Nonlinear instantaneous characteristics and asymmetry of the bilinear system with application to the structural damage estimation

Abstract

Common structural damage usually exhibits bilinear behavior in the vibration. To identify such damage, the nonlinearity and asymmetry shown in the free vibration of the bilinear system are studied. The instantaneous characteristics of the free vibration are analyzed by employing the well-known HT method. The modulated instantaneous parameters and softening stiffness are used as damage indicators. Three new indices are proposed for ‘bilinear-type’ damage detection. For further damage severity estimation, two bilinear-stiffness estimation methods are developed based on the asymmetric restoring force and the asymmetric phase trace, respectively. Numerical study shows that the methods can accurately estimate the bilinear stiffness of the cracked beam with strong noise robustness and low sensitivity to initial weak nonlinearity. Experimental study was carried out on a steel cantilever beam with loose-connection. The damage can be effectively detected by the proposed indices and the stiffness coefficient ratios can be estimated by the two proposed methods.