Analysis Of Acoustic Radiation Research Articles

Acoustic radiation from weakly wrinkled premixed flames

This paper describes a theoretical analysis of acoustic radiation from weakly wrinkled (i.e., u ′ / S L < 1 ) premixed flames. Specifically, it determines the transfer function relating the spectrum of the acoustic pressure oscillations, P ′ ( ω ) , to that of the turbulent velocity fluctuations in the approach flow, U ′ ( ω ) . In the weakly wrinkled limit, this transfer function is local in frequency space; i.e., velocity fluctuations at a frequency ω distort the flame and generate sound at the same frequency. This transfer function primarily depends upon the flame Strouhal number St (based on mean flow velocity and flame length) and the correlation length, Λ, of the flow fluctuations. For cases where the ratio of the correlation length and duct radius Λ / a ≫ 1 , the acoustic pressure and turbulent velocity power spectra are related by P ′ ( ω ) ∼ ω 2 U ′ ( ω ) and P ′ ( ω ) ∼ U ′ ( ω ) for St ≪ 1 and St ≫ 1 , respectively. For cases where Λ / a ≪ 1 , the transfer functions take the form P ′ ( ω ) ∼ ω 2 ( Λ / a ) 2 U ′ ( ω ) and P ′ ( ω ) ∼ ω 2 ( Λ / a ) 2 ( Ψ − Δ ln ( Λ / a ) ) U ′ ( ω ) for St ≪ 1 and St ≫ 1 , respectively, where Ψ and Δ are constants. The latter result demonstrates that this transfer function does not exhibit a simple power law relationship in the high frequency region of the spectra. The simultaneous dependence of this pressure–velocity transfer function upon the Strouhal number and correlation length suggests a mechanism for the experimentally observed maximum in acoustic spectra and provides some insight into the controversy in the literature over how this peak should scale with the flame Strouhal number.

Analysis of broadband acoustic radiation from periodic structures

Radiation from a 2D finite-length plate with periodic discontinuities modeled by line impedances, and with arbitrary boundary conditions, is considered. Under broadband excitation such structures often exhibit a fairly simple directivity pattern that is nearly symmetric and relatively smooth. The differences between single-frequency and broadband response are analyzed. Due to discontinuities the structure exhibits passband and stop-band behavior, with structural waves decaying in stop bands. This behavior leads to a different energy distribution between the structure and the acoustic field for frequencies in different bands. Acoustic radiation from periodic structures is characterized in terms of Bloch waves. Closed-form formulas for harmonic and broadband response from a single structural Bloch wave are obtained. Total response is recovered by superposition of Bloch waves. A single Bloch wave contains a primary harmonic, corresponding to a long-wavelength, smooth global solution, and higher spatial harmonics induced by discontinuities which describe the short-wavelength local solution. Radiation characteristics are discussed in terms of global and local solutions.

CAT'S EYE RADIATION WITH BOUNDARY ELEMENTS: COMPARATIVE STUDY ON TREATMENT OF IRREGULAR FREQUENCIES

This paper reviews a number of techniques developed to overcome the well-known nonuniqueness problem in boundary integral formulations of acoustic radiation. Although the problem has received much attention, comparative studies are hardly known in this field. Furthermore, the problem has often been studied using an unsuitable example, namely a simple radiating sphere. In this case, often the addition of one collocation point in the centre of the sphere suffices to remove the nonuniqueness problem for a large range of wavenumbers. In contrast to the radiating sphere, the radiating cat's eye structure is considered in this paper. Solution of the discretized ordinary Kirchhoff–Helmholtz integral equation, also known as the Surface Helmholtz Equation, reveals a large number of so-called irregular frequencies, i.e. frequencies where the BEM fails. The paper compares the performance of different methods in alleviating this failure. The CHIEF method and its variation due to Rosen et al. are found to encounter difficulties at high frequencies. A much better performance is obtained by combining the Kirchhoff–Helmholtz integral equation with its normal derivative. In particular the method of Burton and Miller and a modification of it which avoids evaluating the hypersingular operator at nonsmooth points are tested. Both methods seem to provide reliable solutions. The modified method encounters minor failures in the frequency response function at a geometric singularity, although performing surprisingly well in many cases. More tests need to be carried out to assess fully the effectiveness of this method which allows easy use of continuous quadratic elements. However, it is the Burton and Miller formulation which appears to be the most reliable for acoustic radiation analysis. The use of CHIEF and its variations cannot be recommended.

