Comparative analysis of earthquake response spectra about viscous and complex damping model

Towards complex and viscous damping model of the SDOF system, this article researches the differences, similarities of the above two system responses. Through calculating the two kinds of system dynamic equations based on harmonic excitation clearly, the result is that: When the excitation's period is less than the natural period of structures, the displacement response of the complex damping system is stronger than the latter. Oppositely, the speed response, the acceleration response are both weaker than the latter. On the contrary, the result is opposite. Based on those work, the acceleration spectra of some representative earthquake records are provided of the two kinds of systems, and also the velocity and displacement spectra. In comparison with the last two spectra in the condition of harmonic excitation, the results show the similar phenomenon. But the acceleration spectra of the viscous damping model are higher than that of the complex damping model at any time. And with the growing damping ratio, the difference is more remarkable. Under certain earthquake records, the structure displacement response values of certain natural period may differ by 15%.The velocity spectra differ by 14%. The acceleration spectra differ by 8%. In the end, the article gives us a suggestion that how to choose damping model to make the structure more Safe and reliable. And also, it provides some help for the further study of complex damping theory, references for engineering application.