Nonlinear supersonic flutter of sandwich truncated conical shell with flexible honeycomb core manufactured by fused deposition modeling

Abstract

The self-sustained vibrations of sandwich conical shell with a flexible honeycomb core manufactured by fused deposition modeling are studied. The interaction of the sandwich thin-walled structure with supersonic gas flow is analyzed. The geometrical nonlinearity of the shell structure is taken into account to predict the self-sustained vibrations. Vibrations of the structure layer are described by three displacements of the middle surface of each layer and two rotations of the normal to the middle surface. The higher-order shear deformation theory is used to describe the strain–displacement relationships. The self-sustained vibrations of the sandwich conical shell are described by a system of nonlinear ordinary differential equations with respect to the generalized coordinates. The assumed mode method is used to derive the equations.The bifurcations of the nonlinear self-sustained vibrations are analyzed numerically using a continuation technique. Quasi-periodic and chaotic self-sustained vibrations are numerically studied for the shell subjected to different boundary conditions. Numerical results show that the amplitudes of quasi-periodic and chaotic vibrations are significantly larger than the amplitudes of periodic vibrations for this shell.