Dynamic Dispersion Properties Of Periodic Frame Structures

Frame structures can be viewed as a kind of periodic structure with its standard floor structure arranged in the height direction.This periodic arrangement also gives frame structures some unique dynamic properties.In this paper,introducing the periodic structure theory into civil engineering,theoretical analysis and numerical simulations are conducted to investigate the dispersion dynamic properties of frame structures.The main works are as follows:(1)Based on the Bloch-Floquet theory and Timoshenko beam theory,a simplified calculation model is proposed to analyze the dispersion property of frame structures;(2)The state space-transfer matrix method(SSTMM)is applied to calculate the dispersion relationships of frame structures,and the dispersion curves of the infinite periodic frame structure are given.The correctness of results is verified by the comparison with the finite element method;(3)Dispersion properties of frame structures are discussed based on phase/group velocity curves and the wave modal analysis,and the approximate expression of the lower bound frequency of the first attenuation zone is given;(4)Influences of the typical parameters of frame structures(beams,columns,plates and infill walls)and model parameters on the first two attenuation zones are studied.Besides,influences of the damping on the filtering characteristics of periodic frame structures are also analyzed;(5)Dynamic responses of finite periodic frame structures are numerically simulated to verify the theoretical results of attenuation zones of infinite periodic frame structures by the Riccati state space-transfer matrix method.Some conclusions are obtained:Because of the geometric periodicity,dispersion curves of infinite periodic frame structures have the characteristics of band.In some frequency bands(called pass bands),there are wave vectors corresponding to the frequency,while in other frequency bands(called attenuation zones)no wave vector exists.Modal analysis results show that the lower bound frequencies of attenuation zones are independent of the rotation constraint of the frame beam on the frame column,and the upper bound frequencies of attenuation zones are independent of the gravity load of the floor,based on which simplified models can be proposed to calculate the boundary frequencies of attenuation zones.The height of the standard floor structure,the section size of the frame columns as well as the stiffness of the infill walls have great influences on the dispersion properties of periodic frame structures.While influences of the section size and concrete strength grade of the frame beams,the plate thickness and the span on the dispersion properties of the periodic frame structures are very small and could be neglected.When the damping effect is included,external excitations out of the attenuation zones are attenuated mainly by the damping energy dissipation mechanism,while external excitations in the attenuation zones are attenuated mainly by the filtering effect of periodic structures.The transfer matrix method based on the Riccati transform can effectively improve the stability of calculation results of the dynamic responses in frequency domain.The dynamic responses of the finite periodic frame structure corresponds well with the vibration attenuation zones of the infinite periodic frame structure.Vibrations in the attenuation zone will be decayed with the propagation in the periodic structures;while vibrations out of the attenuation zones can propagate freely in the periodic structures.