15 Investigation of Notch-Type Damage Identification by Using a Continuously Scanning Laser Doppler Vibrometer System 147 Time (s) Velocity (mm/s) -400 -200 0 200 400 X mirror feedback (°) -2 -1 0 1 2 Velocity response X mirror feedback (a) x/L (%) 0 5 10 15 20 0 20 40 60 80 100 Velocity (mm/s) -250 -200 -150 -100 -50 0 (b) Fig. 15.3 (a) Velocity response of the beam at a sinusoidal excitation frequency of 67Hz and the corresponding X mirror feedback signal with a triangular input signal, and (b) the corresponding ODS obtained by the demodulation method using a curvature damage index (CDI), which can be expressed as ı .x/ D y00d .x/ y00p .x/ 2 (15.5) whereyd .x/ is an ODS from a damaged beam obtained by the demodulation method, yp.x/ is obtained by using a polynomial with order mto fit yd .x/ and is considered as the ODS of the associated undamaged beam, and y00d .x/ and y00p .x/ areCODSs of yd .x/ and yp .x/, respectively. In order to determine the proper order m, the modal assurance criterion (MAC) is used to obtain the least value of mwhen the MAC.yd; yp/ value, which is expressed as [Ewins textbook] MAC yd; yp D ˇ ˇf ypg Tfy dgˇ ˇ 2 fypg Tfy pg .fydg Tfy dg/ 100% (15.6) is above 90%. It is proposed in this work that the proper order mbe two plus the least value of mwithwhichMAC.yd; yp/ is above90%. Two is added here in order to preserve the smoothness of the CODS from the polynomial fit, since the calculation of a curvature incurs second-order differentiation, which reduces the order of a polynomial by two. Damage can be identified near a region of high values of the CDI, which appears as a prominent peak. A dense measurement grid of an ODS can be obtained by using a CSLDV system. Hence, CODSs of higher order modes can be obtained with high qualities, which can increase the possibility to identify small damage, such as a notch. 15.3 Experimental Investigation of Notch-Type Damage Identification To experimentally investigate the proposed methodology in notch-type damage identification, the velocity response of the damaged beam in Fig. 15.2c under sinusoidal excitation by the shaker at different frequencies is measured by the CSLDV system. ODSs of the damaged beam are obtained by the demodulation method and ODSs of associated undamaged beams are obtained by the polynomial fit. CODSs are then calculated and CDIs are used to identify the notch location. An impact test is first conducted on the damaged beam in Fig. 15.2c to measure its first five natural frequencies; a PCB 086C03 impact hammer and the single-point vibrometer in Fig. 15.1 are used to excite the beam at an impact point and measure its velocity response at a measurement point, respectively. Both the impact and measurement points on the beam are arbitrarily selected as long as they do not coincide with nodal points of its first five modes. The beam is then sinusoidally excited by the shaker at different frequencies of 67, 220, 450, 754, and 1133Hz, which are obtained by rounding the first through fifth natural frequencies of the beam in the current experimental setup, respectively.
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