Exterior Acoustic Radiation Research Articles

2.5D singular boundary method for exterior acoustic radiation and scattering problems

In this paper, a numerical methodology based on a two-and-a-half-dimensional (2.5D) singular boundary method (SBM) to deal with acoustic radiation and scattering problems in the context of longitudinally invariant structures is proposed and studied. In the proposed 2.5D SBM, the desingularisation provided by the subtracting and adding-back technique is used to determine the origin intensity factors (OIFs). These OIFs are derived by means of the OIFs of the Laplace equation. The feasibility, validity and accuracy of the proposed method are demonstrated for three acoustic benchmark problems, in which detailed comparisons with analytical solutions, the 2.5D boundary element method (BEM) and the 2.5D method of fundamental solutions (MFS) are performed. As a novelty of the present study, it is found that the 2.5D SBM provides a higher numerical accuracy than the 2.5D linear-element BEM and lower than the 2.5D quadratic-element BEM. Although the results obtained depict that a nodal approximation of the boundary geometry leads to a significant reduction in the accuracy of the 2.5D SBM, the delivered errors are still acceptable. For complex geometries, the 2.5D SBM is found to be simpler and more robust than the 2.5D MFS, since no optimization procedure is required.

A Parameter Study of the Burton–Miller Formulation in the BEM Analysis of Acoustic Resonances in Exterior Configurations

The application of a boundary element technique in combination with a contour integral approach to the numerical analysis of acoustic resonances in exterior configurations is investigated in this paper. Similar to the boundary element analysis of exterior acoustic radiation or scattering problems, spurious eigenfrequencies also turn up in the boundary element solution to exterior acoustic resonance problems. To filter out the spurious eigenfrequencies, the Burton–Miller-type combined formulation is employed to shift them from the real axis to the complex domain. The shifting effect brought by the combined formulation with different types of coupling parameters is investigated. Unlike in acoustic radiation and scattering analyses for which [Formula: see text] is suggested as the coupling parameter, it will be shown that the coupling parameter specified as [Formula: see text] with [Formula: see text] (the time-dependent term herein is [Formula: see text]) is more desirable in distinguishing the spurious eigenfrequencies in the boundary element analysis of exterior acoustic resonances.

A weak-form meshfree coupled with infinite element method for predicting acoustic radiation

To improve the computational accuracy and eliminate the element matching in the traditional method based on the finite and infinite elements, the coupling of the meshfree weak-form method with the variable order infinite acoustic wave envelope element (WEE) is studied in this paper and achieved by forming continuous acoustic shape function on an artificial interface, by which the infinite domain is divided into two subdomains where the meshfree and WEE methods are applied respectively. A coupled meshfree weak-form method is developed for use in predicting acoustic radiation in infinite domain. A key feature of the present method is the ability of properly modelling the amplitude decay of the outgoing travelling wave and significantly improving the prediction accuracy. The impacts of the meshfree shape function approximation/interpolation scheme and the space scale of the region used for the coupling on the proposed method are investigated. Simulation and experiment are performed to test the applicability and performance of the method, and show that the method is a valuable approach for predicting exterior acoustic radiation in infinite domain.

An improved boundary point interpolation method for exterior acoustic radiation problem

In this paper, an improved boundary point interpolation method (BPIM) is developed for solving exterior acoustic radiation problems. With the help of Lagrange basis polynomials, a Lagrange point interpolation method (PIM) is presented to avoid the inversion of the moment matrix in the PIM. Then combining the acoustic double layer potential with the Lagrange PIM, the improved BPIM for exterior acoustic radiation problems is presented. Detailed and efficient computational formulas are established to compute acoustic hypersingular and nearly hypersingular integrals. Numerical results show that the current BPIM can produce efficient numerical solutions to exterior acoustic radiation problems.

A transformation of the CVIS method to eliminate the irregular frequency

The simple-source method implies an interior virtual fluid field for the exterior acoustic radiation problems. Due to the resonance of this virtual fluid field, the emergence of the irregular frequencies (fictitious frequency) will occur on certain frequencies, which lead to the distortion of the results. It is a purely mathematical problem that the boundary integral equation has no solution at irregular frequencies. Based on the closed virtual impedance surface method (CVIS method), a constant transformation factor α is introduced to form a transformation of the CVIS method, the CVIS-α method. Through the method, the irregular frequencies can be effectively eliminated. Meanwhile, the partial derivatives of the Green's function can be ignored in the boundary integral equation, which is for the exterior acoustic problems. This method has natural advantages in the integrated calculation of acoustic radiation and propagation of 3D elastic floating body in the ocean acoustic environment. The validity of the method is verified by the acoustic impedance calculation cases of the spherical and cylindrical floating bodies. Moreover, some optimization principles for building the CVIS are given in consideration of both the computing quantity and the eliminating effect.

