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| Time history integration calculation for theory of frequency dependent viscous damping |
| SUN Panxu1， YANG Hong1,2， LIU Qinglin3 |
1. School of Civil Engineering, Chongqing University, Chongqing 400045, China;
2. Key Laboratory of New Technology for Construction of Cities in Mountain Area of the Ministry of Education, Chongqing University, Chongqing 400045, China;
3. School of Traffic and Engineering, Shenzhen Institute of Information Technology, Shenzhen 518172, China |
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Abstract Viscous damping theory has some disadvantages, one of which is that energy consumption per cycle is related to external excitation frequencies.The general solution to the complex damping theory’s motion equation contains divergent items.Here, with the principle of frequency domain conversion, the complex damping motion equation was equivalently converted into a frequency dependent viscous damping motion equation to overcome the disadvantage of the complex damping theory having instability in time domain, and guarantee energy consumption per cycle being independent upon external excitation frequencies.Using the relationship assumption of velocity and displacement and the principle of energy conservation, the frequency dependent viscous damping motion equation being suitable for time history calculation was built.Combining with the constant average acceleration method, the recursion expression for time history integration calculation of the frequency dependent viscous damping motion equation was derived.The calculation examples showed that the time history integration calculation results of the frequency dependent viscous damping theory are stably convergent to effectively avoid divergent problems in time history integration calculation of complex damping theory.
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Received: 10 July 2017
Published: 28 December 2018
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