In order to establish a governing equation of motion to rationally desc ribe the phenomenon of beats in the vibration of a damaged concrete structure, a new nonlinear physical model is constructed by introducing a spring coil and a damping coil into a single degree of freedom system. In the model, the spring co il is connected in series with the spring of the system constituting a spring wi th complex stiffness, and the damping coil is connected in series with the dampe r of the system constituting a damper with complex damping. By introducing both the equivalent stiffness and damping, a generized governing equation of motion o f the model and the physical explaination of its key parameters are obtained. By energy analysis of the free vibration of the system, a monotonic variation rel ationship between structural damage and the key parameters of the governing equa tion is created, which would probably afford a new idea of finding out an index used to identify the nonlinear damage of structures.