A finite element-boundary element (FE-BE) framework is developed to investigate the vibroacoustic response of a functionally graded acoustic black hole (FG-ABH) panel subjected to thermal loading. The structural response of the panel is obtained using the FE method, while the radiated acoustic field is evaluated through a direct BE formulation. Before the main parametric study, the numerical framework is validated through benchmark comparisons available in the literature and an experimental investigation on a damped one-dimensional ABH beam and plate configurations. The experimental comparison shows that the model can reproduce the ABH-induced vibration localisation observed in the measured operational deflection patterns. The effects of the ABH configuration, damping treatment, thermal environment, and structural stiffening are examined in terms of averaged quadratic velocity (AQV), radiated sound power (RSP), and radiation efficiency. The results show that the FG-ABH panel exhibits a distinct vibroacoustic behaviour compared with the corresponding uniform FG panel. In the lower-frequency range, the local reduction in bending stiffness caused by the ABH profile produces resonance shifts and locally higher vibration amplitudes. With increasing frequency, however, the tapered region promotes flexural-wave localisation, leading to clear reductions in structural vibration and acoustic radiation. Beyond the estimated ABH cut-on frequency of nearly 940Hz, broadband suppression of AQV and RSP is observed. The viscoelastic damping layer further improves the reduction performance, with AQV suppression of nearly 10–15dB in the higher-frequency region. The study further reveals that the unstiffened FG-ABH panel becomes unstable under elevated thermal loading because of thermal softening and stiffness loss in the tapered region. To address this limitation, cross stiffeners are incorporated into the FG-ABH panel. The stiffened configuration preserves the broadband vibroacoustic suppression capability of the ABH while ensuring stable behaviour under thermal conditions. Although thermal loading shifts the structural resonances towards lower frequencies, the broadband sound radiation response remains comparatively less sensitive. The findings indicate that the combined FG-ABH and stiffener configuration can provide an effective passive strategy for reducing vibration and sound radiation in lightweight structures operating under thermal environments.

As part of a joint research project between the Institute of Fluid Mechanics (LSTM) and the Institute of Fundamentals and Theory of Electrical Engineering (IGTE), an international benchmark case for fluid–structure–acoustic interaction was developed. The research focused on an enclosed centrifugal fan, and its aerodynamic, aeroacoustic and structure–acoustic properties were characterised through experimental measurements. This paper provides an overview of the centrifugal fan, its enclosure and the test rig used for the experimental investigations. Rather than interpreting the results, the focus is on presenting the benchmark case and providing an overview of the available data. The entire benchmark dataset is listed and freely accessible via the Zenodo European platform in the EAA benchmark data collection.

The theory of the perturbed convective wave equation for compressible flows (cPCWE) is generalised to spatially varying mean-density fields. The resulting equation is an exact scalar reformulation of the acoustic perturbation equations and describes sound generation and propagation in moving inhomogeneous media using a single unknown. The intermediate variables of the associated workflow, in which a Helmholtz decomposition problem, a Poisson equation and the cPCWE are solved successively, are related to the vortical, entropy and acoustic modes of Kovasznay, providing a physical interpretation of each processing step. The quantitative accuracy is assessed against fully compressible direct numerical simulations (DNS) of two-dimensional isothermal mixing layer and Lighthill's analogy computed in the same framework at Mach numbers between M=0.2 and M=0.4, based on the velocity difference across the layer and the ambient speed of sound. Over this range of Mach numbers, the radiated power spans several orders of magnitude. For M>=0.25, the sound power levels obtained using the three methods agree within 0.9dB, and within 0.5dB for M>=0.3. At M=0.2, where the acoustic fluctuations are weakest relative to the hydrodynamic ones, Lighthill's analogy over-predicts the radiated power by 2.8dB. In contrast, the cPCWE deviates from the DNS reference by only -1.2dB. This closer agreement is because the cPCWE source term is confined to the vortex-pairing region, while convection and refraction are represented by its convective wave operator. Beyond reproducing the far-field sound, the cPCWE resolves the acoustic field within the shear zone itself, where the DNS' fields are masked by vortical fluctuations.