Modal analysis and intensity of acoustic radiation of the kettledrum

The acoustical features of kettledrums have been analyzed by means of modal analysis and acoustic radiation (p/v ratio) measurements. Modal analysis of two different kettledrums was undertaken, exciting the system both by a hammer and a shaker. Up to 15 vibrational modes were clearly identified. Acoustic radiation was studied using two ways. Based on previous experiments of other researchers, a new parameter, called intensity of acoustic radiation (IAR), has been defined and measured. Results show a strict relationship between IAR and the frequency response function (FRF, which is the v/F ratio), and IAR also strongly relates the modal pattern to acoustic radiation. Finally, IAR is proposed for vibro-acoustical characterization of kettledrums and other musical instruments such as strings, pianos, and harpsichords.

Finite difference analysis of acoustic reflection and radiation from fluid-loaded plates

A finite difference/boundary integral procedure to determine the acoustic reflected pressure from a fluid-loaded bi-laminate plate is described. The bi-laminate is composed of a piezo-electric layer and an elastic layer in contact with the fluid. The plate is either of finite length and held at its two ends in an acoustically hard baffle or of infinite length with periodically etched electrodes. In the numerical model, the fluid pressure at fluid/solid interface is replaced by a continuum of point sources weighted by the normal acceleration of the elastic plate, and the governing equation system is solved in the solid domain. It is demonstrated that an appropriate applied voltage potential across the baffled piezoelectric layer has the effect of cancelling the reflected pressure at any chosen field points, and a piecewise constant voltage potential with properly chosen amplitude and phase in the periodic structure has the effect of cancelling the fundamental propagating mode of the reflected waves.

Structural Design Optimization for Reducing Sound Radiation from a Vibrating Plate Using a Genetic Algorithm

This paper presents a numerical method of optimum design of mechanical structures for reducing noise. This method couples an optimization technique based on a genetic algorithm (GA) with both a finite element code for determining structural vibrations and acoustic radiation analysis for determining sound pressure levels at the receiver point. Reducing the sound pressure level associated with the fundamental acoustic resonant mode is accomplished by adding masses to a vibrating plate coupled to an acoustic cavity which is excited by a sound source. The positions of the masses on the plate are adopted as the design variables. By using the presented method, the optimal positions that would not be easy to be found by any intuitive solution are determined so as to effectively reduce the sound pressure level. The numerical prediction of the effect of the optimization is compared with the experimental result.

Estimation of sound power of baffled planar sources using radiation matrices.

A technique is presented in this paper for the analysis of acoustic radiation of baffled planar sources. This method is based on the concept of the radiation matrix which is a representation of the sound field radiated by complex sources. Both sound power and far-field pressure can be estimated using this method. Numerical simulation and experimental investigation were carried out to verify the proposed method. In comparison with the conventional pressure-based method ISO 3745, the proposed technique produced more accurate estimation of sound power. With comparable number of measuring positions as the conventional methods, the proposed approach does not require special measuring environments. Computation complexity can be significantly reduced if only dominant radiation modes in the low-frequency range are retained. Estimation of far-field pressure can also be obtained using the proposed method.

