Structural Intensity Measurement Research Articles

Experimental measurement of structural intensity in the frequency–wave-number domain.

Typical methods of structural intensity measurement involve the use of either contacting transducers or single and dual channel laser vibrometers. Because of the generally limited number of measurement locations, approximations that can limit the accuracy of the measured structural intensity data are implemented. The accuracy of the data can be compromised especially in the case of finite structures. Furthermore, if waves with different wave-number components exist, the measurement schemes used are typically tailored toward only one wave type. Using a multiple channel laser vibrometer, with more than two channels, eliminates the need for the approximations in the measurements. Additionally, by scanning the surface of the structure, the structural intensity components can be decomposed by using frequency–wave-number transforms. The result for the structural intensity in the frequency–wave-number domain will discriminate the intensity component into those associated with in-plane and out-of-plane waves. The frequency and wave-number transforms are obtained using digital signal processing techniques. One disadvantage with this approach is that inherent in discrete signal processing. In this paper, issues associated with the range of frequency and wave number(s), spatial window size, selected window type, and method of processing are discussed. A data processing scheme for frequency–wave-number measurements of structural intensity on finite structures is defined. Results showing the application of this technique using the multiple channel laser vibrometer will also be presented. [Work sponsored by ONR.]

A Study on Structural Intensity Measurement. 3rd Report, Comparison of Several Methods.

A Study on Structural Intensity Measurement. 3rd Report, Comparison of Several Methods.

On measurement of structural intensity in thin‐walled structures

In order to measure structural intensity in a thin‐walled structure (shell), one has to employ intensity expressions given in terms of physical quantities that (a) are measurable and (b) refer to the external surface of the shell. These quantities are surface strains and displacements or displacement derivatives—either velocities or accelerations. Intensity expressions, which can serve as a starting basis for measurements, have been established for flat plates, circular cylindrical shells, and spherical shells. The expressions are given in terms of neutral‐surface displacement and strains, which are reference quantities for any theoretical analysis and, consequently, have to be translated to the external surface domain. Intensity in a flat plate consists of two contributions: one due to extensional, the other due to flexural effects. The shell, in addition, has the influence of curvature, which couples the in‐plane and the normal components of motion. As a result, large number of strains and displacement components have to be simultaneously detected in order to produce intensity readings correctly. The number of transducers required to measure these quantities is even larger, because some of the quantities are given in a differential form, implying use of multipoint finite difference schemes in practical measurements. Furthermore, some transducers, such as accelerometers, cannot measure at the body surface but somewhat above it, which necessitates corrections in readings of in‐plane motions. This and other reasons (transducer cross‐sensitivity, surface loading) make conventional vibration transducers impractical for this work. Preference in practical measurements should go to non‐contact methods which still have to be developed. This paper describes the nature of the intensity expressions related to thin shells. Examples are given of a circular cylindrical shell in contact with an acoustic medium. Various possibilities are described for measurement of intensity using conventional transducers. Sources of measurement errors and limitations are discussed in some detail. Finally, new measurement concepts are shown, aimed at improving accuracy and reducing difficulties encountered with conventional methods.

A study on structural intensity measurement. (2nd report. Experimental investigation).

This paper, following the previous report, descibes structural intensity measurement. Measurement errors, which are caused by the set distance of accelerometers and mutual phase mismatch of them, are examined first. Then the results of an experimental study which were carried out on a simple structure such as beam or plate are introduced. The results show the effectiveness of the structural intensity measurement using an array of accelerometers for the frequency range of 100Hz-1kHz where structure-borne sound becomes a problem. The separation of the wave component is successfully performed in a 1-dimensional experiment to know the reflection coefficient of the boundary.

Experimental Measurement of Structural Intensity on an Aircraft Fuselage

An experimental technique was used to measure structural intensity through an aircraft fuselage with an excitation load applied near one of the wing attachment locations. The fuselage was relatively large, requiring several measurement locations to analyze the intensity flow through the whole of the structure. For the measurement of structural intensity, the use of a transducer array was necessary at every location of interest. A trade-off was therefore required between the number of measurement transducers, the mounting of these transducers, and the accuracy of the measurements. Using four accelerometers mounted on a bakelite platform, structural intensity vectors were measured at locations distributed throughout the fuselage. The results of these measurements, together with a discussion on the suitability of the approach for measuring structural intensity on a real structure, are presented in this paper.

A study on structural intensity measurement. (1st report. Theoretical investigation).

The measurement of structural intensity using an array of accelerometers, which was proposed in the 1970s, but has not been put to pratical use due to its intrinsic complexity, is examined in this study. A theoretical investigation is performed in this paper. Formulation of the relation between bending wave in structures and structural intensity makes it possible to separate the wave component by which one can get a state of the vibration field. Then, the effect of the nearfield, which is thought to be great in the actual measurement, is examined. Comparison between the simple method by a pair of accelerometers and the strict array method, shows that the measurement error of the pair method is rather big especially in a two-dimensional wave.

