Quantify Temperature Effects on Crack Size Studies in Metallic Structures Using Vibration-Based Health Monitoring

This paper examines the vibration-based monitoring technique to quantify the smallest crack size that is detectable in Aluminum beams using piezoceramic excitation and sensing. Having the analytical model of the effect of crack formation on the frequency response of the system, the effect of temperature is also taken into consideration to have a better understanding of the damage effect. The analytical model used in the present work is based on the recent model introduced by Aydin (2008) which is a simplified version of the model used by Khiem et. al. (2001). The beam studied here is assumed to be a uniform Euler-Bernoulli beam having a single fatigue crack and being axially loaded. The crack is treated as a localized reduction in the stiffness and is modeled as a massless rotational spring at the location of the crack, connecting the bisections of the beam. The beam is assumed to be simply supported and subject to a uniform heat flux along the top surface of the beam. For the simplicity in the modeling, it is assumed that the bottom surface of the beam is insulated. The crack is also assumed to be non-breathing during the deformation of the beam. The change in the temperature will alter the modulus of elasticity of the beam and will also cause thermal moments inside the beam which will add terms in both the equation of motion and the boundary conditions of the vibrating beam. First, the effect of temperature on the modulus of elasticity of the beam is studied analytically for different boundary conditions of the beam ends. These modeling results are then compared to the experimental ones. Second, the effect of temperature variation is analytically modeled into the equation of motion of the beam and the boundary conditions. Having the equation of motion of the vibrating beam, the effect of temperature on the frequency response of the beam having a single fatigue crack is studied. Taking into account the effect of temperature on the resonance frequency of the beam will be essential in distinguishing the two effects of damage presence and temperature variation and will be important in quantifying the smallest detectable crack in a structure.