A study on avoiding hyper-singular integrals in exterior acoustic radiation analysis

Burton and Miller's formulation (BMF) is well known for solving non-uniqueness problems in an exterior acoustic problem. In this paper, an IBMF (improved BMF) is presented by directly taking into account of the normal derivatives of solid angles on the surface. The introduction of the normal derivative of solid angles in building the Burton and Miller's formulation will cause the elimination of hyper-singular terms. Here lies the advantage of improved formulation. Then, reproduction of diagonal terms (RDT) is applied to further improve singular integral in IBMF. Three cases are compared for closed axi-symmetric surfaces, including SHF (conventional surface Helmholtz formulation), IBMF and IBMF–RDT. Numerical results show that the combined scheme of IBMF–RDT is valid at all wave numbers, and gives satisfied calculating accuracy, which is about 10 times higher than that of SHF.

Optimization Approach for Reducing Sound Power from a Vibrating Plate by Its Curvature Design.

In many mechanical structures, structural design for noise reduction is becoming increasingly important. Noise reduction is often achieved through structural modifications. However, it is hard to predict the effectiveness of noise reduction by typical approaches. This paper presents an optimal design approach for reducing sound power from a vibrating plate by its curvature design. The method couples an optimization technique based on a genetic algorithm (GA) with the shape representation technique, vibration analysis and acoustic radiation analysis. It is shown that the curvature design of the plate obtained by using this method can achieve effective reductions in radiated sound power. Finally, the robustness of the optimized design candidates obtained is studied by using stochastic simulations in order to find those candidates which are least sensitive to changing design parameters.

Exact global boundary condition with reduced computational complexity for grid truncation in acoustic finite difference time domain simulations

The numerical analysis of transient acoustic radiation by and scattering from inhomogeneous bodies is often carried out using the finite difference time domain (FDTD) method. However, FDTD grids must be truncated with absorbing boundary conditions when the structure of interest resides in an unbounded medium. Local boundary conditions have to be imposed on a convex outer boundary, thereby often inflating the problem size. This drawback is alleviated if the grid is truncated using exact boundary conditions that rely on a retarded-time boundary integral (RTBI) [L. Ting and M. J. Miksis, J. Acoust. Soc. Am. 80, 1825–1827 (1986)]. Unfortunately, for a 3-D computational domain comprising of O(N3) FDTD cells, where N denotes the number of cells per unit length, the evaluation of the RTBI using classical methods requires O(N4) operations per time step, which renders the RTBI approach impractical. In this presentation, it will be shown that this computational bottleneck can be alleviated by employing the plane wave time domain algorithm [A. A. Ergin et al., J. Comput. Phys. 146, 157–180 (1998)] using which the RTBI can be evaluated in O(N2&amp;lt;th&amp;gt;log2&amp;lt;th&amp;gt;N) operations. Numerical results that demonstrate the efficacy and reduced complexity of the method will be presented.

A FINITE ELEMENT MODEL FOR ACOUSTIC RADIATION

In this article, an extension of the finite element technique to the analysis of the acoustic radiation is presented. In the proposed approach, the acoustic domain is split into two parts by an arbitrary artificial boundary enclosing the radiating surface. Then the unbounded medium is discretized with finite elements consisting of only one or two rows in the radial direction up to the artificial boundary. To represent the farfield behaviour, the constraint equation specified on the artificial boundary is formulated with a more straightforward boundary integral equation, in which the source surface coincides with the radiating surface discretized with boundary elements. To ensure the uniqueness of the numerical solution, the composite Helmholtz integral equation proposed by Burton and Miller was adopted. Due to the avoidance of singularity problems inherent in the boundary element formulation, this method is very efficient and easy to implement in an isoparametric element environment. In numerical experiments involving spherical and cubical radiators, it has been demonstrated that the proposed method eliminates the difficulties when the FEM handles the exterior acoustics. It should be noted that the method can be extended to the computation on other branches of the classical field theory.

Sensitivity analysis of coupled structural-acoustic problems using perturbation techniques

The analysis of acoustic radiation and scattering from submerged elastic structures is an important and challenging problem. Often, numerical solutions are hampered by the fact that the acoustic pressure field can be very sensitive to structural detail. In this paper, a procedure for obtaining the sensitivity of a structural-acoustic system to structural perturbations is presented. The theoretical development assumes a finite element description of the structure and a boundary element description of the fluid. The analysis includes full coupling between the fluid and the structure, and can accommodate both internal and/or external fluid regions. The types of perturbations are limited to those that do not alter the geometry of the wetted surface, but are otherwise completely general in nature. The technique is then applied to acoustic scattering from a cylindrical shell. Two perturbations are considered: A change in the shell thickness and a change in the elastic modulus. The effect of these structural perturbations on the surface pressure, surface normal velocity, and scattered pressure are examined for plane-wave scattering.