Abstract Double-wall configurations made of advanced composite materials are widely used in aerospace systems and are often subjected to dynamic loadings in thermal environments. Under such conditions, it is important to analyze their vibroacoustic behavior from both structural and noise control perspectives. The present research work investigates the vibroacoustic response of double-wall configurations made of functionally graded (FG) and laminated composite materials subjected to thermomechanical excitation. A coupled numerical model is therefore developed by combining the finite element (FE) method for structural panels with the boundary element (BE) method for the acoustic domain. Thermal effects are introduced through a prescribed temperature gradient across the thickness of the FG panel. Geometric nonlinearity due to thermal loading is incorporated in the first-order shear deformation theory-based displacement model through Green–Lagrange nonlinear strains. The acoustic cavity is modeled using the BE method and coupled with the structural nonlinear strain–based FE model to compute the vibroacoustic response. The results indicate that increased thermal loading enhances structural–acoustic interaction, resulting in higher vibroacoustic energy transmission, with the radiated sound power increasing by up to 50 dB at the first coupled modes compared to ambient conditions. Symmetric laminate configurations in the interior panel exhibit reduced sound radiation characteristics, highlighting their effectiveness in controlling energy transmission under thermomechanical conditions. It is also noted that the material gradation of the excited panel primarily affects stiffness rather than acoustic energy transmission.

Aeroacoustic measurements and numerical predictions are commonly used to determine the sound generation from fluid flows. This work documents the measurement of the aerodynamic sound generation by a circular cylinder in crossflow. Three different velocities are studied, and based on the experimental data, a simplified aeroacoustic sound prediction workflow is presented to estimate the radiated far-field noise. The experimental dataset and the numerical simulation setup in open-source software packages are provided online. The geometrical and flow definitions, along with the experimental dataset, constitute a standardised configuration (called https://doi.org/10.5281/zenodo.13365560) proposed as a validation benchmark for numerical simulation workflows and as a reference for the design of measurement facilities. A strongly simplified 2D numerical simulation using OpenFoam and openCFS is provided with the emphasis to run on a typical personal computer hardware. As a consequence, the provided numerical simulation of the flow is not resolving the turbulent structures nor the 3D characteristics of the flow which are known from experimental and numerical studies.

This work presents two integration methods for field transfer in computational aeroacoustics and in coupled field problems, using the finite element method to solve the acoustic field. Firstly, a high-order Gaussian quadrature computes the finite element right-hand side. In contrast, the (flow) field provided by the finite difference mesh is mapped by higher-order B-Splines or a Lagrangian function. Secondly, the cut-cell or supermesh integration with geometric clipping. For each method, the accuracy, performance characteristics, and computational complexity are analyzed. As a reference, the trapezoidal integration rule was computed from the finite difference results. The high-order quadrature converges as the B-Spline interpolation order increases, and the finite difference results and mesh resolutions are consistent. The supermesh approach eliminates interpolation and approximation errors at the grid-to-mesh level and improves accuracy. This behaviour is universal for smooth or strongly oscillating field quantities, which will be shown in a comparative study between the Lighthill-like source term and the source term of the perturbed convective wave equation for subsonic flows.

Unspecified material properties and boundary conditions are common culprits for inaccurate vibro-mechanical finite-element predictions of thin-walled ducts. Updating inaccurate modeling assumptions can be challenging, especially when damping is non-negligible. This paper proposes a mode-oriented model-updating workflow that utilizes time-harmonic simulations evaluated only at estimated target-mode frequencies of a reference measurement, enabling straightforward consideration of linear damping. Simulated frequencies are paired with measured spectral bins via the maximum spatial coherence of their frequency-response-function vectors to construct the objective functions. Three variants of scalarized objective functions are investigated, optionally considering the frequency mismatches, spatial coherences, and vibration magnitudes of identified pairs. Parameter identification is performed using global optimization and surrogate models based on Random Forest regressors. Applicability is investigated across three damped, thin-walled scenarios of increasing complexity, evaluated at multiple training-simulation set sizes. S1 recovers known flange elasticity and frequency-constant damping in a simplified compound-structure model, S2 identifies 5 equivalent parameters for de-featured flanges and mountings to emulate a more detailed simulated reference, and S3 updates 14 parameters of a real ventilation-duct model, with laser Doppler vibrometry of the impact-hammer excited structure as reference. Validation is performed by comparing frequency-averaged spatial coherences and relative mean-squared errors within proximity bands across the frequency range. Results yield consistently improving surrogate predictions along increasing training-set sizes in all scenarios, successful recovery of target parameters in S1, substantial improvements over a trivial baseline in S2, and moderate improvements in S3. Most robust performance is achieved by combining only frequency-shift and spatial-coherence penalties in the objective function.

