Scanning laser Doppler technique for model testing of distributed-parameter systems

Abstract

IN conventional modal testing, accelerometers are used to sense structural response data that are processed to obtain the natural frequencies, damping, and mode shapes of the structure under test. In the case of lightweight structures like composites where mass loading and other local effects of these transducers are not eligible, optical instruments like the laser Doppler vibrometer (LDV) are used. The availability of realtime scanning LDVs has introduced many interesting measurement possibilities. In the method developed in this paper, we process the scanning LDV velocity output signal in the frequency domain to directly obtain the deflection shape of the vibrating structure in a functional (series) form. The technique is demonstrated through application to the problem of modal identification of a cantilever beam. The identified dynamic characteristics of the cantilever beam have been compared with analytical solutions. The method employs a noninvasive, noncontact procedure that avoids the problem of transducer mass loading on lightweight structures and makes possible measurements on hard-to-reach and hazardous surfaces. Contents In its basic form, the LDV is essentially a point velocity sensor, with the sensitivity direction being along or perpendicular to the line of sight, depending on the optical configuration. To extend the usefulness of the instrument, manufacturers now offer automatic scanning mechanisms so that the measurements can be performed at a sequence of locations without operator intervention. However, the sensor is stationary during each measurement and the automation has been only in terms of successively moving the sensor to the next measurement point. If we take the concept further along, our system employs a higher scanning rate so that the test data can be considered to be acquired in a simultaneous sense (the sensor is moving continuously while the measurements are in progress). Although high-speed real-time scanning has been reported previously, the data processing has been limited to sampling the scanning LDV output and relating the instaneous velocity to fixed spatial locations, assuming a nonoscillatory velocity field. Using harmonic scanning along a straight line on the surface of a solid test object, our system can be used to obtain the velocity profile along the scan line in a functional form for oscillatory velocity fields also. It is shown that the spatial velocity distribution modulates the velocity output signal from the LDV, and a Fourier analysis of this modulated signal can be used to derive this spatial distribution in a Chebyshev series form. The technique is applicable to systems where the space-time distribution of velocity is of a particular