Nonlinear low-velocity impact of axially moving porous conical shells

This paper investigates the nonlinear low-velocity impact response of an axially moving functionally graded (FG) conical shell. The nonlinear equations of motion are derived based on Reddy’s shell theory and von Kármán geometric nonlinearity. With simply supported boundary conditions, the time histories of deformation and contact force are solved numerically by combining the fourth-order Runge‑Kutta method with the Galerkin technique, and the impact force is determined using the modified Hertzian contact model and Newton’s second law. A key finding regarding the optimal volume fraction is that an intermediate ceramic content minimizes the central deflection under low-velocity impact, indicating a trade-off between stiffness and energy absorption. Additional numerical results reveal several key findings: (1) Increasing the prestress reduces the maximum central deflection while having negligible effect on the peak contact force, indicating an enhanced energy dissipation capability. (2) A larger damping coefficient accelerates the return to equilibrium after impact but only slightly decreases the maximum deflection. (3) Raising either the impactor radius or its initial velocity increases the peak deflection and contact force; however, a larger radius prolongs the contact time, whereas a higher initial velocity shortens it. (4) The axial motion speed of the conical shell affects the deflection more significantly than the contact force, suggesting that contact stiffness remains nearly unchanged. (5) The semi-vertex angle of the conical shell has a weak influence on the impact response. (6) Increasing porosity or the functionally graded index (i.e., reducing ceramic content) reduces structural stiffness, leading to larger contact displacements.