Flow-induced noise effects can significantly influence vehicle passengers' comfort. Cavities resulting from clearances in the vehicle body represent one of the major source mechanisms of flow-induced sound generation. The objective of this study is to investigate a generic deep cavity with an overhanging lip, mimicking a door gap in a vehicle, that is overflowed by air at two different free stream velocities, 26.8 m/s and 50 m/s. The turbulent boundary layer and the acoustic waves interact with the cavity and form a dominant feedback mechanism. We focus on the details of the compressible turbulent flow structures and their variations concerning velocity and boundary layer thickness. Identification of different tonal modes and the assignment to their sound generation mechanisms can be challenging due to their complex interaction. We conduct a dynamic mode decomposition (DMD) analysis to get a profound insight into it. This method allows us to link the emitted tonal sounds to their origin. In doing so, we assigned previously unknown peaks in the pressure spectrum to their corresponding mechanisms. A particular vortex-edge interaction was found for the lower approaching velocity (26.8 m/s), namely an alternating sequence of complete clipping and a subsequent partial escape. The results from this study provide a deeper understanding of the flow-induced noise mechanisms in automotive cavities, offering potential pathways for designing quieter vehicles and thus reducing both passenger and community noise.

Inside hydraulic systems, the fluid is capsuled, and sound emissions are driven by wall pressure fluctuations only. Prediction of these excitation forces is essential in the acoustic design process of hydraulic systems. In contrast to most aeroacoustic studies, the fluid in hydraulic systems is weakly compressible and often highly viscous. Wall pressure fluctuation in such systems originate from turbulent structures near walls, vortex wall interaction, and the compressible transfer behavior from source zones inside the volume to the walls. In this work, a two-chamber piston system, which is used in mechatronic knee prostheses, is investigated. The system is prone to flow-acoustic instability in an L-bend, which can lead to tonal sound emissions. A weakly compressible flow simulation is performed to predict the flow field and the wall pressure fluctuations. The flow-acoustic transfer behavior is modeled by a viscous acoustic approximation model using source distribution based on the Stochastic Noise Generation and Radiation (SNGR) model. The flow field is dominated by laminar flow, while turbulent flow is localized to certain regions. A flow-acoustic feedback mechanism causes Kelvin-Helmholtz instability in a mixing layer flow. The viscous acoustic approximation model is capable of predicting the compressible transfer behavior of the system and also identify the relevant acoustic mode interacting with the mixing layer. With the presented simulation model, the compressible transfer behavior of the system can be predicted and flow-acoustic feedback mechanisms can be identified.

Wind noise impairs the functionality of hearing aids and hearables outdoors or during sports by interfering with communication signals. This study aims to visualize the wind noise generation patterns around the human head by validated scale-resolved flow simulations. For the first time, the three-dimensional turbulent flow field at wind speeds of 10 km/h and 20 km/h around a female, a male and an artificial head is analyzed. It is possible to extract non-accessible data even inside the body, e.g., the pressure field deep inside the ear cavity in front of the eardrum. Head-geometry-independent flow features are identified. In the temple area, large-scale vortex shedding occurs. Small-scale vortices detach at the upper edge of the pinna and across the entire ear area. At typical microphone positions of behind the ear worn hearing devices, the pressure fluctuations are more pronounced than those at the auditory canal entrance. The tragus of the pinna plays a decisive role in attenuating wind noise in front of the entrance to the auditory canal. Anatomically exact ear canals ensure that velocity fluctuations are attenuated more effectively compared to an artificial one. At 20 km/h, the A-weighted pressure levels recorded at the microphone location of a behind the ear worn hearing devices exceed 85 dB(A). The results lead to a first understanding of wind noise effects and how they increase the perception threshold for recognition. Manufacturers can use the model to facilitate the wind noise optimal placement of microphones in new products to enhance communication under windy conditions.

