Vibro-acoustic Model Research Articles

Modelling of noise due to impulsive excitation using nonlinear time series analysis

Early acoustic machine design phases should target safety and comfort requirements, minimising the risk of hearing damage and noise exposure and ensuring a pleasant machine sound. Therefore, physical mechanisms of sound generation, propagation and radiation need to be modelled. Today, nonlinear physical relations in vibroacoustic models such as contact problems are mostly linearised. The aim of this paper is to increase the prediction quality of vibroacoustic models so that physical mechanisms behind sound generation due to complex physical, nonlinear phenomena can be better understood. The focus is on sound generation due to impulsive excitation, which is a significant sound generation mechanism in machinery, e.g. considering gears, forming processes (e.g. punching), or road loads of vehicles. We describe a model setup to simulate impulsive excitation on a laboratory scale, where structural vibrations can be analysed. Physical correlations including nonlinear correlations could be identified using nonlinear time series analysis. Recurrence plots will be used to identify features such as phase space contraction, e.g. to identify damping. These features form the basis to deepen the physical understanding of machinery noise, to contribute to enhanced acoustic machine designs and to enhance data-driven modelling using sparse regression in future research.

A multi-physics approach for modelling noise mitigation using an air-bubble curtain in impact pile driving

Underwater noise from offshore pile driving has raised significant concerns over its ecological impact on marine life. To protect the marine environment and maintain the sustainable development of wind energy, strict governmental regulations are imposed. Assessment and mitigation of underwater noise are usually required to ensure that sound levels stay within the noise thresholds. The air-bubble curtain system is one of the most widely applied noise mitigation techniques. This paper presents a multi-physics approach for modeling an air-bubble curtain system in application to offshore pile driving. The complete model consists of four modules: (i) a compressible flow model to account for the transport of compressed air from the offshore vessel to the perforated hose located in the seabed; (ii) a hydrodynamic model for capturing the characteristics of bubble clouds in varying development phases through depth; (iii) an acoustic model for predicting the sound insertion loss of the air-bubble curtain; and (iv) a vibroacoustic model for the prediction of underwater noise from pile driving which is coupled to the acoustic model in (iii) through a boundary integral formulation. The waterborne and soilborne noise transmission paths are examined separately, allowing us to explore the amount of energy channeled through the seabed and through the bubble curtain in the water column. A parametric study is performed to examine the optimal configuration of the double bubble curtain system for various soil conditions and pile configurations. Model predictions are compared with measured data. The model allows for a large number of simulations to examine different configurations of a single bubble curtain and a double big bubble curtain.

On a hybrid updating method for modeling vibroacoustic behaviors of composite panels

Composite panels, by virtue of their outstanding mechanical properties, have found various applications in different sectors like aerospace and transportation. Under certain assumptions like Kirchhoff–Love and Mead–Markus hypotheses, certain high-order differential equations can be used for vibroacoustic modeling of composite panels. However, for accurate modeling, updating parameters is an essential stage. Herein, we aim to theoretically and experimentally review this stage. For this purpose, a hybrid updating method is proposed, incorporating hierarchical functions, inhomogeneous wave correlation approach, and least squares optimizations. Then various laboratory measurements, including Laser Doppler Vibrometry measurements as well as sound pressure levels, are analyzed. The measurements were performed for a thick composite (sandwich) panel, and a thin composite (laminate) one, along with two isotropic (steel and aluminum) plates for additional validation. The experiments indicate the ability of the hybrid approach to adjust parameters and precisely model vibroacoustic behaviors of the panels. Furthermore, the proposed hybrid method can be used in studies whose goal is accurate vibroacoustic modeling for psychoacoustic issues and perceptual validations, which is also one of the future targets of this research.

Numerical Analysis of Wind Noise Transmission through BEV Underbody

In electrified automobiles, wind noise significantly contributes to the overall noise inside the cabin. In particular, underbody airflow is a dominant noise source at low frequencies (less than 500 Hz). However, the wind noise transmission mechanism through a battery electric vehicle (BEV) underbody is complex because the BEV has a battery under the floor panel. Although various types of underbody structures exist for BEVs, in this study, the focus was on an underbody structure with two surfaces as inputs of wind noise sources: the outer surface exposed to the external underbody flow, such as undercover and suspension, and the floor panel, located above the undercover and battery. In this study, aero-vibro-acoustic simulations were performed to clarify the transmission mechanism of the BEV underbody wind noise. The external flow and acoustic fields were simulated using computational fluid dynamics. The vehicle structural vibration and sound fields of the interior and exterior cabin were analyzed using vibroacoustic models consisting of three subsystems modeled by the finite-element or boundary-element method: The first is an underbody structure finite-element model containing a white body, suspension, battery, and undercover; the second is the interior cabin space boundary-element model; the third is the exterior cabin space finite-element model for analyzing acoustic radiation resulting from vehicle structural vibration for the small space between the floor panel and battery, the motor room and the under-vehicle space between the ground and undercover. The analysis results using the vehicle model reveal that the pressure fluctuations acting on the floor panel are more-dominant inputs for cabin noise than those acting on the outer surface. The pressure fluctuation acting on the floor panel is affected by the acoustic mode of the space between the battery and the floor panel.

