Vibration response of laminated composite plate having weakly bonded layers

摘要

Free and forced vibration response of laminated composite and sandwich plate having weakly bonded layer is studied by using an efficient C~0 continuous two dimensional finite element (FE) model. This FE model is based on higher order zigzag theory (HOZT) in which, in-plane displacements are obtained by superposing a global displacement field having cubical variation across thickness, on a zigzag displacement field having linear variation with a different slope in each layer. The out of plane displacement is assumed constant across the thickness of the plate. In the proposed model, transverse shear stresses are continuous at the layer interfaces and vanish at the top and bottom surfaces of the plate. At the same time, it is computationally as elegant as any single layer plate model since it requires the usual unknowns at the reference plane only. The inter-laminar imperfections are represented by in-plane displacement jumps at the layer interfaces and characterized by a linear spring layer model. In order to circumvent the problem of C~1 continuity associated with the above plate theory at the time of FE implementation, first derivatives of the transverse displacement have been treated as independent variables. It is interesting to note that the plate model having all these refined features requires unknowns at the reference plane only. The LSE method is applied to the 3D equilibrium equations of the plate problem at the post-processing stage, after in-plane stresses are calculated by using the above FE model based on HOZT for forced vibration problems. Numerical problems on free and forced vibration having different geometric and material properties of laminated composite and sandwich plates are solved. Some new problems have also been solved and new results have been presented which would be useful for future research.