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.

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.

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 Numerical Analysis of Structure Acoustic Radiation Based on Wave Superposition Method

2011 ◽  
Vol 2-3 ◽  
pp. 733-738
Author(s):  
Sheng Yao Gao ◽  
De Shi Wang ◽  
Yi Qun Du
Keyword(s):  
Integral Equation ◽  
Acoustic Field ◽  
Acoustic Radiation ◽  
Boundary Surface ◽  
Impact Factors ◽  
Power Calculation ◽  
Superposition Method ◽  
Sound Power ◽  
Wave Superposition ◽  
Equivalent Sources

To overcome the non-uniqueness of solution at eigenfrequencies in the boundary integral equation method for structural acoustic radiation, wave superposition method is introduced to study the acoustics characteristics including acoustic field reconstruction and sound power calculation. The numerical method is implemented by using the acoustic field from a series of virtual sources which are collocated near the boundary surface to replace the acoustic field of the radiator, namely the principle of equivalent. How to collocate these equivalent sources is not indicated definitely. Once wave superposition method is applied to sound power calculation, it is necessary to evaluate its accuracy and impact factors. In the paper, the basic principle of wave superposition method is described, and then the integral equation is discretized. Also, the impact factors including element numbers, frequency limitation, and distance between virtual source and integral surface are analyzed in the process of calculate the acoustic radiation from the simply supported thin plate under concentrated force. The extensive measures of acoustic field at the thin plate are compared with results obtain using different numerical methods. The results show that: (a) The agreement between the results from the above numerical methods is excellent. The wave superposition method requires fewer elements and hence is faster. But the extensive numerical modeling suggests that as long as the volume velocity matching yields more than adequate accuracy. (b) The equivalent sources should be collocated inside the radiator. And the accuracy of a given Gauss integration formula will decrease as the source approaches the boundary surface. (c) The numerical method is applicable to the acoustic radiation of structure with complicated shape. (d) The method described in this paper can be used to perform effectively sound power calculation, and its application range can be extended on the basis of these conclusions.

Fatigue Characteristics of Composite Antenna Structure

2004 ◽  
Vol 261-263 ◽  
pp. 1109-1114
Author(s):  
Dong Hal Kim ◽  
W. Hwang ◽  
Hyun Chul Park ◽  
W.S. Park
Keyword(s):  
Fatigue Life ◽  
Satellite Communication ◽  
Fatigue Behavior ◽  
Load Level ◽  
Tangent Loss ◽  
Antenna Structure ◽  
Antenna Performance ◽  
Bending Fatigue Test ◽  
Structural Surface ◽  
Good Agreement

The objective of this work was to design Surface Antenna Structure (SAS) and investigate fatigue behavior of SAS that was asymmetric sandwich structure. This term, SAS, indicates that structural surface becomes antenna. Constituent materials were selected considering electrical properties, dielectric constant and tangent loss as well as mechanical properties. For the antenna performance, SSFIP elements inserted into structural layers were designed for satellite communication at a resonant frequency of 12.5 GHz and final demonstration article was 16 x 8 array antenna. In cyclic loading, flexure behavior was investigated by 4-point bending and 4-point bending fatigue test. Fatigue life curve of SAS was obtained. Experimental results were compared with single load level fatigue life prediction equations (SFLPEs) and in good agreement with SFLPEs. SAS concept is the first serious attempt at integration for both antenna and composite engineers.

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.

scholarly journals Plate impact shock experiments and numerical modeling of lightweight adobe masonry material

2018 ◽  
Vol 183 ◽  
pp. 01017 ◽  
Author(s):  
Christoph Sauer ◽  
Frank Bagusat ◽  
Andreas Heine ◽  
Riedel Werner
Keyword(s):  
Numerical Model ◽  
Surface Velocity ◽  
Plate Impact ◽  
Shock Response ◽  
Velocity Relation ◽  
Masonry Material ◽  
Strength Material ◽  
Adobe Masonry ◽  
Particle Velocities ◽  
Good Agreement

