The accurate prediction of the vibration behaviour of composite materials is of significant importance, as they are increasingly being used in high-performance components subject to vibration. Due to the adjustable gradual damage behaviour of composites, the vibration behaviour of damaged structures allows the detection and assessment of damage in materials and components, which is a critical task in modern engineering for safety reasons. Focusing on the effects of single transverse cracks on the vibration behaviour, an experimental and numerical study is performed on undamaged and damaged composite specimens. A single crack is analysed using microscopy, computed tomography and optical coherence tomography to show the non-continuous crack path. To represent the phenomenon of restoring the initial stiffness numerically, a material model is proposed which takes into account the change in stiffness when a crack is opening and closing. The results show, that a discrete modelling of the cracks is not necessary to represent the phenomena occurring during crack closure in the experiment. Consequently, the progressive damage behaviour, the localisation of the crack path in a damaged structure and the consideration of the restored stiffness under compression, which leads to tension-compression asymmetry, can be taken into account via the material model.