Impedance tube measurements are a widespread method for determining the sound absorption coefficient (SAC) of porous materials for normal sound incidence. The measurement method is standardised in ISO 10534-2. However, the standards offer limited guidance on sample preparation and mounting. Many impedance tubes have a circular cross-section and can be mounted at various angles. Therefore, it is crucial to investigate the influence of the mounting angle on the SAC and its interaction with diameter imperfections and different thicknesses using different materials. Following the dataset FOAM 01 this work documents the creation of a new dataset (called FOAM 02) containing SAC measurements from the ISO 10534-2 two-microphone method. The following factors are considered: two different materials, four thicknesses, three diameters, and four rotation angles. For each combination of material, thickness, and diameter, three specimens are produced, resulting in 72 specimens. Each specimen is measured three times at each rotation angle, yielding 864 SAC measurements. The dataset contains the SAC measurements and one-hot encoded label vectors, and is publicly available. A cutting device is proposed to saw cylindrical specimens accurately on a band saw with variable thickness and diameter. The workshop drawings of the cutting device are available as supplementary material.

A hybrid computational approach that integrates the finite element method (FEM) with least squares support vector regression (LSSVR) is introduced to solve partial differential equations. The method combines FEM's ability to provide the nodal solutions and LSSVR with higher-order Legendre polynomial kernels to deliver a closed-form analytical solution for interpolation between the nodes. The hybrid approach implements element-wise enhancement (super-resolution) of a given numerical solution, resulting in high resolution accuracy, while maintaining consistency with FEM nodal values at element boundaries. It can adapt any low-order FEM code to obtain high-order resolution by leveraging localized kernel refinement and parallel computation without additional implementation overhead. Therefore, effective inference/post-processing of the obtained super-resolved solution is possible. Evaluation results show that the hybrid FEM-LSSVR approach can achieve significantly higher accuracy compared to the base FEM solution. Comparable accuracy is a achieved when comparing the hybrid solution with a standalone FEM result with the same polynomial basis function order. The convergence studies were conducted for four elliptic boundary value problems to demonstrate the method's ability, accuracy, and reliability. Finally, the algorithm can be directly used as a plug-and-play method for super-resolving low-order numerical solvers and for super-resolution of expensive/under-resolved experimental data.

Sound-absorptive materials such as foam can be described by the equivalent fluid (EF) model. The homogenized fluid’s acoustic behavior is thereby described by complex-valued, frequency-dependent acoustic material parameters. When transforming the acoustic wave equation for the EF model from the frequency domain to the time domain, convolution integrals arise. The auxiliary differential equation (ADE) method is used to circumvent the direct calculation of these convolution integrals. The wave equation and the coupled set of ordinary ADEs are solved in the time domain using the finite element (FE) method. The approach relies on approximating the complex-valued frequency response functions of the inverse equivalent bulk modulus and density by a sum of rational functions consisting of real and complex poles. The order of the rational function approximation defines the number of additionally introduced auxiliary variables per nodal degree of freedom. The presented FE formulation includes a narrow-band non-reflecting boundary condition (NRBC) for normal incidence. The implementation in openCFS shows optimal temporal and spatial convergence for a semi-infinite duct based on the analytic plane wave solution for harmonic excitation. The simulation of a pressure pulse propagating in an infinite EF domain with a scatterer demonstrates the capability for multidimensional, actual transient problems.

Shell-like housing structures for motors and compressors can be found in everyday products. Consumers significantly evaluate acoustic emissions during the first usage of products. Unpleasant sounds may raise concerns and cause complaints to be issued. A prevention strategy is a holistic acoustic design, which includes predicting the emitted sound power as part of end-of-line testing. The hybrid experimental-simulative sound power prediction based on laser scanning vibrometry (LSV) is ideal in acoustically harsh production environments. However, conducting vibroacoustic testing with laser scanning vibrometry is time-consuming, making it difficult to fit into the production cycle time. This contribution discusses how the time-consuming sampling process can be accelerated to estimate the radiated sound power, utilizing adaptive sampling. The goal is to predict the acoustic signature and its uncertainty from surface velocity data in seconds. Fulfilling this goal will enable integration into a product assembly unit and final acoustic quality control without the need for an acoustic chamber. The Gaussian process regression based on PyTorch 2.6.0 performed 60 times faster than the preliminary reference implementation, resulting in a regression estimation time of approximately one second for each frequency bin. In combination with the Equivalent Radiated Power prediction of the sound power, a statistical measure is available, indicating how the uncertainty of a limited number of surface velocity measurement points leads to predictions of the uncertainty inside the acoustical signal. An adaptive sampling algorithm reduces the prediction uncertainty in real-time during measurement. The method enables on-the-fly error analysis in production, assessing the risk of violating agreed-upon acoustic sound power thresholds, and thus provides valuable feedback to the product design units.