Statistical energy analysis simulation of an air-handling cabinet

Statistical energy analysis (SEA) is a vibro-acoustic modeling technique suitable for systems where high modal densities exist. Traditionally SEA is used for predicting system response in higher frequency bands. However, for systems such as an air-handler that contain large, flat panels constructed of sheet metal the usefulness of SEA stretches into mid and lower frequency bands as well. Measured results of an air-handling cabinet were obtained by spatially averaging accelerations of cabinet surfaces caused by an input of white noise into the cabinet side by a shaker. Energy from each sub-panel of the cabinet was normalized with the panel into which the energy was input for easy comparison with modeled data. A simplified model of the air-handling cabinet processed in VA One software yielded results generally within 10 dB of measured results. Some lower frequency band limitations were realized due to cabinet geometry and construction. These results focus primarily on the structure and less so on the acoustic volume of the air-handling cabinet.

Light rail wheel/rail noise radiation model using a coupled FE-BE method

This paper presents the development of a coupled finite element - boundary element model of rolling noise from a resilient light rail wheel on several types of tracks. The vibro-acoustic model utilizes a 3D elastic solid representation for both wheel and rail which are excited by linearized Hertzian interface loads. Estimates of the radiated sound power, radiation efficiencies and wayside noise levels are obtained and then scaled using a parallel impedance framework and a roughness profile. Results are compared to recently measured vehicle passby noise and track decay rates at Sound Transit in Seattle Washington.

The influence of contact relaxation on underwater noise emission and seabed vibrations due to offshore vibratory pile installation

The growing interest in offshore wind leads to an increasing number of wind farms planned to be constructed in the coming years. Installation of these piles often causes high underwater noise levels that harm aquatic life. State-of-the-art models have problems predicting the noise and seabed vibrations from vibratory pile driving. A significant reason for that is the modeling of the sediment and its interaction with the driven pile. In principle, linear vibroacoustic models assume perfect contact between pile and soil, i.e., no pile slip. In this study, this pile-soil interface condition is relaxed, and a slip condition is implemented that allows vertical motion of the pile relative to the soil. First, a model is developed which employs contact spring elements between the pile and the soil, allowing the former to move relative to the latter in the vertical direction. The developed model is then verified against a finite element software. Second, a parametric study is conducted to investigate the effect of the interface conditions on the emitted wave field. The results show that the noise generation mechanism depends strongly on the interface conditions. Third, this study concludes that models developed to predict noise emission from impact pile driving are not directly suitable for vibratory pile driving since the pile-soil interaction becomes essential for noise generation in the latter case.

Trends in the 40 + -year development of advanced structural acoustic and vibration computational modeling

Over the course of the past 40-45 years of computational modeling in the fields of structures, structural acoustics, and vibrations, there have been extreme advancements made in numerous areas that have greatly increased and improved the size, accuracy, efficiency, and complexity of numerical solutions possible. Most of this progress has been made through a combination of improvements in the distinct areas of computer processing approaches/speed and available memory, primarily evolutionary enhancements in detailed numerical material and continuum mechanics models, development of entirely new physics-based numerical vibroacoustic modeling approaches, etc. This paper presents a historical review of the detailed progress made in computational structural acoustics and vibration from the “early days” in the 1980s through current state-of-the-art advanced numerical approaches, much of which would not have been dreamed possible back four decades ago! While most of the examples utilized in this talk are pulled from the speaker’s specific technical area of undersea vehicle/ system structural acoustics, the overall trends presented are certainly represented across the broad spectrum of vibro-acoustics modeling applications.

