Wave dispersion analysis of multi-story frame building structures using the periodic structure theory

Introducing the periodic structure theory in the field of solid-state-physics into the field of civil engineering, this paper conducts a comprehensive theoretical and numerical study on the wave dispersion properties of multi-story frame building structures. At first, the theoretical infinite periodic model for the multi-story frame building structure is developed. Combining the Bloch-Floquet theorem and the State-Space-Transfer-Matrix-Method (SSTMM), the dispersion equation of the infinite periodic system is solved, from which dispersion curves and group/phase velocity curves of a practical multi-story reinforced concrete frame building structure are investigated. Second, a parametric study is performed to investigate the influences of the typical material parameters (density, strength grade of concrete), geometrical parameters (span length, floor height), theoretical simplified parameters as well as the damping parameter of frame building structures on the dispersion relations. Then, harmonic analysis and time history analysis are conducted to analyze the dynamic properties of the finite periodic frame structure in the frequency domain. Numerical results show that, when the main frequency region of the external excitations (like seismic waves) falls into the passing bands, dynamic responses of the multi-story frame building structure are very large; while the main frequency region of the external excitations falls into the attenuation zones, seismic responses of the multi-story frame building structure are very small.