Free vibrations of delaminated unidirectional sandwich panels with a transversely flexible core—a modified Galerkin approach

A theoretical approach for the free vibration analysis of delaminated unidirectional sandwich panels is developed. The theoretical model accounts for the flexibility of the core in the out of plane (vertical) direction and the resulting high-order displacement, acceleration, and velocity fields within the core. The analytical approach is based on Hamiltonʹs variational principle along with the high-order unidirectional sandwich panel theory and the modified Galerkin method. The two types of models investigated include delaminated regions with and without contact. The ability of the model to describe the high-order effects such as the pumping phenomenon and the localized effects in the vicinity of the delaminated regions is examined. A numerical example that focuses on the free vibration behavior of simply supported delaminated unidirectional sandwich panels is presented and discussed. A parametric study that examines the influence of the length of the delaminated region, its location, and the mechanical properties of the core material is presented. The numerical results are also compared with finite element analysis and with some special asymptotic cases for which the free vibrations behavior is analytically evaluated. A summary and conclusions close the paper.