3.5. The effects of debond length and position
The effect of debond length is studied by applying the “with
contact” model. A beam with the properties given in Table 1 has
been considered. It has been assumed that the debonded region is
located at the midspan of the top interface and its length has been
increased up to one third of the beam's length. The frequencies
have been normalized by those of the undamaged beam. The results
for the first three modes are plotted in Fig. 15. The calculations
have been performed for both cases in which the beam's
boundaries can move in circumferential direction (solid line) and
are fixed in this direction (dashed line). Fig. 15 shows that a
debonded area of 33% the beam's length can reduce the frequencies
up to 20%.
The debond position is the other important factor which controls
the significance of a debonding. A debonded region of 13%
total beam length has been considered. The middle point of the
debonded region, am (refer to Fig. 1), has been changed along the
beam span and the variations of frequencies are presented in
Fig. 16-(a).
According to Fig. 16-a, the maximum values of the graphs are
very close to frequencies of a similar intact beam. The first three
frequencies for the intact beam are 371, 857 and 1336 Hz, respectively,
which means that the debonded region may be located
where it has a negligible effect on a particular mode. On the other
hand, the reduction of frequencies in the first three modes may be
raised up to 13.5%, 11% and 9.6%, respectively. To give an explanation
for the changes in the frequencies, the core's shear stress
distribution at the top interface is depicted in Fig. 16-b for the intact
beam. Comparing the graphs of Fig. 16-a and -b for each mode
shows that if the debonded region is located at a position with low
shear stress, it has a slight influence on that mode. As the debonded
region is located closer to a position with high shear stress, it more
reduces the frequency of that mode.