On The Choice of Coupling Parameter in The Time Domain Burton-Miller Formulation

A Burton–Miller-type integral equation for time domain exterior acoustic radiation and scattering problems is considered as a way of overcoming the well-known stability problems associated with collocation-based time domain boundary element methods. The stability of the method is considered and justified using an argument based on the associated frequency domain integral equation. This allows for the justification of a choice of coupling coefficient that is in some sense optimal for the time domain formulation for acoustic radiation and scattering by spheres. Finally, computational results are given in support of these observations and the impact of choosing the optimal parameter in the computations is discussed. Results for non-spherical bodies are also considered to see whether the results may be more widely applicable.

군집행동 알고리즘을 이용한 판넬구조물의 방사소음저감에 관한 연구

In this paper, the author proposes a new method for acoustic radiation optimum design to minimize noise from a vibrating panel-like structure using a collaborative population-based search method called the particle swarm optimization algorithm(PSOA). The PSOA is a parallel evolutionary computation technique initially developed by Kennedy and Eberhart. The acoustic radiation optimization method based on the PSOA consists of two processes. In the first process, the acoustic radiation analysis by an integrated p-version FEM/BEM, which was developed by using MATLAB, is performed to evaluate the exterior acoustic radiation field of the panel. The second process is to search the optimum design variables: 1) Shape of Bezier curves and 2) Shape and position of ribs, to minimize noise from the panel using the PSOA. The optimization method based on the PSOA is compared to that based on the steady state genetic algorithm(SSGA) in order to verify the effectiveness and validity of the optimal solution by PSOA. Finally, it is shown that the optimal designs of the panel obtained by using the PSOA can achieve effective reductions in radiated sound power.

Comments on “The boundary point method for the calculation of exterior acoustic radiation problem” [S.Y. Zhang, X.Z. Chen, Journal of Sound and Vibration 228(4) (1999) 761–772

Zhang and Chen [The boundary point method for the calculation of exterior acoustic radiation problem, Journal of Sound and Vibration 228 (1999) 761–772] proposed a boundary point method (BPM) for exterior acoustic problems. The idea is similar to the CHUNKY CHIEF by Wu [A weighted residual formulation for the CHIEF method in acoustic, Journal of Acoustical Society of America 90 (1991) 1608–1614], but Chunky CHIEF provides constraints using null-field equations while the BPM used the CHUNKY BLOCK singularity outside the domain. The mathematical structure is similar to Trefftz method and method of fundamental solutions [J.T. Chen et al., On the equivalence of the Trefftz method and method of fundamental solutions for Laplace and biharmonic equations, Computers & Mathematics with Applications 53 (2007) 851–879], since the interpolation function satisfies the governing equation. Later, Wu commented twice [Sean F. Wu, Comments on “The boundary point method for the calculation of exterior acoustic radiation” (by S.Y. Zhang, X.Z. Chen, Journal of Sound and Vibration 228(4) (1999) 761–772), Journal of Sound and Vibration, 298 (2006) 1173]; Sean F. Wu, Comments on “Reply to the comments on ‘The boundary point method for the calculation of exterior acoustic radiation’ (by S.Y. Zhang, X.Z. Chen, Journal of Sound and Vibration 228(4) (1999) 761–772)”, Journal of Sound and Vibration, 298 (2006) 1176–1177] that the formulation of BPM is wrong and the authors replied also twice [X.Z. Chen, C.X. Bi, Reply to the comments on “The boundary point method for the calculation of exterior acoustic radiation” (by S.Y. Zhang, X.Z. Chen, Journal of Sound and Vibration 228(4) (1999) 761–772), Journal of Sound and Vibration, 298 (2006) 1174–1175; [X.Z. Chen, C.X. Bi, Reply to the comments on “Reply to the comments on ‘The boundary point method for the calculation of exterior acoustic radiation’ (by S.Y. Zhang, X.Z. Chen, Journal of Sound and Vibration 228(4) (1999) 761–772)”, Journal of Sound and Vibration, 298 (2006) 1178–1179] to defend themselves. Here, we would like to say a few words for the discussions in two aspects. One is the formulation, and the other is the occurrence of fictitious frequencies.

