By introducing the concept of forming springback anti-coupled systems and considering the influence of the self damping effect, meanwhile establishing higher-order geometrical nonlinear equation of a high strength and low alloy (HSLA) steel plate, then a set of nonlinear dynamic springback governing equations of the plate are obtained. The finite difference method, Newmark method and iterative method are applied to solve the whole problem. Numerical results denote that the boundary conditions, thickness-length ratio of the plate and initial impact velocity of the impactor have great influence on the springback amount of the rectangular HSLA steel plate, besides the natural frequency is affected a lot by the boundary conditions and thickness-length ratio. The effect of higher-order geometrical nonlinearity on the springback amount of the plate can be ignored, considering the first-order geometrical nonlinearity is enough accurate for such similar nonlinear dynamic problems.
