Abstract <p>The impact contact of the plate by the rod exhibits different properties from the impact of the sphere. Upon impact, the excitation stress wave reflects back to the rod’s free end, while the bending wave propagates around the plate. Therefore, the wave propagation response in the rod significantly affects the whole impact response process. The mid-rod graded configuration can adjust the wave propagation response. Different graded rod types were designed and implemented. We constructed a variable coefficient wave equation to describe the wave propagation response in the rod. The Zener contact law was applied to model bending wave propagation in the plate for the contact boundary conditions. Subsequently, the Laplace transform was employed to solve the wave equation and give expressions such as the relationship between the displacement and the contact force. The effects of graded configuration and contact stiffness on wave propagation and impact contact response were investigated. Results show that the graded configuration can effectively adjust the wave propagation behavior of the rod and affect its rebound velocity, contact time, and energy conversion. These findings can be used to guide the design of heterogeneous impactors and to explore the mechanism of high-frequency oscillation of low-velocity impacts.</p>