Coupled flexural–longitudinal vibration of delaminated composite beams with local stability analysis

Abstract

A novel analytical model is developed to solve the problem of free vibration of delaminated composite beams. The beam with a single delamination was modelled by six equivalent single layers by establishing the kinematic continuity in the undelaminated portion of the system. In the delaminated region the layers were captured by the traditional theories. First, Timoshenko beam theory is applied to solve the problem, then by reducing the model, the corresponding Euler–Bernoulli solution is presented. Both the free and constrained models were considered. The most important aspect of the present analysis is that the beams of the delaminated region are subjected to normal forces, as well. That is the essential reason for leading to a coupled flexural–longitudinal vibration problem. It is also concluded that delamination buckling can take place if the normal force is compressive in one of the half-periods of the vibration and reaches a critical value. The problem was also investigated experimentally by modal hammer and sweep excitation tests on beams made of E-glass/polyester in order to measure the natural frequencies and mode shapes. The comparison of the analytical and experimental results indicates the importance of the independent rotations provided by Timoshenko beams over the simple beam theory. The delamination buckling of the beams was captured based on the static stability analysis in the first step. Further results show that the problem is more complex than it was thought before, e.g., some nonlinearity, time-dependent stiffness as well as parametric excitation aspects were discovered during the present analysis.