Damage detection of composite structures based on inner product vector

Inner product vector (IPV) is proposed to characterize the cross correlation of the measured vibration responses of the structure. Then a new damage detection method is put forward based on this concept. It is theoretically proved that the elements in the IPV of a structure is the inner product of the time domain vibration responses of corresponding measuring points, and this vector can be directly calculated by using the measured time domain vibration responses. Under white noise excitation, the IPV of a structure is the superposition of the vibration modes of the structure, and the contribution of each mode shape only depends on the modal parameters of the structure. Therefore the IPV involves health information of a structure and the difference of the IPVs between the intact and damaged structure can be used as the damage index. The damage location is identified by the abrupt change of IPV curve of the structure. Numerical simulation of the delamination damage detection for a composite laminated beam and plate demonstrate the feasibility and effectiveness of the proposed method.