Advanced applications of the continuous-scan acoustic measurement method

This presentation will cover recent progress in the development of continuous-scan acoustic measurement (CSAM) methods for imaging, reconstruction, and localization of spatially complex sound fields. CSAM comprises an acoustic array of slowly moving and fixed sensors coupled with position tracking to enable high-spatial-resolution partial field measurements for visualization and source characterization. In previous work, ATA has developed and demonstrated the use of a rotating array for beamforming and acoustical holography. This presentation will focus on one or more advanced applications of CSAM. Examples may include (1) quantifying spatial coherence from sound fields generated by multiple uncorrelated sources, (2) combining multiple test runs to visualize larger 2D spatial apertures and/or 3D sound fields, (3) combining high-resolution measurements with vibroacoustic models to predict scattered sound fields, and (4) exploring alternate array configurations (e.g., a spherical-surface measurement aperture).

Bandwidth widening for sound absorption of a flexible microperforated panel backed by a multi-frequency panel-type resonator

A microperforated panel (MPP) often suffers from a limited absorption bandwidth and poor sound absorption in the low frequency range. The present study aimed to propose an MPP-panel-type resonator (PR) compound structure that can simultaneously widen the half-absorption bandwidth and improve the poor absorption at the low frequency range. A vibroacoustic model is developed and compared to finite element simulations to demonstrate its accuracy. The vibration characteristics of the compound structure and the surface impedance are analyzed to reveal the mechanism forming the absorption characteristics of an MPP-PR structure. It is found that backing an MPP with a panel-type resonator (PR) creates a low frequency absorption peak but followed by an absorption valley that decreases the absorption bandwidth. The analysis showed that the phase difference between velocity of air particles in perforation and the PR panel velocity dictates the absorption characteristics associated with the PR resonance. A multi-resonators panel-type resonator (MPR) is found that the absorption valley associated with the host panel resonance splits into multiple smaller amplitude absorption dips improving absorption performance. The proposed MPP-MPR compound structure demonstrated a relatively wider half-absorption bandwidth with improved low frequency absorption.

On the vibro-acoustic modeling of panels excited by diffuse acoustic field (DAF)

Composite materials along with isotropic materials possess abundant applications to various engineering disciplines like aerospace and mechanical issues. The design optimization of composite materials such as sandwich panels essentially needs an accurate vibro-acoustic modeling. Such a modeling of these materials and a sound synthesis can lead to a design approach based on relevant psychoacoustic analyses. In this research, the mathematical/numerical and experimental steps required by the vibro-acoustic modeling of composite and isotropic plates excited by a diffuse acoustic field (DAF) are discussed. Herein, the analytical modeling was performed by 4th and 6th order problems adapted for the composite and isotropic plates, and moreover, the numerical modeling was carried out via the Finite Element Method (FEM). The experimental observations were also performed by means of an acoustic test cabin used for ideally generating a diffuse acoustic field (DAF). The various types of analytical and numerical simulations including synthesized sounds required by future psycho-acoustic analyses, as well as experimental observations including recorded sounds were investigated and compared. Finally, based on the various analyses, the research illustrates how such investigations and comparisons are necessary for designing and enhancing the mechanical and vibro-acoustic properties of materials.

A fully-coupled vibro-acoustic model of an electronic stethoscope

A piezoelectric based stethoscope picks pressure fluctuations originating from the patient and the physician sides. This may include unwanted acoustic signals from the patient and the doctor sides of the stethoscope, which needs to be filtered either electronically or mechanically by appropriately designing the vibro-acoustic elements of the electronic stethoscope. This work intends to establish a mathematical model of the piezoelectric stethoscope. Initially, a multi-degrees of freedom vibration model of the electronic stethoscope is developed. The model is used to compute the response of the piezoelectric plate due to the pressure excitations on the input side and that due to the displacements of the connected mechanical elements in the stethoscope. Further, a two-port lumped parameter model of the piezoelectric composite plate is developed to compute the output voltage created by the displacement of the piezoceramic disc. Here, an axisymmetric plate vibration model (Kirchhoff's plate theory) is used to find the displacement of the piezoelectric composite plate. Subsequently, the vibration and the lumped parameter piezoelectric models are combined to represent the vibro-acoustic characteristics of the piezoelectric stethoscope. Further, using the developed fully-coupled vibroacoustic model, the output voltage of the device is studied for different patient and physician side excitations.

