| Summary: | Crack detection at an early stage can prevent catastrophic structural failures. In this thesis, the inverse problem of crack detection in frames is studied. The direct problem of calculating the natural frequencies of beams and frames with multiple cracks is first tackled. A new method for natural frequency calculation is devised. The cracks are modelled as rotational springs. 4 × 4 dynamic stiffness matrices for beams are evaluated in a recursive manner, according to the number of cracks, by applying partial Gaussian eliminations. The resulting transcendental eigenvalue problem is solved using the Wittrick–Williams algorithm to extract the natural frequencies. Additional sign counts resulting from the partial Gaussian eliminations must be accounted for when applying the algorithm. The dynamic stiffness matrix of a frame with multiply cracked members is then assembled. The natural frequency calculation method forms a basis for detecting a single crack in a frame using only natural frequency measurements. Each frame member is discretised into a number of points. Selected natural frequencies are calculated accurately in the uncracked case and when the crack is placed individually at each discretisation point. The variation between the uncracked and cracked frequencies is normalised giving a number of curves corresponding to the selected frequencies. The normalisation is then applied on the measured frequencies. For noise free measurements, point crack locations are obtained. Applying the principles of interval arithmetic, noisy measurements give crack location ranges. Empirical probability distributions are used to graphically represent these ranges and their relative probabilities. Crack severity ranges are then obtained. The detection method is validated experimentally on a frame with scaled down dimensions. The fast Fourier transform is used to convert the time domain vibration signal into the frequency domain. Using higher order natural frequencies, two enhancement procedures for the detection method are devised and applied theoretically.
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