Monitoring Fatigue Damage in Concrete
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Mat. Res. Soc. Symp. Proc. Vol. 503 © 1998 Materials Research Society Downloaded from https://www.cambridge.org/core. University of Cambridge, on 02 Feb 2020 at 08:23:28, subject to the Cambridge Core terms of use, available at https://www.cambridge.org/core/terms. https://doi.org/10.1557/PROC-503-151
vibrational resonance frequency measurement, a nondestructive technique, is used to monitor damage throughout the loading process. In this technique the structural vibrational modes which are setup by a light impact on the surface of the specimen are monitored. The vibrational response of a structure is composed of the superposition of distinct vibrational modes, each of which has a characteristic frequency of vibration. In the case of hollow cylinders subjected to excitation by normal impact to the surface, radial, bending, shearing modes and modes which represent combinations of these motions will be excited. Although relations between frequency of vibration of the various modes and material characteristics for finite length cylinders have been established with numerical techniques, exact closed form relation has been developed in the case of plain strain vibrations only [1]. In the case of long cylinders (L/D>=10) subjected to normal impact, the plane strain modes have been shown to accurately predict the dominant vibration modes [2]. The fundamental modes of the "cross-sectional family", which are marked by dominant displacement in the radial direction and constant cross-sectional shape along the length have been shown to be the excited vibrational modes which closely correspond to those predicted by the plane strain model. The circumferential dependence of the radial displacement is given by cos(nO) where 0 is the coordinate in the circumferential direction and n is a nonnegative integer. In the case of long free cylinders it was shown that that the cross-sectional modes n=0,2,3... are typically excited by normal impact [2]. The specimen used in this experimental investigation has L/D ratio equal to 2. Using finite element simulation it was shown that the plane strain model can predict the dominant modes of this short cylinder with fixed end conditions [3]. The fixed end condition simulates the specimen mounted in the test machine. EXPERIMENTAL SETUP Impact
135.
Iso'
16 Receivers
Figure 1• Specimen Crosssection (at midlength)
In the experimental setup, the vibrations are setup by the impact of a 4.75mm diameter steel sphere at the midlength of the specimen. The resulting vibrations are monitored with two miniature accelerometers which are mounted directly onto the curved surface at the midlength of the specimen with circumferential angles of 1350 and 1800 with respect to the impact point. Figure 1 illustrates the alignment of the source and the receivers. modes common to both receivers are monitored. Onlyaccelerometers The have a contact face area of voltage acceleration approximately 25 sq mm; nominal sensitivity of 1.02 mV/(m/s 2); and nominal +10% flat
frequency response over 1 Hz to 25 kHz. The t
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