A tenon connection structure is widely used for the blade-disk connection in turbomachinery, and its contact stiffness and contact damping have caused nonlinear dynamic characteristics. The nonlinear dynamic characteristics of a blade-disk structure are mainly affected by its contact stiffness and damping characteristics, which are difficult to accurately predict and affected by many factors such as the operating speed and the centrifugal force caused by the rotation speed. Based on a single blade and tenon groove structure and the use of the dynamic characteristics experiments and simulations, the influence law of the contact stiffness and damping of the tenon connection structure with the change of the blade root compression force on the dynamic characteristics of the structure is obtained. The average relative error of identifying the contact stiffness is 0.48%; thus, identification of the nonlinear contact stiffness and damping of multiple pairs of contact curved surfaces is realized.