Active sound control in composite regions

In active sound control, noise shielding of a target region is achieved via additional sources (called controls) situated at the perimeter of the region. The sources protect the target region by adjusting the acoustic field near the boundary of the region. In the present paper a numerical model of active sound control based on surface potentials in 3D bounded composite regions is numerically studied. In the composite region setup, it is required that the regions be shielded from noise while allowing admissible sound that is generated in the shielded regions to be preserved. The admissible sound is usually required to propagate freely inside the protected regions or in a (selective) predetermined pattern. The adjusting approach used here does not require any knowledge of the sound sources or the properties of the propagation medium in order to obtain the controls. Moreover, the approach differs sharply from some other approaches where the detailed knowledge of the sound sources and the propagation medium is required. For the first time, numerical test cases involving both free communication and predetermined communication pattern between the regions in three dimensions are considered. In all test cases, these regions are effectively shielded from the noise while any present admissible sound is preserved. In addition, selective propagation of the admissible sound between the regions is enforced. The effect of the number of controls on their operation is also studied. Whether admissible sound is present or not, the level of noise cancellation decreases linearly as fewer controls are used. In addition to the increase in size of the interference zone, the controls become individually distinguishable.     

Synchronous exploration for the control of real-time external noise suppression in a three-dimensional subdomain

A mathematical (difference) model is proposed for a real-time active shielding device that shields an acoustic field in a given subdomain from the influence of sound sources located in an additional subdomain. An algorithm for computing the current control ensuring a prescribed process is based on information produced by the author’s technique of synchronous weak noise exploration. This information can be measured in real time. Active control problems for nonstationary solutions of linear difference equations in a three-dimensional domain consisting of two subdomains are studied using the difference potential method. The shape of the domain and the boundary conditions may depend on time, while the coefficients may depend on time and spatial coordinates. If the difference problem is a mathematical model of sound propagation, the goal of control is to change the acoustic field in the given subdomains, for example, to shield the acoustic field in one subdomain from the undesirable influence (noise) of sources located in the other subdomain.     

On the impact of thermal sources on noise generation

Sound emission is nowadays considered as a major environmental issue. The sound emission is generated, amongst other sources, due to an increasing amount of traffic and transport, i.e. road transport, rail and air traffic. Here, sound emission presents a significant risk to public health and a major cause of stress, especially in industrial countries. In this framework the present work is dedicated to the topic of active noise control with the target of noise reduction. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Approach for Adaptive Sound Power Minimization of Elemental Sources in Theory and Experiments

Low frequency noise is a major issue in future aircraft with counter rotating open rotor engines. Passive noise treatments are bulky and heavy at these low frequencies. That is why active approaches are considered. The well known concept of destructive interference is used by state of the art active noise cancellation methods. The active systems are located closely to the noise source to cancel it. The microphones used for pressure minimization are in the near sound field of the noise source where active and reactive sound intensity are present. The pressure based concept is minimizing just the potential part of the acoustic energy. A new approach is proposed in this paper. It minimizes directly the net flow of acoustic energy that is transmitted into an interior. Simulation results showed that a proper estimation of acoustic power output is achieved by measuring sound intensity at a single point directly on the central axis of each secondary source. The innovative energy based active control approach (TASPM) has also successfully been validated in a laboratory environment. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Nonlinear problem of active sound control

We consider the problem of active sound control, in which some domain is protected from the field generated outside. The active shielding is realized via the implementation of additional sources in such a way that the total contribution of all sources leads to the wanted effect. Mathematically the problem is reduced to seeking the source terms satisfying some a priori described requirements and belongs to the class of inverse source problems. From the application standpoint, this problem can be closely related to active noise shielding and active vibration. It is important that along with unwanted field to be shielded a wanted field is accepted in the analysis. The solution to the problem requires only the knowledge of the total field at the perimeter of the shielded domain. For the first time the active shielding sources are obtained for the nonlinear statement of the problem. It is obtained via the theory of potentials, and the solution is represented in the form of a simple layer. For this purpose, the theory of Calderón-Ryaben’kii potentials is first extended to nonlinear formulations. In the solution, we also take into account the feedback of the secondary sources on the input data.     

