Articles written in Sadhana
Volume 38 Issue 4 August 2013 pp 557-569
Structural damage will change the dynamic characteristics, including natural frequencies, modal shapes, damping ratios and modal ﬂexibility matrix of the structure. Modal ﬂexibility matrix is a function of natural frequencies and mode shapes and can be used for structural damage detection and health monitoring. In this paper, experimental modal ﬂexibility matrix is obtained from the ﬁrst few lower measured natural frequencies and incomplete modal shapes. The optimization problem is then constructed by minimizing Frobenius norm of the change of ﬂexibility matrix. Gauss–Newton method is used to solve the optimization problem, where the sensitivity of ﬂexibility matrix with respect to structural parameters is calculated iteratively by only using the ﬁrst few lower modes. The optimal solution corresponds to structural parameters which can be used to identify damage sites and extent. Numerical results show that ﬂexibility-based method can be successfully applied to identify the damage elements and is robust to measurement noise.