Uniqueness of Solutions to Variationally Formulated Acoustic Radiation Problems

1990 ◽  
Vol 112 (2) ◽  
pp. 263-267 ◽  
Author(s):  
Xiao-Feng Wu ◽  
Allan D. Pierce
Keyword(s):  
Acoustic Radiation ◽  
Axial Direction ◽  
Acoustic Power ◽  
Normal Derivative ◽  
Surface Velocity ◽  
Finite Cylinder ◽  
Uniqueness Of Solutions ◽  
Integral Theorem ◽  
Kirchhoff Integral

Determination of the surface acoustic pressure given the surface velocity of a vibrating body can be formulated in various ways. However, for some such formulations such as the surface Helmholtz integral equation, solutions are not unique at certain discrete frequencies. Such uniqueness problems can also be present for variational formulations of the problem, but the variational formulation based on the normal derivative of the Kirchhoff integral theorem has unique solutions for vibrating disks and plate-like bodies. For bodies of finite volume, but for which each surface point is vibrating in phase, the total radiated acoustic power is always unique, even though the pressure may not be. The latter conclusion is supported by numerical calculations based on the Rayleigh-Ritz technique for the case of a finite cylinder vibrating as a rigid body in the axial direction.

An Acoustic Superposition Method for Computing Structural Radiation in Spatially Digitized Domains

2007 ◽  
Author(s):  
Brian C. Zellers ◽  
Gary H. Koopmann ◽  
Michael L. Jonson
Keyword(s):  
Acoustic Radiation ◽  
Acoustic Power ◽  
Surface Velocity ◽  
Superposition Method ◽  
3D Space ◽  
Mlpg Method ◽  
Distribution Of Points ◽  
Structural Surface ◽  
The Green Function ◽  
Good Agreement

This paper presents a new method for computing acoustic fields of structural radiators based on acoustic superposition methods using meshless, spatially digitized domains (ASMDD). Here the system matrices are assembled knowing only coordinate points in 3D space that describe the geometry of the radiating structure. In contrast to conventional methods, ASMDD does not require numerical, high orders of integration over elemental surfaces to populate system matrices. The system’s Green functions are computed simply between source and receiver locations at their respective points. A new derivation provides an analytical solution for coincident source and receiver points where the Green function is singular. The digital domain of ASMDD is a uniform distribution of points equidistant in the x, y, and z directions. The centroid of each activated voxel (used only as a means for visualizing the 3D surface) represents a point on the structural surface being modeled. Work in this paper exploits the inherent uniformity of neighboring points to formulate a locally determined outward-pointing, surface normal needed for acoustic radiation problems. The ability of the calculated surface normals to model the curvature of the continuous radiating surface depends on the density of the meshless grid, i.e., higher curvature requires higher grid densities. The attractiveness of the digital domain approach is its simplicity for morphing of structural shapes in optimization. Shape iterations in the digitized space reduce to a simple process of activating or deactivating selected points in a contiguous manner depending on the desired shape during an optimization. As an example, the ASMDD formulation is used to compute the modal radiation from a square plate in an infinite and cubic baffle. The ASMDD surface points are shown to blend seamlessly with the surface vibration results of the plate generated via meshless structural dynamics (Meshless Local Petrov Galerkin method - MLPG). This is achieved by solving the modal radiated acoustic power from the plate where the surface velocity is specified by the modal results determined by the MLPG method. The sound power calculations are in good agreement with those generated via conventional BEM codes.

Determination of the Average Energy of Iron Ions in the Axial Direction of a Micropinch Discharge Using an Ion Collector

2019 ◽  
Vol 82 (10) ◽  
pp. 1387-1391
Author(s):  
S. A. Sarantsev ◽  
I. F. Raevskii ◽  
V. A. Kostyushin ◽  
A. S. Savelov
Keyword(s):  
Average Energy ◽  
Axial Direction ◽  
Iron Ions

Acoustic Radiation From Thick Laminated Cylindrical Shells With Sparse Cross Stiffeners

2013 ◽  
Vol 135 (3) ◽  
Author(s):  
Xiongtao Cao ◽  
Chao Ma ◽  
Hongxing Hua
Keyword(s):  
Cylindrical Shell ◽  
Radial Displacement ◽  
Acoustic Radiation ◽  
Periodic Structures ◽  
Cylindrical Shells ◽  
Acoustic Power ◽  
Acoustic Energy ◽  
Parallel Plates ◽  
Wavenumber Domain ◽  
Laminated Cylindrical Shells