Non-stationary problem of active sound control in bounded domains

The present paper deals with the non-stationary problem of active shielding of a domain from undesirable external sources of noise. Active shielding is achieved by constructing additional (secondary) sources in such a way that the total contribution of all sources leads to the desirable effect. The problem is formulated as an inverse source problem with the secondary sources positioned outside the domain to be shielded. Along with the undesirable field (noise) to be shielded the presence of a desirable component (“friendly” sound) is accepted in the analysis. The constructed solution of the problem requires only the knowledge of the total field (noise) on the perimeter of the shielded domain. Some important aspects of the problem are addressed in the paper for the first time, such as the non-stationary formulation of the problem, existence of the resonance regimes and sensitivity of the solution to the input errors. The obtained solution is applicable to aeroacoustics problems.     

On the composites consisting of randomly distributed fibers

The results highlight and interpret the testing and properties of natural fibre composites including, non-destructive and high strain rate testing. The potential of this material for noise enclosures is investigated by using a coupled method cnoidal – Extended Finite Element Method (XFEM). XFEM enables the accurate approximation of solutions with jumps, discontinuities or general high gradients across interfaces. The dissipation of the sound power into a plate/cavity system shows the efficiency of this composite to achieve noise reduction better to that obtained at low and higher frequencies with traditional foams. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Coupling Boundary Elements to a Raytracing Procedure using the Singular Indirect Method

The coupling of Boundary Elements and a raytracing procedure is presented here. Such a hybrid method is best suited to the study of realistic outdoor sound propagation problems: The noise often acts in a domain where many objects like buildings or sound insulation walls scatter the sound. Thus, diffraction has to be taken into account. BEM is well suited. To study the effects of this noise on a sound receiver far away, raytracing may be preferable for such application, because refraction can be implemented more easily. Hence, a Boundary Element Analysis is performed in noisy nearfield regions, a raytracing procedure at a larger distance from the sound sources. First, the direct Boundary Element algorithm is applied to determine the sound pressure at interface points. Second, a singular indirect Boundary Element formulation is used to find intensities of point sources on the same interface which produce the previously determined sound pressure. Finally, these sound intensities are the input data for the raytracing procedure. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Sound transmission into a thick hollow cylinder with the fixed-end boundary condition

In this paper sound transmission through the air filled finite thick cylinders exposed to the different incident acoustic wave is studied. The effect of end boundary conditions on the noise reduction of finite cylinders is evaluated. The uniform incident wave and the wave radiated from monopole and dipole sources are used in this study. Three positions are considered for the dipole source. Every position for the dipole source causes symmetric or antisymmetric pressure distributions on the external surface of the cylinder in tangential or axial direction. For the purpose of sound transmission analysis the linear three-dimensional theory of elasticity utilizing the technique of variables separation for the infinite circular cylinders is used to analyze the vibration of finite circular cylinder. In these analyzes the stress continuity condition on the inner and outer surfaces of the cylinder is satisfied using orthogonalization technique and velocity continuity condition is exactly satisfied on the interfacial surfaces. The sound transmission evaluation is carried out for cylinders with various half-length to outer-radius ratios. The results show that in the case of the fixed-end cylinder, the effect of boundary conditions on the noise reduction can be neglected for the half-length to outer-radius ratio of more than 10. Comparing between the obtained results from different acoustic sources shows that the obtained noise reductions from the uniform acoustic wave are less than those obtained from the monopole and dipole sources.     

Model of real-time active noise shielding of a given subdomain subject to external noise sources

A linear one-dimensional problem is considered, which is interpreted as a mathematical model of sound propagation. Additional sound sources are constructed that shield a given subdomain from sound sources localized in an additional subdomain without changing the solution in the additional subdomain. A complicating point in the problem is that the desired shielding sources can be constructed at the current time as based only on information about the shielded process that has become available by this current time. In an important special case, information in a convenient form is derived via noise exploration introduced in this work.     

Towards a Mathematical Theory of Super‐resolution

This paper develops a mathematical theory of super‐resolution. Broadly speaking, super‐resolution is the problem of recovering the fine details of an object—the high end of its spectrum—from coarse scale information only—from samples at the low end of the spectrum. Suppose we have many point sources at unknown locations in [0,1] and with unknown complex‐valued amplitudes. We only observe Fourier samples of this object up to a frequency cutoff f_c. We show that one can super‐resolve these point sources with infinite precision—i.e., recover the exact locations and amplitudes—by solving a simple convex optimization problem, which can essentially be reformulated as a semidefinite program. This holds provided that the distance between sources is at least 2/f_c. This result extends to higher dimensions and other models. In one dimension, for instance, it is possible to recover a piecewise smooth function by resolving the discontinuity points with infinite precision as well. We also show that the theory and methods are robust to noise. In particular, in the discrete setting we develop some theoretical results explaining how the accuracy of the super‐resolved signal is expected to degrade when both the noise level and the super‐resolution factor vary. © 2014 Wiley Periodicals, Inc.     

