Vibration of delaminated multilayer beams

The free vibration of delaminated multilayer beams is analyzed. Both the ‘free mode’ and ‘constrained mode’ analyses in the study of delamination vibration are used. Two parameters are introduced, namely, the normalized axial stiffness and the normalized bending stiffness. These parameters provide a better insight on the vibration behavior of the delaminated beam. A relative slenderness ratio specific for delamination vibration is further introduced, which is shown to influence the vibration behavior of the beam. Global, mixed and local vibration modes occur depending upon the relative slenderness ratio of the beam. In addition, for three-layer beams with double delaminations, the lower and upper bounds of the natural frequency are obtained by assuming a totally ‘free’ and totally ‘constrained’ deformations of the delaminated layers. These bounds are easy to compute and provide useful approximations.