Larry D. Mitchell

Global noise characteristics of a laser Doppler vibrometer—I. Theory

Abstract The use of a laser Doppler vibrometer to obtain velocity information from vibrating structures has gained wide acceptance in recent years. Although use of such an instrument can yield a spatially dense matrix of velocity information, several users have noted ‘noise’ at certain points in the spatial field. The technique by which the SLDV system operates results in occasional velocity ‘drop-outs’ which are unidirectional, always estimating the velocity response closer to zero than reality. These ‘drop-out’ areas occur more predominately at points of maximum velocity response with small rotational components. Alternatively, points exhibiting minimum velocity response with large rotational components are less susceptible to the ‘noise’. In this paper, an experiment to visualize the speckle pattern motions received by the photodetectors during these vibration conditions is presented. Theories regarding the source(s) of the ‘noise’ are developed.

Positional calibration of galvanometric scanners used in laser Doppler vibrometers

The knowledge of where one has measured the response of a structure is sometimes as important as the response measured. This paper describes a method for the calibration of the horizontal and vertical scanners in a laser Doppler vibrometer. The residual of the scanner position with respect to a first-order and second-order regression model will be discussed. Comparisons will be made to vendor-measured scanner characteristics. Detailed analysis of the scanner calibration data will result in a very accurate knowledge of where the measured data from a structure is located and directed. Moreover, this knowledge will enhance the accuracy of three-dimensional laser vibrometry.

Geometrical method for the determination of the position and orientation of a scanning laser doppler vibrometer

In this paper, a geometrical method is presented to determine the pose (position and orientation) of a Scanning Laser Doppler Vibrometer (SLDV) with respect to a structural coordinate system. Multiple registration points are used simultaneously in a least-squares sense. The structural coordinates and the corresponding scanning angles are known for each of the registration points. In the geometrical method three steps are involved in the determination of the SLDV pose. Its implementation has been tested by simulated data and experimental data. The results have shown that this method and its implementation are correct and effective.

Laser scanning system testing—Errors and improvements

The Scanning Laser Doppler Vibrometry (SLDV) technique has brought modal testing into a new era. A galvanometer-based laser scanning system for SLDV provides the position accuracy, speed, and flexibility for data acquisition. A novel parallel-shift method has been developed for testing and calibration of the scanning system to meet the precision requirements of modal testing. This parallel-shift method can provide a cost-effective means for a systematic laser scanning accuracy test. However, a number of measurement errors could occur during the scanning accuracy test. These errors could severally affect the accuracy of the test itself. Quantitative determination of the effects of these errors is necessary to evaluate and to improve the accuracy of the test. This paper gives a detailed analysis for all the errors involved in the galvanometer-based laser scanning accuracy test using the parallel-shift method. Improvements of the test setup and procedure are also proposed.

Global noise characteristics of a laser Doppler vibrometer—II. Experiments using beam dynamics

Abstract Part I of this paper discussed the presence of ‘laser noise’ in velocity measurements taken with an SLDV system. It was theorized that these noise areas resulted from the velocity ‘drop-out’ points which are a consequence of modulations in Doppler signal amplitudes which fall below the modulation–demodulation threshold. In this paper, an experiment is presented to investigate the optimal operating range of velocities for the SLDV system. Additionally, an experiment investigating the effect of the use of a highly retroreflective surface treatment on ‘laser noise’ is also presented. In order to determine the relative extend of the ‘laser noise’ in these scans, a novel statistical value which quantifies the overall quality of the scan data is developed, presented, and exercised on experimental test data.

Mapping Nonsquare and Unevenly Spaced 2-D SLDV Data of an Aircraft Fuselage by Using Spatial DFT-IDFT Techniques

The scanning laser Doppler vibrometry (SLDV) technique provides velocities of a structure at 2-dimensional (2-D) angularly evenly spaced (in the laser scanning sense) data points. This causes an unevenly spaced data point distribution on the surface of the test structure. In many cases evenly spaced data point distribution with square or rectangular grids is highly desirable. In this study the SLDV velocity data of a partial surface area of an aircraft fuselage were mapped to truly spatial evenly spaced coordinates by using the spatial DFT-IDFT technique with minimum distortion. This 2-D data mapping technique certainly is not limited to the fuselage, hut can he very useful for many other 3-D structures.

