On the improved dynamic analysis of delaminated beams

An improved dynamic analysis of delaminated bi-layer beams is presented in this study with considerations of transverse shear and delamination tip deformations as well as effects of friction and contact ahead of the delaminated tips. Layerwise shear deformable beam theory is applied for both the delaminated sub-layers and intact substrates, and a deformable interface is introduced to establish the continuity condition between the two substrates in the undelaminated regions, thus capturing the delamination tip deformations, such as the differential axial extension and normal peeling of the two sub-layers as well as the root rotation at the delamination tip. The piecewise linear spring model and linear bridging model are, respectively, employed to simulate the contact and friction behavior of the delaminated sub-layers. Frequencies and mode shapes are then solved through a boundary eigenvalue problem. The proposed model is then reduced to the classic ‘free model’ and ‘constrained model’ as special cases by properly selecting specific values of the spring stiffness in the linear spring models. Comparisons of the present solution with the existing experimental test results and theoretical solutions as well as the 2D continuum elastic finite element solutions are conducted to validate the present improved model. The effects of the contact and friction of delaminated surfaces, delamination tip deformations, and delamination locations on the natural frequency and first mode shape are investigated through parametric studies. The improved dynamic solution with the adoption of interface deformable bi-layer beam theory and the consideration of contact and friction of delaminated surfaces facilitates the design analysis and optimization of dynamic behavior as well as the delamination detection of laminated composite beams, and it can be used with confidence in accurate evaluation of dynamic response of delaminated composite structures.

► An improved dynamic model for delaminated bi-layer beams.
► With consideration of the delamination tip deformations as well as the friction and contact effects.
► Application of interface deformable bi-layer beam theory for dynamics of delaminated beams.