The concept of equivalent nodal secant damping coefficients is proposed to diagonalize the stiffness-proportional damping matrix. Additionally, a novel method is proposed to rapidly evaluate stiffness-proportional damping nodal forces for nonlinear elements on the element level. With the assumption of lumped-mass idealization an incremental-iterative procedure is performed to solve the decoupled equilibrium equations for damped systems using the implicit Newmark integration method. The proposed analysis procedure has the advantages of both traditional explicit and implicit integration methods without their disadvantages. Through extensive practical implementations, the results demonstrate that the proposed procedure is simple and robust for analyzing practical damped systems with excellent computational efficiency and stability.