In this contribution, we summarize and extend the experimental and numerical investigation of the shock response of lightweight adobe masonry, previously published in [C. Sauer et al., J. Dyn. Behav. Mater. (submitted)]. It is demonstrated that inverse planar plate impact (PPI) experiments are feasible for lightweight adobe. From the obtained free surface velocity time curves, a linear shock velocity vs. particle velocity relation is derived within the measured range of particle velocities. Numerical simulations of these curves show that the employed homogenous numerical model is capable of properly treating the shock response of this porous, inhomogeneous, and low-strength material. This numerical model is then applied to the example of the ballistic impact of steel spheres on targets consisting of one lightweight adobe brick. The experimentally obtained penetration craters are properly reproduced by the simulated target damage. Moreover, we find good agreement of the measured and simulated residual velocities within the presented range of impact velocities.

scholarly journals Analysis of Vertical Dynamic Cross Interaction between Adjacent Footings for Railway Tracks through Soil

2019 ◽  
Vol 278 ◽  
pp. 03008
Author(s):  
Jue WANG
Keyword(s):  
Harmonic Excitation ◽  
Superposition Method ◽  
Distance Ratio ◽  
Rigorous Results ◽  
Soil Medium ◽  
Railway Tracks ◽  
Boundary Value Method ◽  
Principal Value ◽  
Convergence Study ◽  
The Green Function

An efficient semi-analytical method is presented for the vertical analysis of adjacent railway tracks considering the dynamic cross interaction (DCI) effect through the semi-infinite soil medium. The interfaces between soil and tracks are discretized into a series of strip elements to solve the unknown contact pressure influenced by DCI effect. The Green function for each element under uniform harmonic excitation is derived and calculated by the piecewise integration and Cauchy principal value integral. The vertical impedance matrix is finally obtained by the superposition method. The accuracy and the effectiveness in high frequency range are verified by the convergence study, as well as the comparison study with the rigorous results from the mix-boundary-value method. The influence of the soil properties and the tracks distance on the DCI effect are discussed in detail in the parameter studies. It is shown that the DCI effect increases with the decrease of the distance ratio S/L.

Prediction for Sound Radiated Power from Submerged Double Cylindrical Shells Based on Measuring Vibration of Inner Shell

2013 ◽  
Vol 779-780 ◽  
pp. 602-606 ◽  
Author(s):  
Chao Zhang ◽  
De Jiang Shang ◽  
Qi Li
Keyword(s):  
Prediction Error ◽  
Cylindrical Shells ◽  
Prediction Method ◽  
Superposition Method ◽  
Power Curve ◽  
Mean Square ◽  
Average Prediction Error ◽  
Radiated Power ◽  
Modal Superposition Method ◽  
Good Agreement

A prediction method for the sound radiated power from submerged double cylindrical shells based on measuring vibration of inner shell is presented. The prediction model of submerged double cylindrical shells is established by using modal superposition method. Applied the ratio of the measuring value and theoretical value of the acceleration in one point or mean square velocity of inner shell, and combined with the theoretical value of the sound radiated power, the predicted value of the sound radiated power is derived. The corresponding experiment is carried out in lake. And then the measuring power curve is compared with the predicted power curve based on this method. The result shows that they have good agreement and the average prediction error is less than 2dB.

scholarly journals Sound Radiation due to Modal Vibrations of a Spherical Source in an Acoustic Quarterspace

2004 ◽  
Vol 11 (5-6) ◽  
pp. 625-635 ◽  
Author(s):  
Seyyed M. Hasheminejad ◽  
Mahdi Azarpeyvand
Keyword(s):  
Acoustic Radiation ◽  
Classical Method ◽  
Spherical Wave ◽  
Closed Form Solution ◽  
Addition Theorem ◽  
Form Solution ◽  
Surface Velocity ◽  
Rigid Boundary ◽  
Radiation Impedance ◽  
Spherical Source

Radiation of sound from a spherical source, vibrating with an arbitrary, axisymmetric, time-harmonic surface velocity, while positioned within an acoustic quarterspace is analyzed in an exact manner. The formulation utilizes the appropriate wave field expansions along with the translational addition theorem for spherical wave functions in combination with the classical method of images to develop a closed-form solution in form of infinite series. The analytical results are illustrated with numerical examples in which the spherical source, vibrating in the pulsating (n= 0) and translational oscillating (n= 1) modes, is positioned near the rigid boundary of a water-filled quarterspace. Subsequently, the basic acoustic field quantities such as the modal acoustic radiation impedance load and the radiation intensity distribution are evaluated for representative values of the parameters characterizing the system.

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