Modeling of Active Noise and Vibration Control with Finite Elements and Boundary Elements

A recently developed coupled finite element-boundary element modeling scheme for the design of active noise and vibration control of multi-coupled structural-acoustic systems is presented. The approach allows the computation of structural vibrations and resulting sound fields. By means of an example, the paper describes the theoretical background of the coupled approach. In order to show the performance of the developed approach, test simulations are carried out in the frequency domain. (© 2009 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Modelling of coupled vibro-acoustic interactions in an active casing for the purpose of control

The aim of active casing is to reduce device noise generated to the acoustic environment by controlling vibrations of the walls of the device casing. The article concerns theoretical modelling of an active casing composed of six walls mounted to a rigid frame. The casing is considered as a complex coupled vibro-acoustic system, where the walls are excited by the acoustic field inside the casing, and by actuators bonded to the walls and used for active control. The acoustic field inside the casing is, in turn, formed by the noise originating from the device itself, and the secondary sound generated by all vibrating walls. The structure of such system is described in detail and, after being represented as interconnected subsystems, its state-space model is developed. The model includes fluid loading effect and imperfect fastening of wall edges to the frame. The system of coupled partial differential equations, subject to defined boundary conditions, is reformulated as an abstract first order evolution equation in an appropriate infinite dimensional function space. All assumptions and the structure of the model are chosen to make it useful for the purpose of control. In particular, the model can be used for analysis of controllability and observability of the whole casing as a vibro-acoustic system and, based on that, for optimisation of placement of actuators and structural sensors to efficiently reduce noise over required frequency band. On the basis of the obtained state equation, a block diagram of the system is constructed. It shows the structure of the whole system and the nature of interactions occurring between distinguished subsystems.     

Numerical Investigation of Sound Generation due to Laminar Flow Past Elliptic Cylinders

Numerical investigation of sound generation due to unsteady laminar flow past elliptic cylinders has been carried out using direct numerical simulation $(DNS)$ approach at a free-stream Mach number of $0.2$. Effects of aspect ratio $(0.6\le AR\le 1.0)$ and Reynolds number $(100\le Re \le 160)$ on the characteristics of radiated sound fields are analyzed. Two-dimensional compressible fluid flow equations are solved on a refined grid using high resolution dispersion relation preserving $(DRP)$ schemes. Using present $DNS$ data, equivalent noise sources as given by various acoustic analogies are evaluated. Amplitudes and frequencies associated with these noise sources are further related to characteristics of disturbance pressure fields. Disturbance pressure fields are intensified with increase in Reynolds number and aspect ratio. Thus, radiated sound power increases with increase in Reynolds number and aspect ratio. Among various cases studied here, minimum and maximum values of radiated sound power are found at $Re=120$ & $AR=0.6$ and $Re=160$ & $AR=1.0$, respectively. Directivity patterns show that the generated sound fields are dominated by the lift dipole for all cases. Next, proper orthogonal decomposition $(POD)$ technique has been implemented for decomposing disturbance pressure fields. The $POD$ modes associated with the lift and the drag dipoles have been identified. $POD$ analyses also clearly display that the radiated sound fields are dominated by the lift dipole only. Further, acoustic and hydrodynamic modes obtained using Doak's decomposition method have confirmed the patterns of radiated sound field intensities.     