Vibroacoustic simulations with non-homogeneous TBL excitations: Synthesis of wall pressure fields with the Continuously-varying Uncorrelated Wall Plane Waves approach

A numerical method is presented to predict the vibro-acoustic response of a vibrating structure excited by a spatially inhomogeneous turbulent boundary layer(TBL). It is based on the synthesis of different realizations of the random pressure fluctuations that can be introduced as loadings of a vibro-acoustic model (such as a finite element model). To generate the pressures of the non-homogeneous turbulent boundary layer, the Uncorrelated Wall Plane Wave(UWPW) approach used so far for homogeneous TBL is extended. On a first step, this extension is based on a decomposition of the excited surface into sub-areas and on the averaged TBL parameters for each sub-area. In a second step, it consists in taking into account the interaction between the sub-areas and a refinement of the sub-area decomposition. This leads to the Continuously-varying Uncorrelated Wall Plane Waves (C-UWPW) approach. The accuracy of the proposed approach is investigated on a panel with a varying thickness and excited by a growing TBL triggered at one edge of the plate. The interests of the proposed approach in terms of accuracy and computation time are discussed. Finally, an illustration of the proposed approach to predict the radiated noise from a blade immersed in a water flow is proposed.

An efficient analytical method to obtain the homogenised frequency-independent elastic material properties of cross-laminated timber elements

Cross-Laminated Timber (CLT) is a renewable, sustainable, and cost-efficient building element that has been growing in popularity in recent years. To improve one of CLT’s weaknesses, its suboptimal noise and vibration isolation performance, computationally efficient, accessible, and extensible CLT vibro-acoustic models are required. An effective approach to achieve such models is the homogenisation of layered materials. This paper presents a validated homogenisation method based on First-order Shear Deformation Theory (FSDT) that obtains the frequency-independent elastic material properties of CLT. This method is applicable to arbitrary linear elastic material properties, orientations, and stacking sequences of the layers. The homogenised material properties are utilised with FSDT Equivalent Single-Layer (ESL) models that are readily implemented with many finite element method codes to calculate the vibro-acoustic behaviour of CLT elements, even including thickness resonance effects when applied with an appropriate model. The presented homogenisation method for CLT is validated in a numerical study by comparing the mechanical mobilities of ESL models against layerwise dynamic models. The numerical study is conducted based on an experimentally validated 5-ply model for 2- to 7-ply CLT plates with proportionally increasing thicknesses and three idealised boundary conditions. The frequency-independent material properties also allow for the graphical exploration of the anisotropic nature of CLT and the calculation of the universal anisotropic index. The flexibility of the homogenisation method, combined with its ready implementation in already widely implemented FSDT models, can have an application and impact beyond the vibro-acoustic considerations of CLT into the general mechanical modelling of CLT as it is implemented in ever more advanced applications.

Vibroacoustic modeling and radiation impedances of a finite cylindrical shell filled with flowing fluid

This paper presents an analytical study of the acoustic radiation modeling of a finite cylindrical shell with infinite rigid extensions. An infinite fluid at rest surrounds the shell, which contains a flowing fluid and excited by a harmonic driving force. The external pressure is calculated with a single layer integral equation, while the internal one is obtained with both a single layer integral equation on the shell surface and a double layer on an internal surface presenting pressure discontinuity. The modeling takes into account the shell modal behavior, the fluid loading and the radiation in both internal and external medium. The resolution is made by expanding the shell motion in the modes of the simply supported shell in vacuo. The main presented results are dealing with the internal radiation impedances and the influence of the flowing fluid (heavy and/or light) on the acoustic power radiated in both external and internal medium.

Development of High-Fidelity Numerical Methodology for Prediction of Vehicle Interior Noise Due to External Flow Disturbances Using LES and Vibroacoustic Techniques

A pleasant and quiet cabin in driving a car is one of the most critical factors affecting a customer’s choice in a market. As the traditional noise sources such as power trains become less, the relative contribution of aerodynamic noise to the interior noise of a road vehicle becomes even more critical. In this study, a high-fidelity numerical methodology is developed for the reliable prediction and analysis of the interior transmitted noise due to external flow disturbance. The developed numerical methodology is based on the sequential application of the high-resolution LES technique, wavenumber–frequency transform, and vibroacoustic model. First, the compressible LES techniques with high-resolution grids are employed to accurately predict the external turbulent flow and aeroacoustic fields due to the turbulent flow, at the same time, of a vehicle running at a speed of 110 km/h. Second, surface pressure fluctuations on the front windshield and side windows, obtained from the LES simulation, are decomposed into incompressible and compressible ones using the wavenumber–frequency transform. Lastly, the interior sound pressure levels are predicted using the vibroacoustic model, which consists of the finite element (FE) and statistical energy analysis (SEA) methods. For the efficient computation of the vibroacoustic interaction between the vibration of the vehicle windows and the acoustic field inside the cabin room, the FE and SEA methods are applied in low- and high-frequency ranges, respectively. The predicted interior sound pressure spectral levels agree well with the measured ones. In addition, although the magnitudes of the compressible pressure components are generally lower than those of the incompressible ones, the compressible field is found to contribute more to the interior noise in high-frequency bands. The physical mechanism of the higher transmission is shown to be related to the coincident effect between the compressible pressure field and the structural vibration of the vehicle window.

