Free vibration analysis of delaminated soft-core sandwich plates

Abstract

This paper presents a numerical solution for analyzing the free vibration of delaminated soft core sandwich plates. The delaminated sandwich plate was modeled as six interconnected sub-plates, with the delamination serving as their boundaries. To account for the compressibility of the core, a semi-layerwise approach was adopted. The first order shear deformation theory (FSDT) was applied to the face sheets, while higher-order polynomial terms were used to model the displacement field of the core. Hamilton's principle was utilized to derive the equation of motion and relevant boundary conditions. To solve the problem, four novel layerwise C0 efficient nine-node quadrilateral elements were introduced. The elements were selected based on the thickness-wise position of the delamination. The delamination region was modeled using the point continuity method, while various boundary conditions were simulated using the penalty method. The study concludes that the developed elements and proposed procedure are accurate and efficient, as demonstrated by a comparative analysis with previous research. The effects of delamination on the vibration behaviour of the system were investigated in detail through a parametric analysis. The study found that the natural frequencies of the structure were predominantly influenced by the longer delamination, and this issue was more significant in higher modes. The results for various length-to-thickness ratios, boundary conditions, and the size, planar and thickness-wise position of delamination were reported, which can be used as a benchmark in future studies.