| Evaluation of integrity of structures using the vibration based techniques has become increasingly appealing, as they offer a viable means of assessing local information of crack-induced damages in a complex structure based upon the measured structure vibration characteristics, namely, the natural frequencies. Existing vibration based NDE techniques, however, often require the use of dynamic finite element programs to generate the "sensitivity" matrix, a process so tedious that it tends to inhibit the wide application of these vibration based NDE techniques.;A unified function, termed ;The validity of the developed NDE methodology was confirmed via the case studies consisting of both numerical simulations and laboratory-controlled experimental results. Simple structures such as beams, bars and 2-D plates with either uniform or non-uniform cross-sections were studied for a spectrum of damage scenarios and boundary conditions. These case studies not only confirmed the assumptions made in the mathematical equation, but also proved the simplicity and practicality of the method.;For the first time, unified and practical mathematical relationships for relating the natural frequency changes and the damage characteristics such as crack location and crack severity have been derived and presented in this dissertation. The mathematical relationships were derived independently from two damage modeling techniques: an equivalent spring model and a continuum mechanics based model. The validity of the derived mathematical relationships was further investigated by comparisons with the equations derived from the rigorous beam vibration theory in conjunction with a symbolic computational package MACSYMA. The equations for bar structures derived from the receptance concept were shown to converge to the ones derived herein as well. |
