Dynamic response of a delaminated composite beam with general lay-ups based on the first-order shear deformation theory

The dynamic response analysis of a delaminated composite beam with a general lay-up traversed under an arbitrary moving/non-moving force is presented. By employing the energy method and introducing a new finite element, the global mass and stiffness matrices for a Laminated Composite Beam (LCB) of Timoshenko type are derived in which the material couplings (bending–tension, bending–twist, and tension–twist couplings) with the Poisson’s effect are considered. In deriving the governing equation the non-penetration condition is imposed by employing the method of Lagrange multipliers. Out of a self-developed finite element program, the natural frequencies and time response of such LCB are obtained. To check on the accuracy of the derived equation and hence, developed program, the obtained results are compared with the results from other available references out of which very good agreements are observed. Finally, by changing the laminate’s lay-ups, beam geometrical parameters and type of external force, the LCB’s natural frequencies and time responses are obtained as a primary base for the structural design.