The beam is modelled as a bilinear single-degree-of-freedom system excited at two frequencies. The theoretical results show that the inherent nonlinearity of the fatigue crack causes strong mixing effects resulting in the appearance of additional response components at frequencies equal to the sum and difference of the excitation frequencies. The amplitude of the response components at the difference frequency increases with increasing crack depth following definite trends and therefore, can be used for the evaluation of crack size.

To validate the theoretical predictions, a series of measurements on cracked Plexiglas beams were performed. During the experiments the relation between amplitude of the mixing components and crack size was verified and proved to have potential for crack size evaluation.

The amplitude, however, of the nonlinear response components may be small, in particular for small cracks. Therefore, for practical applications the limitations of conventional signal processing techniques like amplifier distortions or other noise sources should be overcomed or reduced to avoid masking of the nonlinearities. For that purpose, bispectral analysis is employed, which has been proved very sensitive for accurate measurement of nonlinearities due to its insensitivity to noise.

Both predicted and measured results are analysed using bispectral analysis. A relation between bispectrum value and crack size is established and can be used as a reliable, sensitive measure of damage. Experimental results in good agreement with predictions, demonstrate that cracks down to 7% depth can be reliably detected. The proposed nonlinear method combined with bispectral analysis is superior compared to existing methods exhibiting higher sensitivity for crack detection at an early stage.

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