A time-domain integration method with equivalent complex damping model based on viscoelastic material constitutive relation

Author:

Fan Jia12,Wang Shuxia3ORCID,Sun Panxu2ORCID

Affiliation:

1. School of Civil Engineering, Luoyang Institute of Science and Technology, Luoyang, China

2. School of Civil Engineering, Zhengzhou University, Zhengzhou, China

3. School of Materials Science and Engineering, Zhengzhou University of Aeronautics, Zhengzhou, China

Abstract

The complex damping model is only applied in frequency-domain. Based on the constitutive relation of viscoelastic materials, a vibration equation is equivalent to the constitutive relation of complex damping theory and the frequency response function satisfying the causality constraint. Compared with the existing equivalent complex damping model, the proposed equivalent damping model can consider more natural frequencies. The calculation formulas of Gauss precise integral method and improvement constant average acceleration method are derived. By the equivalent complex damping, the seismic time-history response of the typical example could carry on the numerical calculation. Compared with the Gauss precise integral calculation results of complex damping vibration equation, some conclusions can be analyzed. The proposed two methods could avoid divergent phenomenon in the time-domain numerical solution of complex damping vibration equation. The time-domain integral method of equivalent complex damping theory is stable and convergent. The Gauss precise integral method has strong equivalence and big computational complexity. The improvement constant average acceleration method has weak equivalence and small computational complexity.

Funder

Henan Province Science and Technology Research Funding Project

Postdoctoral Research Foundation of China

National Natural Science Foundation of China

Key Research Project of Henan Higher Education Institutions

Publisher

SAGE Publications

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