Theory of Damage Detection Using Constrained Vibration Deflection Shapes

Various techniques have been developed that use changes in the mode shapes, Ritz vectors, or the operational deflection shapes of a structure to detect damage. These techniques generally have been applied using single excitation forces at low frequencies. This paper shows that the frequency range and number of simultaneous excitation forces used significantly affects the sensitivity of damage detection. Based on this idea, a model independent method of damage detection using measured constrained vibration deflection shapes (VDS) and predamage data is presented. The constrained VDS are the vibration shapes of the structure that occur when the forcing vector contains elements that cause the structure to vibrate in a desired pattern. The method is analytically tested using a finite-element model of a fixed-fixed beam wherein simulations are performed using one and two rotational excitations, and then a prescribed excitation vector that is comprised of the rotational degrees-of-freedom (DOFS) of one of the mode shapes of the healthy structure. The rotational excitation is used because it is convenient to apply at a large number of locations on the structure using thin piezoceramic patches. The translational vibration of the beam is used in the damage detection algorithm because the translational DOFs are convenient to measure using a scanning laser vibrometer. The simulations show that small damage can be located using distributed high frequency excitation applied as a symmetric mode shape at the rotational DOFs of the beam.