Generalized Nearfield Acoustical Holography Research Articles

Accuracy Improvement of Reconstruction in Near-Field Acoustical Holography by Applying Data Extrapolation Method

Near-field acoustical holography (NAH) is a non-contacting measurement method to visualize structural vibrations by means of backward reconstruction. A relevant data-smoothing process is necessary for the NAH experiments. We had previously proposed a new data-smoothing method with the aid of data extrapolation. In this paper, we report the effectiveness of this proposed method based on the experimental results. Furthermore, our data-smoothing method is modified for applications to the generalized NAH (GENAH). The experimental results show that the reconstruction error of the surface velocity by the proposed method is less than one-fifth of that by the conventional real-space window method for S/N=33 dB. These results indicate that the prospect of improving the accuracy of reconstruction in NAH for the quantitative analysis of structural vibrations is obtained by the proposed method.

Vibration of two concentric submerged cylindrical shells coupled by the entrained fluid

The vibrational characteristics of a point-driven ‘‘double shell’’ (two concentric submerged cylindrical shells coupled by the entrained fluid) are investigated theoretically and experimentally. Of particular interest are the shielding effects, if any, of the outer shell upon the inner shell. The theory on the double shell is based on Flügge’s infinite-shell equations, the Helmholtz wave equation, and boundary conditions at the fluid–structure interfaces. This theory is used to model a finite double-shell structure in wave number-frequency space. Experiments are carried out in which generalized near-field acoustical holography (GENAH) is employed to provide the experimental vibration characteristics in wave number-frequency space of the finite double shell. It is confirmed theoretically and experimentally that the outer shell of the double shell exhibits two separate dispersion curves: A higher-frequency dispersion curve exhibits in-phase vibrations with respect to the inner shell, and a second lower-frequency curve, out-of-phase vibration. The higher-frequency dispersion curve of the double shell is very similar to the dispersion curve of the single shell (the inner shell without the outer shell), and thus is identified as a forced wave number response. The lower-frequency curve seems to be dependent on the free wave number response of the outer shell alone of the double shell. A double-shell structure can usually reduce its vibrational amplitudes by splitting the response of single-shell’s forced vibration into the responses of inner-shell’s forced vibration and outer-shell’s induced vibration. However, it radiates low-frequency underwater sounds inevitably according to the lower-frequency dispersion curve. Furthermore, the appearance of the inner shell’s dispersion curve on the outer shell seems to indicate that the shielding influence of the outer shell is not completely effective.

Application of Generalized Near-Field Acoustical Holography to Scattering Problems

Generalized near-field acoustical holography (GENAH) is applied to scattering problems, making use of its wavelength-limitation-free characteristic in the reconstruction process. GENAH signal processing is directly adapted for the reconstruction of the scattered field, while a method to extract the scattered-pressure hologram is independently proposed to create scattering GENAH. The measurement of the near field of a scatterer yields the superimposed incident and scattered fields. Their decomposition is carried out by subtracting the incident-pressure hologram from the superimposed-pressure hologram in K space. The validity of this decomposition method was demonstrated by comparing the experimental and theoretical results of finite submerged shells. Reconstruction of shell-surface vibration induced by scattering displayed a reasonable result.

29 近距離場音響ホログラフィによる水中物体の振動映像化

The principle and signal-processing method of generalized near-field acoustical holography (GENAH) to the vibration of radiating surface are described. While the conventional acoustical holography is based on the acoustic pressure in far field, GENAR on that in near field. Much higher completeness of transformation of the measured field pressure to the surface vibration is then achieved by back-propagating evanescent waves in near field onto the surface. GENAH signal-processing utilizes the K-space analysis on the basis of the spatial Fourier trans-form, and it is able to visualize the correspondence between theory and experiment on vibroacoustical problems. As a specific example, it is illustrated how GENAH was applied to the study on the vibration of two concentric submerged cylindrical shells coupled by the entrained fluid.

Fluid-structure coupling by the entrained fluid in submerged concentric double-shell vibration.

