A key goal in several structural dynamics studies is to define the locations on a structure where failures are most likely to occur. Fatigue damage is a result of fluctuating strain. Therefore, it is extremely desirable to identify the locations of maximum strain.
It is also necessary to calculate the distribution of dynamic strain on these structures to ensure dynamic and fatigue strength. It is crucial to attain an accurate and full-field strain distribution when utilizing experimental data to verify and update a finite element (FE) model.
Using strain gages is one of the most basic techniques to measure strain, but there are many drawbacks to this technique. The strain gage is fixed to one location, and in lightweight, small structures, the strain gages and their connecting cables cause a further mass-loading effect and added damping.
Establishing the exact position of the strain gage on the test surface can be another challenge, since the strain maxima in real components can deviate from the model-predicted locations because of, for example, manufacturing variations and tolerances.
It is extremely difficult to ensure that you can pinpoint the precise location of maximum strain without the guidance of an FE model because it is not practical to use a large number of strain gages. A lot of optical techniques were developed in the search for a superior strain measurement method.
A non-contact optical technique, which has high spatial and vibration resolution that has been employed since the 1990s is Scanning Laser Doppler Vibrometry (SLDV). It was recently optimized for 3D measurements, resolving the vibration into the out-of-plane and in-plane components.
Only the transverse displacement w of a vibrating plate can be correctly measured when utilizing one SLDV. According to small deformation theory, the strain components in a plate due to bending are given by:
With z the transverse distance relative to the center of the plate, w(x, y, t) the transverse displacement, x and y coordinates of a point along the surface of the plate, and t the time. However, strain at the surface of a structure is equal to the spatial derivative of the in-plane surface displacement.
Surface strains are often of great concern because they are generally greater than internal strains and so are more likely to result in failures. The in-plane displacements can only be measured by utilizing the 3D Scanning Vibrometer.
Experimental Setup and Measurement
An aluminum fan blade was chosen as a test component, which came from the fan assembly as shown in Fig. 1. The part was especially interesting due to its high resonant frequencies, low weight, 3D curvatures, small size, and expected small strains.
Figure 1: Fan blade with strain gages in complete fan.
Figure 2: Measurement setup: (a) PSV-400 scanning heads; (b) video camera; (c) fan blades mounted on (d) shaker.
Figure 3: Frequency spectrum of the fan blade without strain gages.
Figure 4: Frequency spectrum of the fan blade with 10 strain gages.
Next, a second fan blade was equipped with strain gages, and both blades were mounted on a shaker and placed in front of the PSV-400-3D Scanning Vibrometer (Fig. 2). The measurement grid was created by utilizing Polytec’s PSV software. It could also be imported from an FE model instead.
To compare the results from the measurement and the FE model (same global coordinate system) the coordinates of three points from the FE model were utilized in the PSV software. Using the Geometry Scan Unit and Video Triangulation feature of the PSV software, the next step was to carry out a precise measurement of the coordinates of all grid points.
Throughout the measurement with the Scanning Vibrometer, a frequency sweep was executed to gather a frequency spectrum of the fan blade without strain gages, as can be seen in Fig. 3. The resonant frequencies were determined by selecting the peaks in the frequency spectrum, visualizing the corresponding mode shapes and comparing them with the FE model.
Next, the strain measurements were performed at these resonant frequencies by utilizing a sine excitation at different vibration levels. The signals were produced using Polytec’s onboard waveform generator and externally amplified. It was extremely simple to obtain vibration levels of 0 dB (10 V), -20 dB and -40 dB using the attenuator button.
The influence of these strain gages can be seen clearly in Fig. 4, which displays the frequency sweep measurement of the fan blade with strain gages attached. Several resonant frequencies are shifted and the amplitude of the associated peaks is decreased because of the added damping. Most notably, the peak round 2 kHz has almost totally disappeared.
This confirms how vital a non-contact (optical) technique can be for small size structures. It would be nearly impossible to identify all the resonant frequencies and the correct (maximum) strains by using only strain gages.
The experimental results of both the 3D Scanning Vibrometer and strain gages are compared with an FE model in this section. The FE model was updated to acquire similar resonant frequencies after the measurements were performed. The resonant frequencies acquired by the 3D-SLDV and FE model can be seen in Table 1. Attaching strain gages has a big influence on the (higher) resonant frequencies.
The differences between the resonant frequencies were not relevant since the mode shapes of the FEM match the mode shapes measured with the Vibrometer, so no more effort was needed to further update (the boundary conditions of) the FE model.
Table 1: Comparison of the resonant frequencies.
||FE Model 3-D
||Blade without gages
||Blade with gages
||Rel. diff. [%]
||Rel. diff. [%]
Figure 5: Normal strain at 3975 Hz. Left: FE model; right: vibrometer results; top: X-axis; middle: Y-axis; bottom: Z-axis.
Comparison of Strain Results
The strain distributions obtained from the 3-D Scanning Vibrometer measurements compared to the FEM results are described in this section. As can be seen in Fig. 5, there is an excellent agreement in the normal strain between vibrometer and the FE model. Only the measurement of the normal strain perpendicular to the curved surface (X-direction) exhibits more deviation.
Further investigations show that it is possible to gather satisfying results for the shear strain. The agreement for the shear strain in the XY-plane is still satisfactory, but slightly worse than for the other planes.
This investigation shows that it is viable to gather reliable dynamic surface strains from 3D displacement data acquired using a 3D Scanning Vibrometer. Shear strains, in addition to the normal strains, can be measured accurately, as shown, by comparing the vibrometer measurement results with both strain gage measurements and a finite element model.
It was demonstrated that, by attaching strain gages to a fan blade, the dynamic behavior of the structure is modified. At certain resonant frequencies, some resonant frequencies were shifted and the peaks were reduced greatly. Non-contact measurements clearly do not show these drawbacks. Furthermore, it was shown that the sensitivity of the vibrometer is much higher than strain gages.
Compared to strain gages, strains can be measured up to one order of magnitude smaller. The 3-D Scanning Vibrometer has the potential to measure small (full-field) normal and shear strains accurately at both high and low frequencies, where other optical methods would fail.
This information has been sourced, reviewed and adapted from materials provided by Polytec.
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