Comments on “Reply to the comments on ‘The boundary point method for the calculation of exterior acoustic radiation’ (by S.Y. Zhang and X.Z. Chen, Journal of Sound and Vibration 228(4) (1999) 761–772)”

Comments on “Reply to the comments on ‘The boundary point method for the calculation of exterior acoustic radiation’ (by S.Y. Zhang and X.Z. Chen, Journal of Sound and Vibration 228(4) (1999) 761–772)”

Comments on “The boundary point method for the calculation of exterior acoustic radiation” (by S.Y. Zhang and X.Z. Chen, Journal of Sound and Vibration 228(4) (1999) 761–772)

Comments on “The boundary point method for the calculation of exterior acoustic radiation” (by S.Y. Zhang and X.Z. Chen, Journal of Sound and Vibration 228(4) (1999) 761–772)

Reply to the comments on “Reply to the comments on ‘The boundary point method for the calculation of exterior acoustic radiation’ (by S.Y. Zhang, X.Z. Chen, Journal of Sound and Vibration 228(4) (1999) 761–772)”

Reply to the comments on “Reply to the comments on ‘The boundary point method for the calculation of exterior acoustic radiation’ (by S.Y. Zhang, X.Z. Chen, Journal of Sound and Vibration 228(4) (1999) 761–772)”

Reply to the comments on “The boundary point method for the calculation of exterior acoustic radiation” (by S.Y. Zhang, X.Z. Chen, Journal of Sound and Vibration 228(4) (1999) 761–772)

Reply to the comments on “The boundary point method for the calculation of exterior acoustic radiation” (by S.Y. Zhang, X.Z. Chen, Journal of Sound and Vibration 228(4) (1999) 761–772)

Treatment of Sharp Edges & Corners in the Acoustic Boundary Element Method under Neumann Boundary Condition

Boundary element method in acoustics for Neumann boundary condition problems including sharp edges & corners is investigated. In previous acoustic boundary element method, acoustic pressure and normal velocity are the two variables at sharp edges & corners. However, the normal velocity at sharp edges & corners is discontinuous due to the indefinite normal vector. To avoid the indefinite normal vector and the discontinuous normal velocity at sharp edges & corners, normal vector of elemental node is defined and applied in the numer- ical implementation. Then the normal velocity is trans- formed to velocity which is unique even at sharp edges & corners. Such treatments make sure that all variables in the acoustic boundary element method are definite. Computational efficiency and accuracy of the new model are demonstrated by threecases of interioracousticprob- lems for which analytical solutionscan be found and one classical exterior acoustic radiation problem. Curvilin- ear quadrilateral isoparametric elements are applied in the computation. It is found that the numerical results agree with corresponding analytical solutions quite well. keyword: Boundary element method, Sharp edge, Sharp corner, Normal velocity, Normal vector, Helmholtz integral equation

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.

THE BOUNDARY POINT METHOD FOR THE CALCULATION OF EXTERIOR ACOUSTIC RADIATION PROBLEM

A new numerical method, the boundary point method, used for calculating the acoustic radiation problem caused by a vibrating body is presented. The gist of the new numerical method is to replace the coefficient matrices [A] and [B] in the system equation with the particular solution matrices which are formed of the particular solutions generated by fabricated sources. In the boundary point method, it is unnecessary to consider the interpolating operation and the singular integral which is indispensable for the BEM also does not exist. By avoiding the direct computation for the coefficient matrices, the boundary point method can improve the calculation speed substantially while maintaining the calculation precision. Another advantage of the method is that it can be used for calculating the acoustic parameters (such as the sound pressure, etc.) at any desired point in the sound field without calculation of the acoustic parameters on the surface. Finally, the boundary point method can overcome the non-uniqueness problem at the characteristic wavenumbers effectively.The boundary point method put forward by the authors is applied to the calculation of the exterior acoustic radiation problem caused by a vibrating body. A detailed description of this method is presented. A test for the boundary point method is carried out on the aspects of its calculation precision and speed, adaptation to the geometric shape of vibrating body as well as effectiveness to overcome the non-uniqueness problem through various examples with different shapes and different boundary value distributions. An experiment on the exterior acoustic radiation of a vibrating rectangular box is performed in a semi-anechoic chamber.

A boundary integral approach for acoustic radiation of axisymmetric bodies with arbitrary boundary conditions valid for all wave numbers

A boundary integral method for solving the exterior acoustic radiation problem of axisymmetric bodies with arbitrary boundary conditions is developed. The new formulation derives from the method proposed by Burton and Miller [Proc. R. Soc. London Ser. A 323, 201–210 (1971)], which uses a linear combination of the Helmholtz integral equation and its normal derivative to ensure the uniqueness of the numerical solution at all frequencies. It is shown that the use of tangential operators enables one to easily compute the hypersingular integral without much extra effort. By taking advantage of the properties of axisymmetric geometry, and using the expansion of the boundary conditions and the surface distribution functions in Fourier series with respect to the angle of revolution, the surface integral is reduced to a line integral along the generator of the body, and Fourier integrals of the Green’s function and its derivatives over the circumferential angle. The Fourier integrals with singular kernels are evaluated using recurrence formulas in terms of the complete elliptic integrals. A new approach is then proposed to evaluate the Burton and Miller formulation at a corner by using the left-hand and right-hand limits of normal derivatives. Doing so, isoparametric elements throughout the surface of the body are able to be used. In order to demonstrate the validity and accuracy of the method, numerical results with quadratic isoparametric curvilinear elements are presented for radiation problems of a pulsating sphere, an oscillating sphere, and a finite cylinder with various boundary conditions.