A space-time finite element method for the exterior acoustics problem

In this paper, the development of a space-time finite element method for the solution of the transient acoustics problem in exterior domains is discussed. The space-time formulation for the exterior acoustics problem is obtained from a time-discontinuous Galerkin variational equation for coupled structural acoustics, specialized to the case of zero normal velocities on the wet surface, i.e., a rigid scatterer. The formulation employs a finite computational acoustic domain surrounding the scatterer and incorporates high-order time-dependent nonreflecting (radiation) boundary conditions on the fluid truncation boundary as ‘‘natural’’ boundary conditions in the space-time variational equation, i.e., they are enforced weakly in both space and time. The result is an algorithm for direct transient analysis of acoustic radiation and scattering with the desired combination of good stability and high accuracy. The method is especially useful for the application of adaptive solution strategies for transient acoustics in which unstructured space-time meshes are used to track wavefronts propagating along space-time characteristics. Optimal stability estimates and convergence rates are reported together with two representative numerical examples involving transient radiation and scattering which illustrate the high-order accuracy achieved by the method for the exterior acoustics problem.

Radiation sensitivity of baffled plates to structural perturbation

The analysis of acoustic radiation and scattering from submerged elastic structures is an important and challenging problem. Often, numerical solutions are hampered by the fact that the acoustic pressure field can be very sensitive to structural detail. In this presentation, a baffled plate submerged in a semi-infinite acoustic medium is used study this sensitive. A finite element description of the structure and a boundary element description of the fluid are used to model the plate-fluid-baffle arrangement. The sensitivity information is obtained by applying perturbation techniques to the matrix equations that arise, yielding exact derivatives of the chosen field variable. Several types of local structural perturbations (point masses, springs, dampers, and ribs) as well as global perturbations (Young’s modulus, density, damping) are considered. The nature of the structural sensitivity is examined and some investigation is made into what types of structural features have the greatest impact on radiation and scattering. Finally, the use of the sensitivity information for engineering and design is discussed.

Acoustic intensity and structural power flow methods for scientific visualization

Interpreting large data sets that result from the application of high-resolution computational and experimental methods to the solution of structural acoustics problems is a difficult, time-consuming task. The use of scientific visualization techniques expedites the process of data interpretation by condensing these large quantities of data into small packets of visual information. As generally applied, scientific visualization techniques are used to produce color coded plots of the acoustic pressure magnitude and of the structural motion. The focus of this paper is to show that the vector quantities, acoustic intensity and structural power flow, are very useful for the visualization of the complex phenomena that result when a vibrating structure interacts with its surrounding acoustic fluid. Results will be shown for applications to both two- and three-dimensional data sets resulting from the analysis of acoustic radiation from a submerged elastic shell. Algorithms for the required computations will also be given.

Virtual sources, guided wave paths, and far-field radiation from an internally excited ribbed cylinder

An experimental analysis of structural dynamics and acoustic radiation associated with a large scale (7.5 m long, 1.5 m diam) immersed hull structure is presented. Pressure data were collected with an automated scanning frame and an array of hydrophones at 0.3-m intervals over a measurement surface conformal to and 0.3 m distant from the body. Visualizations of the pressure field in the measurement plane were analyzed to verify data quality and to characterize dominant phenomena (hull resonances, low-order mode shapes, virtual source locations, and scattering discontinuities). The data were then backprojected to the hull using near-field acoustical holography algorithms to obtain (normalized) pressure, velocity, and intensity distributions on the hull. Finally, algorithms based on the Helmholtz integral were employed to determine far-field radiation patterns. [Work sponsored by NAVSEA.]

