On the dynamic stability of delaminated composite beams under free vibration

Abstract

AbstractThis work deals with the analysis of the free vibration problem of elastic delaminated composite beams. The work mainly consists of a model development and improvement stage based on the first-order shear deformable beam theory. A general model is developed taking the bending-extensional coupling into account. The specified problem is a built-in beam with free end, and one of the novelties of this work is the consideration of the fact that a built-in beam cannot be fixed rigidly in reality. Thus, a Winkler-type elastic foundation is applied along the built-in length. The total potential energy and the governing equations of the delaminated and intact parts of the beam are also captured. The problem is solved in two ways: analytically and numerically by using the finite element method, respectively. Applying the developed models the natural frequencies, mode shapes as well as the stress resultants are determined. The comparison of natural frequencies to those measured experimentally shows that the built-in length resting on Winkler-type elastic foundation influences significantly the agreement between model and experiment. In the final stage, the parametric excitation phenomenon taking place in the delaminated part is analyzed using a local model and the harmonic balance method. The dynamic buckling is characterized by some stability diagrams, and it is shown that the applied model is very sensitive to the frequency leading to somewhat controversial critical amplitudes compared to measurements.