High Sensitivity Damage Detection With Vibration Mode Shape Tuning Through the Optimal Design of Piezoelectric Actuators

Abstract

This paper develops an advanced technique to significantly increase the frequency based damage detection sensitivity on a beam structure through a mode shape tuning process with the optimal design of the piezoelectric actuators. Piezoelectric sensors and actuators are mounted on the surface of the host beams to generate the feedback voltage and the active controlled excitations respectively. The excitations induced by the piezoelectric effect will be utilized to change the curvature distribution of the vibration mode shapes of the host beam structure so as to magnify the natural frequency difference between the intact beam and the damaged one to realize the high sensitivity damage detection. In this paper, theoretical models of the cantilever beams with and without mode shape tuning induced by piezoelectric layers are built first, while the damage is represented by a fixed end crack. Then, through the numerical simulations, the vibration mode shapes and corresponding natural frequencies of the beams can be solved to study the sensitivity improvement by using the proposed technique. In order to improve the detection efficiency, a couple of piezoelectric actuators are installed symmetrically on the upper and lower surface of the host beam, generating shifty bending moments to tune the vibration mode shapes. The actuation voltages applied on the actuators are determined by applying certain gain to the voltage from the piezoelectric sensors. Different gain factors are applied to the mode shape tuning process to reveal their effects on damage detection sensitivity improvement. As a result of the control process with proper gain factor, the curvature is more concentrated at the position close to the crack in the first vibration mode shape of the damaged beam comparing with the one without mode shape tuning. Therefore, the first natural frequency variation induced by the crack effect with mode shape tuning is much more significant than the one without mode shape tuning. In addition, further numerical simulations also indicate that the improvement of the detection sensitivity is closely related to the dimensions of the piezoelectric actuators. To realize better detection results, the optimal design of the size of the piezoelectric actuators is presented. The optimal length of the piezoelectric actuators is found leading to the best performance on damage detection. The theoretical studies and numerical simulations reflect that the proposed technique with mode shape tuning and optimally designed actuators is effective and promising in the field of damage detection. It is noted that the proposed technique can also be applied to improve the sensitivity of frequency based damage detection on other structures, e.g. plates and frames.