Vibrational characteristics of a point-driven “double shell” (two concentric submerged cylindrical shells coupled by the entrained fluid) are investigated. Strong-and weak-coupling theories are proposed to model the interaction of how the inner and outer shells are coupled by the entrained fluid. Each theory is based on Flugge's infinite-shell equations, the Helmholtz wave equation, and boundary conditions at the fluid-struc tureinterfaces which depend on the coupling situation. Strong coupling forms a stand ingwavefield in the entrained fluid; weak coupling, a free wavefield. Experiments are carried out where generalized near-field acoustical holography (GENAH) is employed to provide the experimental vibration characteristics in wavenumber-frequency space of the finite double-shell. It is confirmed theoretically and experimentally that the outer shell of the double shell exhibits two separate dispersion curves: A higher-frequency curve bears in-phase vibrations with respect to the inner shell and suggests a forced response of the inner shell; the other lower-frequency curve, out-of-phase vibrations, and an induced response of the outer shell. Fluid-structure coupling condition de finitelyaffects the lower-frequency curve, but barely the higher-frequency one. Com parisonbetween theoretical and experimental results demonstrates the validity of the strong-coupling model.

Projection of near-field measurements of scattered pressure to the far field

NRL has successfully produced the first scattered hologram of an underwater shell, ensonified by a bow-incident plane wave. The total acoustic pressure is measured as a hologram on a cylindrical surface concentric to and in the near field of the shell. The scattered pressure is constructed by subtracting a hologram of the incident field, measured without the shell, from the total field hologram, with the shell in place. Using generalized near-field acoustical holography (GENAH), the scattered hologram is processed to reconstruct the pressure and radial velocity on the surface coincident with the shell exterior. The Helmholtz integral equation (HIE) is then applied to the pressure and velocity to compute the far-field directivity pattern. The shell used in the holographic measurement had its far-field response directly measured as well: the two measurements will be compared. Sources of error, including scattered energy escaping from the ends of the unclosed cylindrical contour used in the HIE, will be examined.

Theory and experiment of two concentric submerged cylindrical shells coupled by the entrained fluid

In this paper theory and experiment for the coupled vibration of two concentric cylindrical shells (double shell) are described; the inner shell contains air, the outer shell is surrounded by water, and water exists in the annular space between them. A point force is applied to the inner shell, whose displacement produces acoustic pressure in the annular space and in turn this pressure wave drives the outer shell. The nature of acoustic field in the annular fluid and its coupling effect on the shells is investigated. Using Flügge's shell equations and the Helmholtz equation, the normal modes of an infinite double shell are calculated. The theory includes the effect of initial prestress (uniform axial compression). The results of these numerical calculations in wave‐number space will be compared with the results from generalized near‐field acoustical holography (GENAH) experiment on a simply supported finite double shell. The wave‐number/frequency representation of this double shell will be also compared with that of a single submerged shell.

Modal analysis of fluid‐loaded, axisymmetric shells using nearfield acoustical holography data

Because typical methods of performing experimental modal analysis on structures in air do not apply well to those in water, an alternative, noncontact method was sought to measure vibration of thin, axisymmetric, submerged shells. Generalized nearfield acoustical holography (GENAH) provides a method for computing the normal velocity on the surface of these shells. The reconstructed velocity responses along the axis of the shell for each nth circumferential order form a series of “sensors.” The multiple reference Ibrahim time domain technique (MRITD), a high‐resolution modal decomposition, is applied to the data from these “sensors.” The MRITD is an eigenanalysis method that allows for multiple inputs and outputs. Its eigenvalues yield the mode frequencies and damping factors; its eigenvectors are the mode shapes. Repeated iterations and cluster analysis are used to locate true mode poles in the presence of noise. A least‐squares technique is further applied to generate participation factors for each mode. This technique has been applied to real data from axisymmetric, fluid‐loaded shells with endcaps. Results are presented for several mode sets.

Broadband nearfield acoustical holography for vibrating cylinders

Generalized nearfield acoustical holography (GENAH), a noncontact technique to measure the vibration and radiation from vibrating cylinders, has been applied in the past to study submerged cylinders excited into vibration at a single frequency. The technique has been expanded to broadband excitation, so that from a single experiment several octaves of acoustic data can be provided. With this new capability GENAH reaches its full power as an experimental technique for studying the complete acoustics of a vibrating, fluid-loaded cylinder. GENAH is used to reconstruct the radial velocity on the surface of a capped cylinder driven into vibration with a miniature shaker. Important validation of this reconstruction is provided by an accelerometer attached to the surface, which is compared to the reconstructed velocity. Agreement between them over the band of measurement (2.0–8.0 kHz) is better than 2 dB.

