Model Validation of a Bolted Beam Using Spatially Detailed Mode Shapes Measured by Continuous-Scan Laser Doppler Vibrometry

Abstract

The mode shapes of a structure are typically more sensitive than its natural frequencies to local features such as cracks, joints or other anomalies. However, when updating a finite element model for a complicated structure, the analyst is typically only provided with mode shape measurements at a very small number of sensors, so they must rely primarily on the frequencies. With the advent of the Laser Doppler Vibrometer (LDV), one can obtain an unprecedented level of spatial resolution in an automated manner. However, there still may be limitations on the information that can be obtained due to variation in the input to the structure from point to point, the large time required to acquire measurements at each point sequentially for some structures, and logistical issues. Continuous-scan laser vibrometry has the potential to overcome some of these limitations. The continuous-scan approach involves sweeping the laser spot continuously over the structure during a measurement, and then processing the measurement to estimate the mode shapes over a line or surface from that single measurement. This work explores the impact of a spatially detailed measurement set on model validation of a simple structure comprised of a straight beam with a bolted lap joint. The natural frequencies of the system are found to change by 1-3% due to the joint, but when the experimental natural frequencies are compared with those of the model the expected trends are not observed, so it is difficult to ascertain whether the joint model is correct based on the natural frequencies alone. On the other hand, mode shapes measured by CSLDV clearly reveal the presence of the joint, showing a 16-26% reduction in a few of the shapes in a 10-20 centimeter region surrounding the joint. The observed changes in the mode shapes correlate well with those estimated by the model.

An adaptive continuous scanning laser Doppler vibrometry technique for measuring vibrational mode shapes of structures with holes

“…As a non-contact vibration testing technique, CSLDV has been widely applied to structures with complete surfaces and regular shapes [7], such as beams [8][9][10][11] and plates [12]. Since high-resolution results can be obtained, it has been used for model updating, fault diagnostics [13], and health monitoring [14]. Liu et al [15,16] transformed the normalized rectangular scan path into an arbitrary continuous scanning path based on the method of using reference points to establish a mapping relationship to test irregularly shaped leaves.…”

Output-only Modal Analysis using Continuous-Scan Laser Doppler Vibrometry and application to a 20 kW wind turbine

“…The response stands out above the noise (due to imperfection in the LDV and to the non-flatness of the input spectrum) by about one order of magnitude. Table 1 shows the normalized Fourier coefficient vectors identified from the 5 harmonics shown in C and 1,7 C in Table 1), but those terms are from weakly represented peaks in the spectrum and so they become much smaller applying the weighted average. The mode shapes reconstructed from these Fourier coefficient vectors are plotted in Figure 5, as well as the averaged mode shape from the weighted average of all of the Fourier coefficients.…”

“…Indeed, CSLDV may be the only viable method for obtaining mode shape measurements from structures that change with time or which are subjected to inputs that are difficult to replicate. One may also obtain measurements with greatly increased spatial detail, leading to insights into the dynamics of a structure that may be helpful when performing model correlation and updating [1].…”

Vibrometer Steering System for Dynamic In-flight Tracking and Measurement

“…Laser scanning has been used with vibration measurements by letting the laser dwell on each point to record the individual frequency response. Another approach, continuous-scan laser doppler vibrometry (CSLDV), uses periodic scans to find the transient behavior of a set of points [12]. Signal processing then determines the global vibration modes.…”