The wheel-rail impact noise caused by welding joints and rail corrugation will cause great disturbance to passengers, which is unbearable in severe cases, and is also an urgent problem to be solved at present. Resilient wheels, which feature complex structures, have demonstrated efficacy in reducing noise and vibration levels. However, the complex structure, nonlinear material behavior, and nonlinearity in the wheel-rail contact pose challenges in assessing their performance in reducing noise and vibration. To solve this problem, based on the three-dimensional wheel-rail rolling contact model, the nonlinear vibration and impact noise characteristics of resilient wheels when passing through welded joints and corrugated rails are analyzed. Research indicate that the use of resilient wheels can significantly reduce the amplitude of wheel-rail impact forces and associated noise when traversing short-wave welded joints. And it is worth noting that resilient wheels demonstrate a certain level of nonlinearity in their performance. Furthermore, we observed that the noise reduction effect of the resilient wheel is not linearly proportional to the depth of the welding joint, but is instead linked to the frequency of the corresponding corrugation wavelength. Especially, When the characteristic frequency of the corrugation is 390 Hz, the noise reduction effect of the resilient wheel can reach 6.6 dBA.