Free and forced vibration analysis of laminated composite beams with through-the-width delamination by considering the in-plane and out-of-plane deformations

The present paper investigates in-plane and out-of-plane vibrations of laminated composite beams with through-the-width delamination based on the first-order shear deformation theory. The finite element method is adopted to obtain the numerical results, and the energy approach is used to acquire the stiffness and mass matrices. The dynamic contact condition based on the physically real mode of vibration is introduced to satisfy the non-penetration condition. The time-dependent equations have been solved using the Newmark algorithm. Finally, the natural frequencies for in-plane and out-of-plane vibrations and the beam's time response under nonmoving harmonic load and moving point load with constant velocity are obtained. The results of the present study are verified by comparing them with those available in the literature. It is worth noting that the delaminated beam's vibration modes in all directions, i.e., axial, in-plane bending, and out-of-plane bending modes, have been obtained in the present study.