PSI - Issue 5

H. Lopes et al. / Procedia Structural Integrity 5 (2017) 1205–1212

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H. Lopes et al. / Structural Integrity Procedia 00 (2017) 000 – 000

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being the shearing amount adjusted by controlling the angle of one of the mirrors in the interferometer. The shearing amount considered in the experimental measurement is always along the longitudinal direction of the beam. The temporal phase modulation was implemented by changing the length of one of the arms of the Michelson interferometer through the translation of a mirror. The translation of the mirror is achieved by a piezoelectric actuator. A DALSA-Falcon 4M60 digital CMOS camera and a Leica 50 mm lens are used to record the intensity pattern of the laser light reflected by the surface. A Coherent model Verdi continuous wave laser with a wavelength of 532 nm and maximum output power of 2 W is used. The system allows the recording of a full-field with up to 4 million points (2352×1728). The recorded intensity pattern is integrated by the sensor of the camera. The time integration is normally much higher than the vibration period. This problem is solved by recording the intensity pattern at the same instant. To achieve this, the laser light is pulsed using an InterAction Corp. ADM-70 acousto-optic modulator, which is synchronized with the vibration of the beam. The excitation of the beam at their natural frequencies is made without contact using a loudspeaker mounted near and on the opposite side of the measurement surface. For this purpose, the beam natural frequencies in free-free condition were identified from previously measured frequency response functions. The phase maps corresponding to the modal rotations are obtained by correlating the interference phase measured without motion of the beam and at its maximum vibration amplitude. Since there is a relationship between the amplitude of the acoustic excitation and the vibration amplitude of the beam, the latter is defined by adjusting the pressure generated by the loudspeaker using an audio amplifier. The devices used in the measurements are on top of a Newport® optical table with pneumatic suspension to minimize the influence of external mechanical perturbations. In order to investigate the influence of the shearing amount and the vibration amplitude on noise in the modal rotations, two sets of measurements were carried out. The first set involves the determination of modal rotations with the same vibration amplitude, but considering three different shearing amounts: 2, 5, and 10 mm. In the second set, the determination of modal rotations is made with four progressive levels of vibration amplitudes with a fixed shearing amount of 10 mm.

Fig. 2. Experimental setup for the measurement of modal rotation fields of an aluminum beam.

4. Results and discussion

The measured unfiltered phase maps corresponding to the first four modal rotation fields are presented in Fig. 3. They were obtained using a time phase modulation technique of four recorded intensity patterns with a constant phase shift of π/2. The phase maps are represented in a grayscale for an easier interpretation, corresponding each gray level to points of equal phase value. Phase discontinuities are observed along the beam, which are characterized by abrupt