Abstract: A practical mechanical model of damping system considering the stiffness of the connection element was proposed, based on the research of mechanical models of traditional energy dissipation system. Firstly, the transfer function and frequency characteristic of the practical damping system were derived using the Laplace transform and the Fourier transform of the mathematical method. Subsequently, the fixed-point theory was used in the frequency response curves to examine the frequency characteristic. The results showed that the fixed-point of the frequency response curves was the theoretical lowest point the curves' peak value could reach. The optimal damping ratio and the minimum peak value of the frequency response curves were derived. Finally, the existence of the optimal damping ratio was verified by using a single degree of freedom system. A recommended range of the support stiffness coefficient was provided. Moreover, the importance of the support stiffness coefficient in energy dissipation structure designing was revealed by studying a project example.