The generalization of Physics-Informed Neural Networks (PINNs) used to solve the inhomogeneous Helmholtz equation in a simplified three-dimensional room is investigated. PINNs are appealing since they can efficiently integrate a partial differential equation and experimental data by minimizing a loss function. However, a previous study experienced limitations in acoustics regarding the source term. A challenging but realistic excitation case is a confined (e.g., single-point) excitation area, yielding a smooth spatial wave field periodically with the wavelength. Compared to studies using smooth (unrealistic) sound excitation, the network’s generalization capabilities regarding a realistic sound excitation are addressed. Different methods like hyperparameter optimization, adaptive refinement, Fourier feature engineering, and locally adaptive activation functions with slope recovery are tested to tailor the PINN’s accuracy to an experimentally validated finite element analysis reference solution computed with openCFS. The hyperparameter study and optimization are conducted regarding the network depth and width, the learning rate, the used activation functions, and the deep learning backends (PyTorch 2.5.1, TensorFlow 2.18.0 1, TensorFlow 2.18.0 2, JAX 0.4.39). A modified (feature-engineered) PINN architecture was designed using input feature engineering to include the dispersion relation of the wave in the neural network. For smoothly (unrealistic) distributed sources, it was shown that the standard PINNs and the feature-engineered PINN converge to the analytic solution, with a relative error of 0.28% and 2×10−4%, respectively. The locally adaptive activation functions with the slope lead to a relative error of 0.086% with a source sharpness of s=1 m. Similar relative errors were obtained for the case s=0.2 m using adaptive refinement. The feature-engineered PINN significantly outperformed the results of previous studies regarding accuracy. Furthermore, the trainable parameters were reduced to a fraction by Bayesian hyperparameter optimization (around 5%), and likewise, the training time (around 3%) was reduced compared to the standard PINN formulation. By narrowing this excitation towards a single point, the convergence rate and minimum errors obtained of all presented network architectures increased. The feature-engineered architecture yielded a one order of magnitude lower accuracy of 0.20% compared to 0.019% of the standard PINN formulation with a source sharpness of s=1 m. It outperformed the finite element analysis and the standard PINN in terms time needed to obtain the solution, needing 15 min and 30 s on an AMD Ryzen 7 Pro 8840HS CPU (AMD, Santa Clara, CA, USA) for the FEM, compared to about 20 min (standard PINN) and just under a minute of the feature-engineered PINN, both trained on a Tesla T4 GPU (NVIDIA, Santa Clara, CA, USA).

The co-rotating vortex pair arrangement is a frequently applied test case in computational aeroacoustics. Its flow quantities and far-field radiated sound pressure can be computed analytically, assuming delta-distribution potential vortices. When this configuration is used for verification in a numerical computation, the singular vortex cores cannot be modeled directly; they have to be desingularized, which affects the associated flow and acoustical fields. Closed-form expressions for the aeroacoustic source terms are derived for the Scully vortex model and used for detailed numerical computations of the radiated sound pressure. The effects of desingularization and finite source region size are analyzed in the frequency domain for Lighthill’s equation and the perturbed convective wave equation by means of an efficient numerical approach that computes the convolution of the aeroacoustic source terms and the 2D free-field Green’s function. It is shown that the deviations of the far-field radiated sound pressure from the idealized analytical solution depend on the Mach number, vortex core radius, and truncation limit of the source region. A significant increase in the effective size of the source region due to the desingularization is demonstrated. Minimal error bounds compared to the analytic far-field pressure solution are established. The presented converged numerical results serve as reference solutions for validating implementations of hybrid computational aeroacoustic workflows.

Many numerical simulation tools have been developed and are on the market, but there is still a strong need for appropriate tools capable of simulating multi-field problems, especially in aeroacoustics. Therefore, openCFS provides an open-source framework for implementing partial differential equations using the finite element method. Since 2000, the software has been developed continuously. The result is openCFS (before 2020, known as CFS++ Coupled Field Simulations written in C++). In this paper, we present pyCFS-data, a data processing framework written in Python to provide a flexible and easy-to-use toolbox to access and manipulate, pre- and postprocess data generated by or for usage with openCFS.