Dynamic instability of variable angle tow composite plates with delamination

In this paper, the dynamic instability of variable angle tow (VAT) plates with a single rectangular delamination is studied using an analytical model. The analytical model is derived from the principle of potential energy based on the classical laminated plate theory. Both global and local behavior of delaminated VAT plates in the dynamic instability analysis are accurately captured by the use of multiple Legendre polynomial series. The equations for the motion in dynamic instability problem are derived using Hamilton's principle. The dynamic instability regions are determined from the resulting Mathieu differential equations, which are solved using Bolotin's approach. To validate the proposed analytical model, both critical buckling loads and natural frequencies of delaminated VAT plates are evaluated and compared with FEM results. The influence of delamination on the buckling load, natural frequency and dynamic instability region (DIR) of delaminated VAT plates is examined by numerical examples. A parametric study is subsequently carried out to analyze the effect of linearly varying fibre orientation angles on the dynamic instability response of delaminated VAT plates. Finally, the mechanism of applying variable angle tows to improve the dynamic stability performance of delaminated composite plates is studied.