Frequency response of bimodular cross-ply laminated cylindrical panels

With the in-plane inertia, the response of bimodular material laminated cylindrical panels computed using direct time integration shows numerical instability. This instability is due to the sudden change in the restoring force from positive/negative half cycle to negative/positive half cycle. The sudden change in restoring force with in-plane inertia excites higher harmonics at every instant of a cycle change leading to numerical instability. This numerical instability can be eliminated if the switch over from positive to negative half cycle or vice versa is exactly at the instant when restoring force is zero. However all the elements of restoring force vector do not become zero simultaneously when direct time integration is performed. Thus it is not possible in the numerical time integration approach to find time instant when restoring force vector becomes a null vector. Therefore, an approach based on Galerkin method in time domain is proposed for the steady-state response of bimodular material structures that eliminates the instability. Its efficacy is demonstrated for the first time for frequency response of bimodular material laminated cylindrical panels modelled using finite element based on Bert's constitutive model.