A general method for predicting acoustic radiation from multiple periodic structures is presented and a numerical solution is proposed to find the radial displacement of thick laminated cylindrical shells with sparse cross stiffeners in the wavenumber domain. Although this method aims at the sound radiation from a single stiffened cylindrical shell, it can be easily adapted to analyze the vibrational and sound characteristics of two concentric cylindrical shells or two parallel plates with complicated periodic stiffeners, such as submarine and ship hulls. The sparse cross stiffeners are composed of two sets of parallel rings and one set of longitudinal stringers. The acoustic power of large cylindrical shells above the ring frequency is derived in the wavenumber domain on the basis of the fact that sound power is focused on the acoustic ellipse. It transpires that a great many band gaps of wave propagation in the helical wave spectra of the radial displacement for stiffened cylindrical shells are generated by the rings and stringers. The acoustic power and input power of stiffened antisymmetric laminated cylindrical shells are computed and compared. The acoustic energy conversion efficiency of the cylindrical shells is less than 10%. The axial and circumferential point forces can also produce distinct acoustic power. The radial displacement patterns of the antisymmetric cylindrical shell with fluid loadings are illustrated in the space domain. This study would help to better understand the main mechanism of acoustic radiation from stiffened laminated composite shells, which has not been adequately addressed in its companion paper (Cao et al., 2012, “Acoustic Radiation From Shear Deformable Stiffened Laminated Cylindrical Shells,” J. Sound Vib., 331(3), pp. 651-670).

scholarly journals Determination Of Snow Facies and Ice Velocity Using Synthetic Aperture Radar Imagery

1990 ◽  
Vol 14 ◽  
pp. 330-330
Author(s):  
R.A. Bindschadler ◽  
P.L. Vornberger
Keyword(s):  
Synthetic Aperture Radar ◽  
Liquid Water ◽  
Snow Accumulation ◽  
Surface Velocity ◽  
Synthetic Aperture ◽  
Stream Network ◽  
Backscatter Signal ◽  
Volume Scattering ◽  
Aperture Radar

The properties of synthetic aperture radar (SAR) imagery are appropriate for its use to map snow facies. These facies, defined by Benson (1962), are subdivisions of the accumulation area of an ice sheet or polar glacier and represent the interaction of the ice mass with the climate through the processes of snow accumulation and melting. Changes in these climatic parameters are expected to cause changes in the extent and character of these facies. The ability of SAR to discriminate these facies is due to the significant amount of sub-surface volume scattering in the measured radar backscatter signal and the strong absorption of radar energy by liquid water. The amount of volume scattering is dependent on the size and distribution of scatterers in the medium. This dependence varies over the size range of snow grains to ice lenses. Specific examples of the ability to detect different scatterer populations in ice sheets with SAR are shown. Other examples are given to demonstrate the reduction of backscatter signal when liquid water is present.Another important application of SAR data is the determination of surface velocity. Coregistration of a SAR and a TM image spanning an eight-year period was completed for an area in south-western Greenland. The composite image shows that, while the network of surface streams is nearly unchanged, their distance from lakes upstream increased over the eight-year interval between images. Because the lakes are likely fixed in space, a result of surface depressions whose positions are determined by the stationary bedrock topography, the displacement of the stream network was used to calculate a surface velocity of 40 ± 10 m per year near the equilibrium line.

Relationships Between Acoustic Radiation Modes, Complex Acoustic Power, and Radiation Efficiency

1997 ◽  
Author(s):  
Pei-Tai Chen
Keyword(s):  
Acoustic Radiation ◽  
Acoustic Power ◽  
Radiation Efficiency ◽  
Acoustic Energy ◽  
Normal Velocity ◽  
Far Field ◽  
Surface Complex ◽  
Surface Integral ◽  
Complex Power ◽  
Mass Spring

Abstract The paper explores the physical meaning underlying the surface complex acoustic power of a vibrating body, and its relationship to radiation efficiency under mono-frequency oscillations. The vibrating can be the entire wetted surface, or only a part of the surface with the remaining surface being held rigid. The surface complex acoustic power can be computed by the surface integral of pressure multiplying the complex conjugate of normal velocity. Based on the Gaussian Divergence theorem, it is shown that the real part of the complex power is the power radiated into a far field, while that the imaginary part pertains to the volume integral of the difference between the acoustic kinetic energy density with the potential energy density over the volume between the vibrating surface and the far field. The dynamical behavior of the acoustic field can be viewed as an infinite degree of freedom mass/spring/dashpot system, where the mass and spring are the inertia effects and acoustic compression effects of the acoustic particles and the dashpot is due to the plane wave relationship of the pressure waves at the far field that the acoustic energy propagates away from the acoustic field. By the model of the mass /spring/dashpot system, the phase angle of the complex acoustic power is identified as an indication of the ability of the vibrating surface to radiate acoustic power. The phase angle of the complex power depends on the distribution of the surface normal velocity. In order to study the normal velocity profile in relation to the ability to radiate acoustic energy, the previously established radiation mode (Chen and Ginsberg, 1995) is introduced and extended to situations in which a part of the surface is held rigid. An orthogonal condition for the velocity radiation modes is also established such that arbitrary velocity profiles can be decomposed into radiation modes. The acoustic modal radiation efficiency, defined as the radiated modal acoustic power divided by the surface integral of mean square normal velocity, is investigated in terms of the acoustic eigenvalue of that mode. Several different geometries of vibrating bodies are used to demonstrate the correlation of radiation efficiencies to eigenvalues of radiation modes, which include a rectangular baffled vibrating membrane, a box with only one of the six surfaces vibrating, a slender spheroidal body, and a spherical body. This correlation of acoustic radiation characteristics for different geometries is also demonstrated for a spheroidal body vibrating at some areas with other areas being held rigid.

