Nonlinear dyamics of cracked structures for non-destructive evaluation

The power plant and aerospace industries have been facing a huge loss, due to structural failure. The structural failure occurs due to the presence of the crack in it. Hence, it becomes necessary to monitor the structural health under operating condition. Most of the techniques, for structural health monitoring are used for a specific purpose. Some of these techniques require structure dismantling, which is very much expensive and time consuming. So the vibration based structural health monitoring is advantageous, compared to other techniques. Most of the vibration based Structural Health Monitoring (SHM) approaches, use linear vibration theory. But, these linear vibration based procedures, have inherently low sensitivity to crack. Since crack introduces nonlinearities in the system, their merits in damage detection need to be investigated for SHM. In this thesis, the problem is focused on studying nonlinear dynamics of cracked structures for Structural Health Monitoring. For this, simulations and experiments are performed. The new procedure for the simulation is developed using Matlab-Simulink. It uses the numerical approximation for dynamic compliance operators and a nonlinear model of cracks contact faces interaction to study the dynamic behaviour of the cracked bar. Furthermore, the finite element model of the cracked cantilever bar with crack- tip plasticity is developed and the dynamic behaviour of the elasto-plastic bar is studied. Additionally, numerous experiments are performed to study the dynamics of cantilever bar with the fatigue crack in it. The results from Matlab-Simulink simulation shows the distribution of higher harmonics generated along the bar length, as a function of distance from the crack. In finite element simulation, comparison is made between the resonance frequency of cracked cantilever bar with and without crack-tip plasticity. It is found that, there is decrease in resonance frequency of the cracked bar with cracked tip plasticity, when compared with the resonance frequency of cracked bar without crack-tip plasticity. This reduction in resonance frequency is due to the crack-induced plasticity near the crack tip which affects the overall stiffness of bar. In experiments, the response is measured at four different points on the cracked cantilever bar at a given resonant frequency of excitation at lower and higher vibration amplitude. For lower vibration amplitude, it is found that the response obtained near the vicinity of the crack shows the presence of higher harmonics of resonant frequency, which disappears in the response obtained far away from the crack. For higher vibration amplitude, it is found that the response obtained near the vicinity of the crack shows the presence of higher harmonics along with the low frequency component. This low frequency component causes modulation, which leads to the generation of side band frequencies near the resonant frequency. The occurrence of low frequency component and side band frequencies is due to the vibro-impact behaviour of crack. The amplitude of these side band frequencies and higher harmonics are reduced in the response obtained far away from the crack. This indicates that crack-induced nonlinearity has a localized effect on the dynamics of bar. It is also observed that the magnitude of low frequency component is proportional to the magnitude of resonant frequency of excitation. This indicates that crack behaves like a signal modulator, detector of low frequency component and amplifier as the magnitude of low frequency component is proportional to the magnitude of resonant frequency excitation. From the Matlab-Simulink simulation and experimental results, it is concluded that crackinduced nonlinearity affects the dynamic behaviour of the cracked bar significantly, which will be effective in structural health monitoring. Keywords: vibro-impact, crack, dynamic compliance, harmonics, modulator, detector, amplifier, crack-tip plasticity, resonance frequency, structural health monitoring.