Temperature-induced variations in structural dynamic characteristicspart II: analytical

Precise and detailed knowledge of the dynamic characteristics of structures has become increasingly important in recent years. As a consequence, the accuracy of experimental data, which is often used to validate and to update finite element models, has become extremely important. It has been shown experimentally that small changes in ambient temperature can cause distinct variations in the natural frequencies of a lightly damped structure which, in turn, may result in significant errors in experimental and analytical results. Therefore, a good understanding of the physical driving mechanisms involved is necessary so that adequate stability control measures may be implemented. This paper presents an analytical investigation of the variations in natural frequency caused by small changes in temperature. An analytical plate dynamic model is developed accounting for the effects of temperature- dependent material properties. Changes in temperature influence Youngs modulus, structural dimensions (via thermal expansion), and boundary condition effects. These change cause variations in the natural frequencies which result in marked changes in structural dynamic response at frequencies near resonance, especially when damping is low. Natural frequencies decrease linearly with increasing temperature over the limited temperature range in this study. A sensitivity analysis indicates that the temperature-dependence of Youngs modulus is the dominant factor influencing the variations in natural frequency, but boundary condition effects may also be important.

Error analysis and improvements for using parallel-shift method to test a galvanometer-based laser scanning system

The Scanning Laser Doppler Vibrometry (SLDV) technique has brought modal testing into a new era. A galvanometer-based laser scanning system for SLDV provides the position accuracy, speed, and flexibility for data acquisition. Testing and calibrating such a scanning system to meet the precision requirements of modal testing has led to the development of the novel parallel-shift method for testing and calibration of the scanning system. This parallel-shift method can provide a cost-effect means for systematic laser scanning accuracy test. However, a number of measurement errors could be involved during the scanning accuracy test. These errors could severally affect the accuracy of the test itself. It is necessary to quantitatively determine the effects of the measurement errors to evaluate and to improve the accuracy of the test. This paper gives a detailed analysis for all the errors involved in the galvanometer-based laser scanning accuracy test using the parallel-shift method. Improvements of the test setup and test procedure are also proposed.

Temperature-induced variations in structural dynamic characteristics part I: experimental

When using conventional or laser Doppler vibrometer methodologies, the resonance-dwell technique is used to characterize the response shapes of structures vibrating near resonance. If the structure is large (and/or complex) and if high spatial density data is required, data acquisition could take a significant amount of time. During that time, changes in structural characteristics can occur with cause very large variations in the vibration response amplitudes at the same structural point. An understanding is needed of why such changes occur and of how a structure can be stabilized during prolonged dynamic testing. The goal is to make the measured response data as accurate as possible. This paper presents an experimental investigation of the variations in natural frequency caused by short- or long- term temperature changes. The rectangular steel plate natural frequencies were determined at temperatures slightly above and below standard room temperature. Two boundary condition configurations were studied: a clamped (pseudo- cantilever, C-F-F-F) configuration, and a free (F-F-F-F) configuration. The results indicate that natural frequencies decrease with increasing temperature, resulting in large variations in the response near resonances. Furthermore, larger natural frequency variations are observed in the clamped configuration than in the free configuration, indicating that temperature-induced boundary condition effects are important.

Using spatial DFT-IDFT techniques for mapping of nonsquare and unevenly 2-D velocity data acquired by scanning laser Doppler vibrometer

The state-of-the-art Scanning Laser Doppler Vibrometry (SLDV) technique provides an efficient data acquisition method for modal testing, especially on a large structure with high spatial data density. Two-dimensional angularly evenly spaced (in the laser beam scanning sense) data point distribution are generated. This causes an unevenly spaced data point distribution on the surface of the test structure in the most cases. The interval variations between data points can be quite large if the surface of the structure is not flat, such as an aircraft fuselage. The grid of data points will also become non-square. However, in many cases evenly spaced data point distribution with square or rectangular grids is highly desirable. One such case is when the structure is too large for one scan. A few separate scans are required to be patched together to describe the entire structure. The second example is when a structure needs to be scanned from different viewing angles and data points from different scans need to be coincident to extract 3-D velocity data of the surface of the structure. The third example is where the data points are used to obtain the wavenumber of the vibrating surface of the structure. In this paper, the original velocity data of a partial surface area of an aircraft fuselage were acquired to busing the SLDV technique with a high spatial density. The 2-D angular evenly spaced data then were mapped to a truly spatial evenly spaced coordinates by using the spatial DFT-IDFT technique. This DFT-IDFT technique can preserve original measured velocity information (even including the noise) during the mapping process. This 2-D data mapping technique certainly is not only limited to the fuselage, but also can be very useful for any 3-D structures, large or small, that require more than one scan to compleate surface velocity data acquisition.