A unique boundary integral approach for acoustic radiation of axisymmetric bodies with arbitrary boundary conditions

A boundary integral method for solving the exterior acoustic radiation problem of axisymmetric bodies with arbitrary boundary conditions has been developed. The new formulation derives from the method proposed by Burton and Miller, which uses a linear combination of the Helmholtz integral equation and its normal derivative to ensure the uniqueness of the numerical solution at all frequencies. By taking advantage of the properties of axisymmetric geometry, and using the expansion of the boundary conditions and the surface distribution functions in Fourier series with respect to the angle of revolution, the surface integral is reduced to a line integral along the generator of the body, and Fourier integrals of the Green’s function and its derivatives over the circumferential angle. A main feature of this formulation is that new recurrence formulas of the Fourier coefficients have been developed to evaluate accurately the Fourier integrals with the singular kernels in terms of the complete elliptic integrals. In order to demonstrate the validity and accuracy of the method, numerical results with quadratic isoparametric curvilinear elements are presented for radiation problems of a pulsating sphere, an oscillating sphere, and a finite cylinder with various boundary conditions.

On the exterior acoustic radiation modes of structures

The use of a modal-style approach for the analysis of the exterior radiation characteristics of structures has recently received increasing attention. This approach generally seeks to find a set of orthogonal functions, or acoustic modes, that diagonalizes a radiation operator. These acoustic modes are found through an eigenfunction or singular value decomposition of the radiation operator. The eigenvalue or singular value associated with a given acoustic mode is directly proportional to the radiation efficiency of that acoustic mode. The acoustic mode represents a particular velocity pattern on the surface of the radiator. As with the analogous problem of finding structural natural frequencies and mode shapes, the accuracy of the acoustic modal representation depends on the number of degrees of freedom in the radiation operator. The radiation efficiency of the most efficient acoustic mode has a finite upper bound, and converges fastest with increasing degrees of freedom. Each additional degree of freedom in a model introduces a new least efficient acoustic mode. In fact, the radiation efficiency of the least efficient acoustic mode may be forced arbitrarily close to zero by introducing sufficient degrees of freedom. The most efficient acoustic modes are least sensitive to perturbations in their velocity patterns, while the least efficient acoustic modes are most sensitive. These characteristics of the exterior modal acoustic representation have significant implications for the use of the modal representation in design, optimization, and active noise control. This paper explores these issues using the example of a finite baffled beam.

Acoustic radiation from cylinders with a plane of symmetry using internal multipole line source distributions. I

A new method is proposed to address the two-dimensional exterior acoustic radiation problem from infinite cylinders with a plane of symmetry. This approach, which has its roots in fluid mechanics, is based on the use of internal monopole and dipole line source distributions within the surface. The monopole and dipole line source distributions are determined by prescribed normal velocity conditions over the surface of the shell and are subsequently used to determine the associated surface pressure. The exterior acoustic field is then simply calculated using the surface velocity and pressure via the usual surface Helmholtz integral equation. In contrast to earlier integral equation formulations of the problem the present method does not suffer from either nonuniqueness or result in hypersingular integral equations. Numerical results are presented to illustrate the accuracy of the new internal source density method for the case of a circular cylinder subjected to various specified normal velocity boundary conditions and frequencies. Additional numerical results are also presented for the exterior acoustic radiation problem for a strip on an elliptical cylinder. These results show the characteristics of the surface pressure as a function of the surface velocity and strip width.

A modified Burton-Miller algorithm for treating the uniqueness of representation problem for exterior acoustic radiation and scattering problems

A modification to the Burton-Miller algorithm is formulated for exterior acoustic radiation and scattering problems which resolves the uniqueness of representation problem associated with the Helmholtz integral equation method (HIEM) at the interior eigenvalues. In particular, this modification reduces the required number of integral equation evaluations and allows for the continued use of the popular higher-order Lagrangian shape functions. Several example problems are considered to demonstrate the difficulties and subtleties of the uniqueness of representation problems associated with the Helmholtz integral equation method and to demonstrate the effectiveness of the modified Burton-Miller algorithm in overcoming these problems.