Nonaxisymmetric acoustic radiation from a pair of sources embedded in a fluid sphere

The general analysis of nonaxisymmetric acoustic radiation in a spherical coordinate system, contained in a companion paper [S. A. Lease and W. Thompson, Jr., J. Acoust. Soc. Am. 90, xxx–xxx (1991)], is specialized to the case of two, identical, in‐phase monopole sources similarly positioned within a fluid sphere. This special case allows the truncated system of equations to be reduced to a set involving (N+1)2 unknowns. Special considerations in the development of a fortran program to solve the system of equations are discussed. Numerical results for the radiated acoustic power, directivity patterns, and source radiation impedance for this specific case can be calculated by the program. Some numerical results are presented for a few specific choices of the many physical parameters that characterize the problem. The performance of the program for the various choices of physical parameters is discussed.

An Acoustic Variational Principle and Component Mode Synthesis Applied to the Analysis of Acoustic Radiation from a Concentrically Stiffened Plate

This study concerns the effects of circumferential ring stiffeners on the vibration and acoustic radiation of a submerged circular elastic plate supported by an infinite rigid baffle. The analysis employs variational principles, in which surface pressure and velocity are represented by assumed modal functions. It is shown that the use of a Fourier series expansion of the Green’s function, along with Bessel function pressure modes, greatly simplifies computation of the fluid-structure interaction. Two structural formulations are addressed, differing by whether the connection between the plate and stiffeners is implicitly or explicitly enforced. The results for surface response are used in conjunction with the Kirchhoff-Helmholtz integral theorem to evaluate near- and farfield pressures. An example of a single stiffener illustrates the influence of stiffener location on radiated power.

Acoustic transmission and radiation analysis of adaptive shape-memory alloy reinforced laminated plates

A theoretical analysis of sound transmission/radiation of shape-memory alloy (SMA) hybrid composite panels is presented. Unlike other composite materials, SMA hybrid composite is dynamically tunable by electrical activation of the SMA fibers and has numerous active control capabilities. Two of the concepts that will be briefly described and utilized in this paper are referred to as active property tuning (APT) and active strain energy tuning (ASET). Tuning or activating the embedded shape-memory alloy fibers in conventional composite materials changes the overall stiffness of the SMA hybrid composite structure and consequently changes natural frequency and mode shapes. The sound transmission and radiation from a composite panel is related to its frequency and mode shapes. Because of the capability to change both the natural frequency and mode shapes, the acoustic characteristics of SMA hybrid composite plates can be changed as well. The directivity pattern, radiation efficiency, and transmission loss of laminated composite materials are investigated based on “composite” mode shapes in order to derive a basic understanding of the nature and authority of acoustic control by use of SMA hybrid composites.

Time‐based energy analysis of acoustic radiation and structural vibration using generalized near‐field acoustical holography measurements

A time‐based energy analysis of structural vibration and radiation is carried out with near‐field acoustical holography measurements. By using the force driving the structure as a reference for the measured pressure, the impulse response can be determined over the frequency range of the force signal. Assuming that the signals are linear and shift invariant in time, the structural vibration and radiated acoustic field due to a synthetic force are determined. This is done by multiplying the frequency domain descriptions of the measured impulse response and the synthetic force. The signal processing, which will be outlined, occurs in the frequency domain. The results are then transformed into the time domain via discrete Fourier transforms where the analysis is done. Thus, from a single measurement, the response to force time histories other than the original measurement force can be studied, assuming that the new force signal can be described with the frequency range of the original measurement. Results for a fluid‐loaded, point driven finite cylindrical shell will be shown, with emphasis placed on examining the energy radiated to the acoustic far field, the energy in the acoustic near field, the energy delivered by the driver to the structure, and the energy absorbed by damping in the structure. For finite time length forces, a large amount of acoustic energy enters the structure rather than radiating to the far field. This time‐based analysis provides many insights into the mechanisms of fluid/structure interactions that are not observable by a purely frequency based analysis.