A Modal Strain Energy Distribution Method to Localize and Quantify Damage

A method based on modal strain energy distributions is presented to localize and quantify damage in structural systems. The method is based on the fact that most forms of damage can be characterized as changes in the stiffness properties, reflecting localized increases in the structural compliance and changes in the modal shapes. The method considers a finite element representation of a system whose experimental modal parameters are known for the undamaged and damaged states. The strain energy stored in each of the elements due to the static shapes of the normalized modes are computed for the two states. The differences in the modal strain energy reflect the location of the damage as apparent increases in the energy. Energy relationships between the two states provide the means for quantifying the magnitude of the damage. The method is validated with experiments conducted in cantilever beams. In the experiments, the modal parameters were measured through laser Doppler velocimetry. Four different double-cantilever aluminum beams were tested to generate ten different damage scenarios. In all the scenarios, the damage was inflicted by milling out about one-tenth the thickness over one-tenth the length of the beam. For each case, 14 modes were extracted and used to localize and quantify the damage. A second set of experiments was also conducted on four different composite plates with a honeycomb core sandwiched between four ply T300 plane weave graphite cloth laminate. One of the plates was undamaged and the other three had engineered flaws which consisted of a) four-inch diameter disbond between the laminate and the core, b) four-inch diameter region of the honeycomb core filled with fluid, and c) a four-inch diameter delamination between the plies of the graphite laminate. The modal strain energy distribution method was implemented for both systems. For the cantilever beam experiments, the location of the damage was accurately identified. The magnitude of the inflicted damage was predicted within a 10 percent margin of error. For the composite plate tests, difficulties were encountered in localizing the damage due to the fact that only two of the modes have significant energy content in the vicinity of the defect.