Analytical coupled vibro-acoustic modeling of tensioned membrane backed by the rectangular cavity

This paper proposes a unified approach to establish the analytical vibro-acoustic coupled model consisting of the tensioned membrane and the closed cavity. A 2-D Fourier cosine series with auxiliary functions is used to derive the displacement of the membrane structure. The sound pressure inside the cavity is expressed as a 3-D Fourier series with additional terms by the method of wave acoustics. Then, the vibro-acoustic coupled model between the membrane and the closed cavity is established based on the Hamilton's principle, which is suitable for different boundary conditions. The program developed by this method can be used to study the sound radiation power and sound transmission loss of coupled systems with various parameters. To demonstrate the accuracy of the proposed method, the free and forced responses of the coupled model are compared with results obtained by finite element method. The membrane with general boundary conditions is well investigated. Besides, the acoustic characteristics of the coupled model are analyzed by adjusting membrane thickness, membrane tension, cavity depth, membrane mounting position and source position, including sound radiation power and sound transmission loss. And the findings have been interpreted appropriately.

Vibro-Acoustic Modelling of Aeronautical Panels Reinforced by Unconventional Stiffeners

The purpose of this work is to characterise the vibro-acoustic behaviour of rectangular flat panels reinforced by “unconventional” stiffeners. Such panels are being increasingly employed in the aircraft industry in the case of composite fuselage, so that the assessment of the most efficient and accurate numerical techniques and modelling procedures to correctly predict their dynamic and acoustic behaviour is required. To this end, an analytical method, available from literature, has been initially employed to investigate on the main attributes of sound transmission loss properties of stiffened panels driven by an acoustic diffuse field excitation. Based on existing commercial codes, different numerical techniques have been implemented and deeply examined to assess their potentiality and restrictions. Among them, the Hybrid method has been eventually identified as the best compromise in terms of accuracy and computational effort. The drawbacks of deterministic and even Hybrid numerical approaches for medium–high frequency vibro-acoustic analysis when dealing with large structures, make use of the pure SEA approach compulsory. In particular, a refined tuning of a specific feature made available within the employed SEA analysis environment when dealing with reinforced shells is implemented as a potential solution to overcome the complexity in correctly modelling the examined unconventionally stiffened panels.

Variational Autoencoders for Dimensionality Reduction of Automotive Vibroacoustic Models

<div class="section abstract"><div class="htmlview paragraph">In order to predict reality as accurately as possible leads to the fact that numerical models in automotive vibroacoustic problems become increasingly high dimensional. This makes applications with a large number of model evaluations, e.g. optimization tasks or uncertainty quantification hard to solve, as they become computationally very expensive. Engineers are thus faced with the challenge of making decisions based on a limited number of model evaluations, which increases the need for data-efficient methods and reduced order models.</div><div class="htmlview paragraph">In this contribution, variational autoencoders (VAEs) are used to reduce the dimensionality of the vibroacoustic model of a vehicle body and to find a low-dimensional latent representation of the system. Autoencoders are neural networks consisting of an encoder and a decoder network and they are trained in order to learn the identity mapping between a reduced approximation and the initial input while enforcing a dimensionality reduction in the latent space. This allows decoding the hidden data generating structure behind the data and enables an interpretation based on the latent variables, which is extremely valuable in the engineering design process. The performance of the VAE approach is compared to a conventional principal component analysis. Finally, the trained VAE is used as a deep generative model and it is investigated to which extent the pre-trained decoder network can be used to generate new artificial realizations at low costs. These artificially generated samples can then be used to enhance the training data basis for other neural network approaches or data-driven surrogate models.</div></div>

Equivalent dynamic model of multilayered structures with imperfect interfaces: Application to a sandwich structured plate with sliding interfaces

This works aims to build an equivalent model of multilayered structures with imperfect interfaces for vibro-acoustic modeling and characterization. To take into account imperfections, new interface conditions including constitutive equations, that describe the imperfections, are implemented. Once the displacement field with imperfect interfaces is obtained, the dispersion relation of the structure is derived from the equivalent model. The bending wavenumbers are then used to compute the equivalent flexural rigidity and the damping of the sandwich panel. In this paper, the methodology is applied to a sandwich panel with sliding interfaces. The equivalent parameters are computed and compared to the reference case, i.e. perfect interfaces model. The main impact of the imperfection on the results is a shift towards the low frequency of the equivalent parameter curves.