Crack localisation in frames using natural frequency degradations

• A new method is devised for locating a single crack in a frame.
• Simulated noise free and contaminated natural frequency measurements are considered.
• Noise free measurements yield pointed predictions.
• Noisy measurements yield crack location ranges.
• Empirical probability distributions can be used to illustrate the crack location ranges.

A new method is devised for locating a single crack in a frame using natural frequency degradations. Simulated noise free and contaminated natural frequency measurements are considered. The frame is discretised into a number of points. Selected natural frequencies are calculated using the Wittrick–Williams algorithm in the uncracked case and when the crack is placed at each point individually. The variation between the uncracked and cracked frequencies is normalised in the analytical and measured cases. Exact simulations yield point crack locations. Applying interval arithmetic, simulated contaminated measurements give crack location ranges. The combined ranges are illustrated by empirical probability distributions.