Non-linearities in the vibrations of elastic structures with a closing crack: A state of the art review

•Non-linear effects caused by a closing crack in structural elements are illustrated.•Single-degree-of-freedom oscillators simulating cracked elastic bodies are compared•Non-linear effects at free and forced vibrations of cracked beams are analysed.•The features of vibrations of damaged plates and rotating shafts are addressed.•Advantages, problems and prospects of non-linear vibration diagnostics are discussed.

The main purpose of the present review paper is to illustrate the principal achievements of numerous researchers who have studied the non-linear effects caused by a closing crack in the most common types of structural elements such as beams, shafts and plates, the aim being to assess the potential and future prospects of using non-linear behaviour to detect damage. Indeed, for a wide range of practical applications, in order to avoid catastrophic failure, the development of diagnostics techniques which are sufficiently sensitive to incipient cracks in structures and machines is a crucial issue. The main potential advantage of using vibration diagnostics based on the use of non-linear effects is the relatively high sensitivity to the damage of the closing crack type, especially for application to beam-like structures and rotating shafts; instead the potential for application to plate-like structures has been found to be limited.After analysing the state-of-art on this subject in detail, a discussion of the respective merits, drawbacks and prospects of a range of non-linear vibration methods for structural damage detection is presented. The general conclusion which can be drawn from the highly encouraging results of recent research is that further development of these techniques for non-destructive testing of structures with closing cracks would be highly worthwhile.