On nonlinear free vibration of externally compressible fluid-loaded sandwich cylindrical shells: Curvature nonlinearity in bending and impermeability condition

Abstract

A nonlinear fluid–structure interaction (FSI) model is presented for nonlinear vibration analysis of sandwich cylindrical shells subjected to an external compressible flow by considering the curvature nonlinearity in impermeability condition and bending. The sandwich shells are made of two face sheets and a central core of advanced materials including functionally graded (FG), metal foam, and anisogrid lattice composite. Based on the Kirchhoff–love hypotheses with the geometric nonlinearities in the normal strain and curvature of mid-surface, one decoupled nonlinear integral–differential equation is obtained for axisymmetric bending vibration of sandwich cylindrical shells. For the first time, the nonlinear impermeability condition is developed in order to take into account the large deformation of thin structures in FSI modeling. In both subsonic and supersonic regimes of steady irrotational compressible flow, a closed-form expression for nonlinear pressure distribution is presented according to the conservation of mass and generalized Bernoulli equation of extended potential theory. Using the Galerkin’s method in conjunction with the multiple-scale perturbation technique, the decoupled equation is solved to obtain nonlinear frequency and time–history response. Finally, parametric studies are carried out to investigate the effects of geometric ratios, boundary conditions, fluid specifications, and material variation on the responses of sandwich shells with different layups such as [Al; FG core; ZrO2], [Al; foam core; ZrO2], [Al; lattice core; Al]. Significant differences in pressure variation due to curvature nonlinearity are observed for short shells with larger vibration amplitude and larger number of half-waves in the axial direction. Therefore, the linear vibration analysis is inadequate for analyzing short sandwich cylindrical shells surrounded by an external fluid flow especially in the case of movable ends.