Damage detection of mono-coupled periodic structures based on sensitivity analysis of modal parameters

A sensitivity-based method for localization and assessment of damage in mono-coupled periodic structures is presented in this paper, in which slopes and curvatures of mode shapes are used to localize damage, and natural frequencies are then utilized to quantify the damage. The expressions of sensitivity coefficients of mode shapes, slopes, and curvatures of a mono-coupled periodic system are first derived in terms of receptances of periodic element. A mono-coupled periodic spring-mass system with 10 degrees of freedom is used to carry out a sensitivity study to compare the sensitivities of natural frequencies, mode shapes, slopes, and curvatures to damage. The results show that the sensitivities of these modal parameters in a mono-coupled periodic structure do not depend on the structural parameters, and therefore there is no need for a prior analytical model of the structure. The study also demonstrates that among these modal parameters, curvatures of modal shapes are most sensitive but slopes of mode shapes seem to be more indicative of damage location. A 20-element mono-coupled periodic spring-mass system is adopted to demonstrate the capacity of the proposed method to localize and quantify damages in the mono-coupled periodic system. Finally, a 3-storey near mono-coupled periodic experimental building is used to verify the actual application of the proposed method in consideration of the influence of measurement noise and non-perfect periodicity of actual engineering structures. Numerical and experimental results illustrate that only using a few lower modes with or without noise pollution can accurately detect damages in a mono-coupled periodic or a near mono-coupled periodic structure, either single or multiple damage locations and slight or severe damages.