impedance tube termination is maximized. Numerical experiments demonstrate the importance of viscothermal dissipation and its impact on the optimization outcome. The resulting resonator shapes, optimized using a lossy assumption, yield significantly better performance compared to their lossless counterpart, with near-perfect absorption at the desired optimization frequencies.

In recent years, the boundary element method has shown to be an interesting alternative to the finite element method for modeling of viscous and thermal acoustic losses. Current implementations rely on finite-difference tangential pressure derivatives for the coupling of the fundamental equations, which can be a shortcoming of the method. This finite-difference coupling method is removed here and replaced by an extra set of tangential derivative boundary element equations. Increased stability and error reduction is demonstrated by numerical experiments.

Sound waves in fluids are subject to viscous and thermal losses, which are particularly relevant in the so-called viscous and thermal boundary layers at the boundaries, with thicknesses in the micrometer range at audible frequencies. Small devices such as acoustic transducers or hearing aids must then be modeled with numerical methods that include losses. In recent years, versions of both the Finite Element Method (FEM) and the Boundary Element Method (BEM) including viscous and thermal losses have been developed. This paper deals with an improved formulation in three dimensions of the BEM with losses which avoids the calculation of tangential derivatives on the surface by finite differences used in a previous BEM implementation. Instead, the tangential derivatives are obtained from the element shape functions. The improved implementation is demonstrated using an oscillating sphere, where an analytical solution exists, and a condenser microphone as test cases.

In recent years, boundary element method (BEM) and finite element method (FEM) implementations of acoustics in fluids with viscous and thermal losses have been developed. They are based on the linearized Navier–Stokes equations with no flow. In this paper, such models with acoustic losses are applied to an acoustic metamaterial. Metamaterials are structures formed by smaller, usually periodic, units showing remarkable physical properties when observed as a whole. Acoustic losses are relevant in metamaterials in the millimeter scale. In addition, their geometry is intricate and challenging for numerical implementation. The results are compared with existing measurements.

Viscous and thermal losses of acoustic waves are usually neglected or accounted for as boundary impedance. It is known, however, that acoustic losses become relevant in devices with some dimension in the millimeter range or below. On the other hand, the new class of structures called acoustic metamaterials can be affected by acoustic losses, but in this case the extension of these effects is less known. Acoustic metamaterials are intricate periodic structures where, at frequencies low enough (corresponding to wavelengths much larger than the structure period), elementary units interact producing interesting unusual effects. In this paper advanced modeling tools based on the Boundary Element Method (BEM) and the Finite Element Method (FEM) are used to study the effect of losses in an acoustic metamaterial scaled to different sizes. The conclusions are expected to give insight on the practical limitations when using acoustic metamaterials.