Nonlinear dynamic analysis of nonlocal composite laminated toroidal shell segments subjected to mechanical shock

Abstract

The present study deals with the nonlinear forced vibration of composite shallow nano toroidal shell segments. The improved Donnell shell theory is used with the nonlinear geometric strains, i.e., von Karman, Stein, and McElman’s assumptions. A coupled nonlinear partial differential equations using nonlocal theory, including the influence of nano-scales, is derived. The boundary conditions are simply supported and clamped–clamped, and the nano toroid shell is subjected to impulse radial dynamic excitation. The linear solution is verified by comparing natural frequencies with the available results using Galerkin’s method. The approximated linear mode shapes of the free vibration, which satisfy the boundary conditions, are used as the assumed multi-mode displacement functions required to solve the nonlinear vibration. Using Hamilton’s principle, the nonlinear equations of motion in generalized coordinates are solved using the displacement field by applying Galerkin’s and Runge–Kutta’s methods. Using the presented model, the effects of layer stacking, toroidal shell segments curvature (convex and concave toroidal shells), length scale parameter, and material properties are studied in detail, and some conclusions are surveyed. It is observed that the nonlocal parameter demonstrates a considerable effect on the dynamics behavior characteristics response of the toroidal shell segments. Furthermore, different fiber orientation effects, displacement fields, time response, and geometry parameters, i.e., thickness, and length are studied. Results indicate that natural frequencies significantly depend on the toroid dimensions, boundary conditions, layer stacking, curvature change, and considered wave numbers.