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Some of the factors influencing the stress wave factor measurement and other integrative techniques are boundary conditions, type of damage, severity of damage, and area of damage. This paper suggests that a finite-element model can be used to study some of the factors influencing the ultrasonic stress wave evaluation of materials. To demonstrate this, a hypothetical case of the resonant frequencies on damaged and undamaged plates was studied. Finite-element modeling, which is the most widely used technique for incorporating local discontinuities, was used. The first step was to check the conformity of the finite-element results with those obtained experimentally and by exact methods. This was attained by studying the resonant frequencies of two undamaged plates, which were simply supported on all edges. The two plates studied were a 0.2667- by 0.2667- by 0.003175-m, aluminum plate and a 0.2667- by 0.2667- by 0.0001036-m graphite-epoxy (08) plate. Good correlation was obtained between the approximate and exact methods (within 8%). The frequencies predicted by the finite-element model were observed in the experiment with the aluminum and graphite-epoxy plates. Additional frequencies were observed in the graphite-epoxy plate, which could not be accounted for.
Classical vibration theory is applied to predict the resonant frequencies and the mode shapes for a given reduction in stiffness and given damage area in the case of damaged plates. This will help determine the region to be monitored and the location of the sensor in order to see the resonant frequencies. This selection would most likely be based on the two criteria (1) minimum damage severity, but of large extent, and (2) minimum damage size, but of maximum severity. By knowing the percentage reduction in resonance frequencies caused by damage, a certain threshold can be established, which will determine the sensitivity of the monitoring system to be used.
In studying the resonant frequencies of damaged plates, the severity was increased by reducing the stiffness by 10 and 50%. In modeling the case of constant severity with increasing damage area, the damaged area was increased by decreasing the area of the plate while keeping the damage area constant. The ratios of damaged to total plate area studied were 1:16, 1:4, and 1:1. Results of this analysis are presented.
Engineer, National Technical Systems, Hartwood, VA
Professor, Virginia Polytechnic Institute and State University, Blacksburg, VA
Stock #: CTR10316J