Strains To derive the strains a filter with m = 8 was chosen。 A smaller filter width leads to a  considerable

Fig。 11  Experimental and numerical results of the displacements ux and uy for the rectangular plate with the circular hole

amount of noise and a larger filter width proved to be too aggressive。

The strains derived from the measured data are compared to the numerical solution in Fig。 12。 The right column represents the strains computed with a third order SG filter and the left column represents the strains calculated with Ansys [21]。 The surface plots demonstrate that the strain field can qualitatively be well approximated with 3D scanning laser vibrometer measurements。 However, the maximum values for the numerical solution are slightly higher than those from the measured data。 One principal reason is the inability of the laser vibrometer to measure kinematic variables directly on an edge of a structure。 As the maximum strain values for all strain components lie on the edge of

the hole, the maximal strains can not be measured。 This especially affects the solutions for εxx because its values change significantly in the vicinity of the edge of the hole。 The asymmetry in the experimental data, that is most clearly visible in the solution for εxx, is presumably due to the misalignment of the specimen。

The most significant value of the given stress field is the stress intensity at the edge of the hole for σyy for y = 0。 For an infinite plate with a circular  hole under uni-axial tensile loading, this peak value equals

three times the nominal stress。 However, the stress concentration decreases for finite plates in terms of their width。 Therefore, the strain measured at y = 0 is compared to a numerical solution, as illustrated in Fig。  13。  Due  to  the  misalignment of  the specimen,

(e) (f)

Fig。 12 Strains for the rectangular plate with the circular hole。 The experimental results are derived from the displacements with the filter parameters m = 6 and k = 3 and the numerical results are computed with Ansys

the results for both sides of the  hole  are  consid- ered。 The numerical solution yields a maximum strain of  569  με  in  the  vicinity  of  the  hole,  whereas the

extrapolated  values  for  the  measured  data equal 564 με and 563 με on the right and on the left side, respectively。

Fig。 13 Comparison of the experimental and numerical  solution of εyy for y = 0

Conclusions

It has been shown that it is possible to use 3D displace- ment data obtained from a scanning laser vibrometer to estimate the dynamic in-plane strain over the surface of a planar structure。 The process is very sensitive to systemic errors in the vibrometer measurement system, in particular misalignment errors between heads。 A great deal of attention needs to be paid to minimize noise。 Therefore the measurement technique is best suited to cyclic loading conditions in which averaging via Fourier analysis made be used。论文网

A quasi-static experiment was chosen to provide a comparison against a FEA simulation for validation。 For such quasi-static measurements, the measurement time can be significant。 However, the strain measure- ment technique is not restricted to low frequencies, and thus may be applied to measurement of dynamic strain up to frequencies where the spatial wavelength is twice the measurement grid size (Nyquist limit)。 This would lead to dramatic reductions in measurement times (approximately inversely proportional to the sample frequency)。

Despite the sensitivity of the technique to errors, it shows great promise in providing a new fast non- contact method for accurately measuring the dynamic strain field across the surface of a structure。