Wave-vector filtering of holographic data on point-driven cylinders

Generalized nearfield acoustical holography was used to provide the radial velocity ν(z,φ,ω) at over 8000 locations on a complete cylindrical surface tangent to a point-driven, submerged capped cylinder. Because of circumferential periodicity, circumferential waves can be extracted by the use of simple FFT methods, yielding ν(z,n,ω)einφ, where n is the circumferential wavenumber. To obtain an axial decomposition of the waves, the FFT fails due to insufficient resolution and spectral leakage. Instead a high-resolution method is used, the extended Prony method. Key to the success of this method is the use of singular value decomposition to estimate the number of waves (model order) present at a particular frequency and value of n. With the model-order estimation, the Prony method provides accurate location of the poles corresponding to the desired wavenumbers. An iterative scheme is used to refine the whole process. The resulting waves can be related to the fluid-loaded modes of the driven structure.

Simulated wave-vector filtering of impact-generated flexural wave disturbances on a finite thin-walled cylinder

The authors have recently undertaken a theoretical simulation of experiments similar to those performed recently at NRL by Earl G. Williams and his colleagues, in which a submerged cylinder is transiently excited and normal displacements are inferred using the generalized nearfield acoustical holography (GENAH) technique. In the present paper, the cylinder is modeled as a thin-walled shell with rigid immovable end caps and with the end conditions taken as being that of simply supported. A short duration point force f(t) is applied normally to the surface and one seeks to describe the resulting normal displacement field using a high-frequency (and short wavelength) asymptotic theory of propagating and evanescent flexural wave pulses on a curved plate. Fluid loading is taken into account approximately with modifications derived using the assumption that the flexural wavelengths are short compared to the length and radius of the cylinder. One asks for the time and surface position dependence of the normal surface displacement within a local region of the cylindrical surface before and after a simulated wave vector filtering has been applied. The filtering process is such that one seeks to isolate only that contribution from a narrow frequency band and from a localized region of wavenumber space. The exercise is intended to demonstrate that one can isolate and follow traveling wavelets propagating away from the source, spiraling around the cylinder, and undergoing successive reflections at the end caps. [Work supported by ONR.]

Generalized nearfield acoustical holography for cylindrical geometry: Theory and experiment

From the measurement of the acoustic pressure on a cylindrical, two-dimensional contour located close to the surface of an underwater, vibrating cylinder, the complete three-dimensional sound field can be reproduced (reconstructed) with the aid of a computer. This reconstruction technique, called GENAH (generalized nearfield acoustical holography), is unlike conventional holography because it provides a super resolution image of the sound-pressure field from the surface of the cylinder to the farfield. At the same time, GENAH reconstructs, from this two-dimensional measurement, the vector velocity and the vector intensity fields (energy flow) in the nearfield of the source, and identifies modes of surface vibration of the cylinder. Experimental results are provided and the accuracy of GENAH is demonstrated by comparison with the two-hydrophone technique.

Broadband generalized nearfield acoustical holography

Generalized nearfield acoustical holography (GENAH) has been applied to the study of the radiation from the vibration of cylinders radiating underwater. This experimental technique provides a complete description of the acoustic field from the surface of the vibrator to the farfield. Pressure, vector velocity, and vector intensity fields in three dimensions are reconstructed from a (two‐dimensional) cylindrical hologram of the acoustic pressure measured in the nearfield of the source. One of the limitations of GENAH has been the use of a discrete excitation frequency, usually a resonance frequency of the cylinder structure. A new hologram had to be measured for each frequency of interest. We have eliminated this restriction by developing a broadband excitation technique, so that a single broadband hologram contains several octaves of information. The broad frequency band is derived from a one‐cycle, modified sine wave, which powers a mechanical shaker driving the shell. Narrow‐band holograms are then created from this broadband hologram by data reduction. Applying GENAH to these holograms provides a complete, three‐dimensional description of the radiation from the cylinder over several octaves. Also, the modes of radial vibration are obtained along with a three‐dimensional mapping of the vector velocity and intensity fields. Experimental results will be shown.