PSI - Issue 5

Andreas Kyprianou et al. / Procedia Structural Integrity 5 (2017) 1192–1197 Andreas Kyprianou / Structural Integrity Procedia 00 (2017) 000 – 000

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Fig. 1. The cantilever experimental set-up.

2.2. Data acquisition and organization

The time response of the excited by pink noise cantilever was optically measured as follows. Images of the vibrating cantilever were first recorded using Mega Speed MS70K MDG2 High Speed Camera, MegaSpeed (2007). This camera has a maximum resolution of 504 x 504 pixels, frame rates of up to 100,000 FPS and a shutter speed in the range of 1 μ s to 30 ms. The images acquired were collected in an image sequence, while the time step between consecutive frames of the image sequence was kept constant. As it will be explained in section 3 the spatio-temporal wavelet transform analyses a sequence of one dimensional time series obtained from different points of the cantilever beam. Taking the contours, through edge detection, of each frame of the image sequence mentioned earlier the response of the cantilever can be transformed into a sequence of one dimensional time series. The edges can be located by searching for such discontinuities in the image using wavelet transform edge detection as suggested in Gentile et al. (2003), Tjirkallis et al. (2016), and Tjirkallis (2016). The result of the application of edge detection on each frame of the image is a contour, fig. 2, that represents the deformation of the beam of the corresponding instance. The motion of the vibrating structure studied in this article is confined in the 2D space, with the third dimension being time. The changes in the response of the structure with respect to time can be obtained from the displacement of the edge contours across the frames. In order to obtain the time responses at each pixel along the length of the cantilever beam, a conversion of the measurements from pixels to real world units, and a line tracking algorithm resulting in the displacement of the cantilever beam from image sequence, as described in Tjirkallis (2013) was employed. These data were collected in a matrix whose columns represent the position of the beam measured in pixels and the rows the displacements at each time instant. Data in this format is amenable to SPT-CWT analysis.