An inverse problem in structural diagnostics: damage identification in rods based on natural frequency and antiresonant frequency measurements

In this paper it is shown that natural frequency and antiresonant frequency shifts induced by structural damage in an axially vibrating rod contain information on certain generalized Fourier coefficients of the stiffness variation caused by the degradation. This property is used to define a reconstruction procedure based on iterative updating of the undamaged configuration. The results of numerical simulations on rods with localized or diffuse damages are in good agreement with the theory, provided that mean frequency and antiresonant frequency shifts are bigger than modelling/measurement errors. Experimental results obtained on cracked steel rods showed that, in the inverse problem solution, noise and modelling errors on antiresonances are usually strongly amplified with respect to cases in which frequency data are used.