Mechanics of delaminated composite beams subjected to retarded follower force with multiple time delay

Abstract

In this work the problem of a delaminated composite cantilever beam subjected to a retarded periodically changing follower axial force is taken into consideration. The equation of motion is deduced based on a previous work including finite element discretization in space. On the other hand the delayed system is captured by the Chebyshev polynomials of the first kind in the time domain. The most important aspect of the model is that multiple time delay is considered, i.e., the principal period of the parametric excitation is not equal to the delay. Under these conditions the stability of the system is investigated using the Floquet theory and the unit circle criterion. The stability diagrams are determined for large number of cases focusing essentially on the effect of delamination on the stable domains. The main conclusion is that although the delamination length and thicknesswise position does not have an essential effect on the stability domains, the definite offset of the limit curves may be observed. In contrast, the relation of time delay and principal period influences substantially the shape and nature of limit curves on certain parameter planes.