Non-Model-Based Multiple Damage Identification of Beams Under Spatially Dense Vibration Measurement

Abstract

An effective non-model-based multiple damage identification method for beams by using a continuously scanning laser Doppler vibrometer (CSLDV) system is presented. Velocity response of a beam along a scan line under sinusoidal excitation is measured by the CSLDV system and a spatially dense operating deflection shape (ODS) of the beam along the scan line is obtained by the demodulation method from velocity response. The ODS of an associated undamaged beam is obtained by using a polynomial with a proper order to fit the ODS from the demodulation method. The curvature of an ODS (CODS) is used to identify abnormality induced by multiple damage. A curvature damage index (CDI) using differences between CODSs associated with ODSs that are obtained by the demodulation method and the polynomial fit is proposed to identify multiple damage. An auxiliary CDI obtained by averaging CDIs at different excitation frequencies is defined to further assist identification of multiple damage. Experiments on three beams with three damage on each beam in the form of three small cuts are conducted. Widths and depths of the three damage are varied from 3 mm to 9 mm with an increment of 3 mm and from 5% of thickness reduction to 15% with an increment of 5%, respectively, and their effects on ODSs, CODSs, and CDIs are investigated. Three frequencies close to natural frequencies of the beams and one randomly selected frequency that is not close to any natural frequencies of the beams are used as sinusoidal excitation frequencies. Each damage is successfully identified near regions with consistently high values of CDIs at different excitation frequencies when the damage is not close to a nodal point of an ODS. The three damage on each beam is successfully identified with the auxiliary CDI by obvious peaks at locations of the three damage.