Comparison of nearfield and farfield structural intensity by scanning laser vibrometry

A new measurement technique is being developed to measure true nearfield and farfield structural intensity by remote sensing and noncontacting instrumentation. A system composed of a scanning laser vibrometer with computer-controlled optical scanner allows for noncontacting measurement of the amplitude and phase of the vibration velocity of a structural member. The laser vibrometer has a dynamic range of 160 dB and broadband frequency response of up to 25 kHz. The vibrometer is held steady on a seismically isolated optical table and a mirror is positioned accurately by a computer-controlled stepper motor. The measurement of nearfield or farfield structural intensity at a point requires the measurement of the structural velocity at a minimum of four points for a beam and eight points for a plate about that point. Thus the amplitude and phase of the velocity field on the surface of a structure is measured at a fine mesh of discrete number of points. Error analysis is performed to assess the theoretical error introduced by the mesh size, number of points used for evaluating the structural intensity, random phase and amplitude errors, and errors introduced by nonsimultaneous measurements.

Measurement of structural intensity in submerged plates and shells using nearfield acoustical holography

Nearfield acoustical holography provides a complete mapping of the normal surface velocity distribution on the surface of a plate or cylindrical shell. For plates this measurement completely determines the full structural intensity (SI) in the plate and no assumptions need to be made about the wave field on the plate. In shells this normal velocity is not sufficient to determine the SI accurately (below the ring resonance) because of the coupling between in-plane velocity and out-of-plane velocity. Several techniques are presented to predict the in-plane velocities from a knowledge of the normal (radial) velocity taken from measured holographic data and the corresponding SI is calculated and compared. In addition, the instantaneous energy exchange between the shell and the nearfield in the fluid (the coupling between structural and acoustic intensity) is obtained from measured data and presented.

Structural intensity measurement techniques for single and multiple sources

The information available for power flow measurements may be used to determine the transmission paths of vibration sources. In multiple source situations, direct measurements of structural intensity do not give information on the contribution of each source. Reference signals associated with each source may be used to condition the spectra obtained at the measurement point to provide an estimate of the power flow due to each input. This technique has already been successfully applied to acoustic measurements. Results are presented using the direct method and these “selective techniques” for measurements using two, three, and four accelerometers, and for single and multiple inputs. The structure used for these experiments was a lightly damped bar and the results, using different types of reference signal and various estimators for the source contributions, illustrate the problems and the advantages of such methods in structural intensity measurements.

Scanning laser vibrometer system for structural intensity measurements

The steady‐state real‐time velocity response at successive locations on a beam are measured with a laser vibrometer and stored in a computer. The scanning system associated with the vibrometer consists of precision linear translation stages to control a lens/mirror combination. The laser beam is scanned along the length of the beam and the flexural vibration of a sinusoidally driven beam is measured at several locations. The amplitude and phase data are recorded at each location as well as a signal proportional to and in phase with the driving force. Knowing the distance between measurement locations, the recorded data are used to compute any of the following: spatial derivatives, transfer functions, and intensity.

Measurement of structural intensity in building constructions

When designing buildings with a maximum of sound insulation, it is important to know the different sound transmission paths in building structures, which are often complex. A direct measurement of the structure-borne sound intensity has been tried earlier on thin-plate constructions in laboratory set-ups. In this investigation an equivalent technique has been tried on practical building constructions, and the results appear to be promising even on relatively thick and heavy concrete walls with normal junctions to the surrounding constructions. The technique uses normal sound intensity measuring equipment. The experimental work was carried out in a specially designed flanking transmission laboratory during the author's stay at the French Building Research Establishment, CSTB, Grenoble.

Power flow measurements in beams with small localized damping

In an effort to establish the limitations of structural vibration intensity measurements for determining power flow in reverberant fields, classical power flow measurements were made on a free-field beam with point force excitation at one end and small local damping at the other. These classical methods were based on standing wave ratio measurements, measurements using force gauge/accelerometer combinations, and reverberation decay measurements. An investigation into the factors influencing the accuracy of these measurements was conducted. The force gauge/accelerometer measurements were found to be extremely sensitive to sensor phase inaccuracies if large reactive power components were present. These problems were avoided by conducting the experiment at frequencies where this reactive component was negligible (resonance) and by choosing damping materials which were mostly dissipative at these frequencies. Having established error bounds for these classical measurements it was possible to experimentally study the accuracy of intensity measurements by measuring known power flow in the presence of known reverberation. The results of this experiment will be discussed along with theoretical predictions of errors associated with intensity measurements in reverberant fields. [Research supported by David Taylor Naval Ship Research and Development Center, Washington, DC.]

Coupling loss measurements using an intensity approach

Cross-spectral methods for measuring structureborne noise intensity can also be employed to determine coupling-loss coefficients between elements of a complex structure such as a building or a ship. Experimental determinations of coupling-loss coefficients are needed in order to perform a statistical energy analysis of structural vibrations in cases where it cannot be assumed that strong coupling exists between all elements in the structure. In this talk the statistical energy analysis formulation of structural vibration problems will be reviewed. A method for determining the coupling-loss coefficient between two weakly coupled beam elements will be described. The method is based on a two-accelerometer, cross-spectral intensity measurement approach. In the case of weak coupling, high reverberation levels often exist (relative to the level of power flow between the structural elements). An experimental investigation of the errors introduced into structural intensity and coupling loss measurements will be reported. The relevance of this measurement concept to practical structural and acoustical noise localization problems will be discussed.