A precise non-destructive damage identification technique of long and slender structures based on modal data

This paper presents numerical and experimental studies on modal behavior of cylindrical, lightly damped beam structures containing a notch-like crack with variable position and geometry. The numerical investigation utilizes the Finite-Element-Method (FEM) and a discretization strategy is developed that enables a crack to be represented in three dimensions. A test procedure capable of delivering a broadband impulse excitation to a flexible supported test specimen was developed. The customized excitation unit was used in conjunction with a Laser-Scanning-Vibrometer (LDV) to analyze a frequency range up to 40 kHz. The first 15 bending mode shape pairs with their corresponding eigenfrequencies are numerically and experimentally identified. The model updating is performed for the elastic parameters and the boundary conditions to minimize the deviation between experimentally determined and numerically calculated results in terms of eigenfrequencies. The acquired data are used in a two-stage damage identification procedure, in which suitable start vectors are found by the evaluation of objective function plots. Subsequently, geometrical crack parameters are identified. The deviations between real and determined crack positions range between 0.05 and 0.28 percent for crack depth/diameter ratios of less than 7 percent.