Modelling, detection and identification of flexural crack damages in beams using frequency response functions

Abstract

In this paper, the original receptance method first proposed by Bishop (The mechanics of vibration. Cambridge University Press, Cambridge, 1979) is further generalized and extended to the vibration modelling of stepped beams and truss structures with multiple crack damages. Cracks are physically treated as rotational springs representing local flexibilities at crack locations induced by crack depths. Frequency response functions (FRFs) with any given number of crack locations and depths are first established from which numerically exact natural frequencies and mode shapes are extracted. Since these FRFs can be measured in practice in a typical modal testing, a crack location method is then developed by using rotational FRFs which can be estimated from these measured translational FRF data. Substantial slope discontinuities are observed and are further employed to construct a crack location matrix to locate cracks. Finally, to identify crack parameters such as crack depths, a new Numerical Inverse FRF Sensitivity method is developed. Unlike the case of analytical model updating where an analytical model is available from which sensitivities can be derived, FRF sensitivities needed in this case have to be numerically computed. Such numerical sensitivity approach is believed to have wider applications in inverse dynamics problems such as analytical model updating. A stepped beam and a GARTEUR structure are employed in numerical case studies and very encouraging results have been achieved even when FRF data are contaminated with substantial measurement noise.