A prediction of the acoustical properties of induction cookers based on an FVM–LES-acoustic analogy method

The FVM–LES-acoustic analogy method (FVM–LES-AAM), which is a hybrid prediction technique for the acoustical property computation, is presented and performed in this paper. The FVM–LES-AAM was developed by combining the finite volume method (FVM), the large eddy simulation (LES), and the Ffowcs Williams-Hawkings analogy algorithm (FWH-AA). To predict the acoustical properties of induction cookers, the FVM is used for discretizing the calculation field and building numerical equations, and the LES and FWH-AA are performed for computing the sound sources and predicting the far-field sound, respectively. Using the FVM with the unstructured grids method to discretize the control equation of Navier–Stokes was introduced for illuminating the above numerical simulation procedure. To prove the FVM–LES-AAM method is feasible for predicting the acoustical property of induction cookers, the simulated results were compared with some measured experimental data. The comparisons suggest that the hybrid method is accurate and reliable for the aeroacoustics analysis of induction cookers. Considering the temperature performance, furthermore, some new configurations for the noise reduction of induction cookers were designed, simulated, and discussed. The FVM–LES-AAM prediction technique shows promise as a feasible and computationally affordable approach for not only noise analysis of induction cookers, but also for other aeroacoustics problems in engineering.     

On the Production of Sound by Turbulent Boundary Layer Flow over a Compliant Coating

A theory is proposed of the generation of sound by turbulentboundary layer flow over a nominally plane, compliant wall coating.It is argued that, at sufficiently low mean flow Mach numbers,the principal noise production mechanism involves the scatteringof energy into sound from the hydrodynamic region of the wallpressure fluctuations by time dependent irregularities in thefree surface of the coating induced by the turbulent flow. Theeffective noise sources are equivalent to a distribution ofaerodynamic dipoles over the surface of the coating whose axesare parallel to the wall. The far field acoustic pressure spectrum,and the wavenumber-frequency wall pressure spectrum in the acousticdomain are expressed in terms of the behaviour of the wall pressurespectrum in the hydrodynamic domain. A simple empirical modelof the hydrodynamic region, defined in terms of measurable parameters,is used to obtain explicit representations of the acoustic spectra.     

Mathematical modelling of noise around a Y-shaped windy road

In this study, we investigated the sound radiation from vehicles moving on a road with a Y-shaped fork in windy conditions. First, we consider the problem for two point sound sources moving in opposite directions along a road with an arbitrary bend. The background of the road is modelled as an elastic half-space. The solution to this problem is obtained using the integral Fourier transforms over space variables and time, and the stationary phase method. Next, the solution to the general case for many sources moving along a Y-shaped road fork is obtained as the superposition of the partial solutions. We performed a numerical analysis of the traffic noise characteristics for a Y-shaped fork on a city road in the town of Lodz, Poland as an example.     

The Study of Psychoacoustic Effects of Noise Emitted by the Machine Tools Structure

The main sources of noise at work, in industrial environments, are machine tools: namely, mechanical transmission structure composed of gears, bearings, electric motors drive and the cutting process. Generated vibrations are transmitted through structures, carcasses or directly to environment, developing a complex acoustic field around machine tools. In terms of occupational medicine, the noise is generated by a combination of vibrations producing sounds with different characteristics and that are produced in the workplace [2]. It is important to identify the dominant noise source, the cause of exceeding the admissible limits (87dB) and noise transmission mode to make an objective correlation with effects on humans [1]. Hearing loss can occur immediately at extreme sound levels, but, in general, the problem is noise exposure over time. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Near-field fluctuations and far-field noise of a three-element airfoil system by a discrete vortex method

A circulation-based discrete vortex method is used on a three-element airfoil system. Kutta conditions and Kelvin’s circulation theorem are additional conditions required for this method to determine the circulation distributions on each element and to determine vortex shedding. Discrete shed vortices are introduced near the four sharp edges to represent the sharp-edge vortex shedding caused by unsteady flow separation. The computational procedure warrants neutrally stable solutions of the self-sustained fluctuating flowfield that can provide broad-band spectral information for far-field noise predictions. The near-field vortex method directly calculates the parameters used in an asymptotic formula for far-field sound computation that attributes the noise sources to vortex interactions among the shed vortices and the surface circulations of the three-element airfoil system. The far-field noise characters are then analyzed and compared to the experimental data in the literature.     

An accurate program for radiation modelling in the desigh of high-tempersature furnaces

The zone method is well established for determining radiativeheat transfer. It has been used successfully in simple geometries.However the task of determining the required exchange areashas limited its use in more geometrically complex enclosures.In this paper, a computer program, RADEX, is descrilxd. Thisprogram will calculate direct and total exchange areas usinga Monte Carlo method for enclosures with complex geometries.Some results from a validation study of RADEX are given. Finally,as an illustration of its potency as a design tool, the resultsof a comparative study of nine different designs of radianttube furnace are given.