Numerical Modelling of Boundary Layers and Far Field Acoustic Propagation in Thermoviscous Fluid

2019 ◽  
Vol 105 (6) ◽  
pp. 1137-1148
Author(s):  
Nicolas Joly ◽  
Petr Honzík
Keyword(s):  
Finite Element ◽  
Integral Representation ◽  
Acoustic Radiation ◽  
Element Formulation ◽  
Open Domain ◽  
Uniqueness Of Solutions ◽  
Resonant Frequencies ◽  
Time Harmonic ◽  
Finite Element Node ◽  
Thermoviscous Fluid

To model linear acoustics in a thermoviscous fluid in open domain and time-harmonic regime, a Finite Element formulation in a bounded meshed domain is combined with the integral representation of the field for the propagative solution. The integrals are non-singular and involve the only Finite Element node values for temperature variation and particle velocity variables. To overcome the non-uniqueness of solutions at fictitious resonant frequencies, a Burton-Miller combination of integral representation is used. This formulation is suitable to compute acoustic radiation, scattering and diffraction by objects or mutual interaction between transducers. Two-dimensional computational experiments are presented in an infinite, open domain (exterior), showing that the model can be achieved in meshing only a thin domain surrounding the physical boundaries of a device.

Research on Vibro-Acoustic Characteristics of Underwater Finite Plate-Shell Structure under Multiple Excitations

2013 ◽  
Vol 834-836 ◽  
pp. 1351-1359
Author(s):  
Yong Yong Zhu
Keyword(s):  
Shell Structure ◽  
Acoustic Radiation ◽  
Radiation Power ◽  
Acoustic Vibration ◽  
Finite Cylinder ◽  
Acoustic Characteristics ◽  
Theory Of Plates ◽  
Plates And Shells ◽  
Vibration Coupling ◽  
Finite Cylindrical Shell

An analysis based on the first kind of Lagranges equations was presented for investigating the vibration and acoustic radiation of underwater finite cylindrical shell with interior plate under multiple excitations. The strain energy and kinetic energy of cylinder and plate were gained by the theory of plates and shells, and the potential energy of excitation and fluid loading was found based on acoustic-vibration coupling, and the connection conditions of plate and cylinder were expressed by Lagrange multipliers, then the vibro-acoustic equations of finite cylinder with interior plate under shafting excitation were established. The influences of excitations and plates position to the vibro-acoustic characteristics were studied by the equations. The results show that the frequency components of plate-shell structure are more complex. For the double excitations on plate, the distance between excitations is larger, the average velocity and sound radiation power are lower, while the radiation efficiency is larger. The modeling and analytical methods adopted in this paper are also available for more complex composite structure.

A modal boundary element method for axisymmetric acoustic problems in an arbitrary uniform mean flow

2020 ◽  
pp. 1475472X2097838
Author(s):  
Bassem Barhoumi ◽  
Jamel Bessrour
Keyword(s):  
Boundary Element Method ◽  
Boundary Element ◽  
Singular Integrals ◽  
Acoustic Radiation ◽  
Normal Derivative ◽  
Boundary Integral ◽  
Meridian Plane ◽  
Mean Flow ◽  
Transform Method ◽  
Element Method

This paper presents a new numerical analysis approach based on an improved Modal Boundary Element Method (MBEM) formulation for axisymmetric acoustic radiation and propagation problems in a uniform mean flow of arbitrary direction. It is based on the homogeneous Modal Convected Helmholtz Equation (MCHE) and its convected Green’s kernel using a Fourier transform method. In order to simplify the flow terms, a general modal boundary integral solution is formulated explicitly according to two new operators such as the particular and convected kernels. Through the use of modified operators, the improved MBEM approach with flow takes a convective form of the general MBEM approach and has a similar form of the nonflow MBEM formulation. The reference and reduced Helmholtz Integral Equations (HIEs) are implicitly taken into account a new nonreflecting Sommerfeld condition to solve far field axisymmetric regions in a uniform mean flow. For isolating the singular integrations, the modal convected Green’s kernel and its modified normal derivative are performed partly analytically in terms of Laplace coefficients and partly numerically in terms of Fourier coefficients. These coefficients are computed by recursion schemes and Gauss-Legendre quadrature standard formulae. Specifically, standard forms of the free term and its convected angle resulting from the singular integrals can be expressed only in terms of real angles in meridian plane. To demonstrate the application of the improved MBEM formulation, three exterior acoustic case studies are considered. These verification cases are based on new analytic formulations for axisymmetric acoustic sources, such as axisymmetric monopole, axial and radial dipole sources in the presence of an arbitrary uniform mean flow. Directivity plots obtained using the proposed technique are compared with the analytical results.

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