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Dynamical shakedown analysis of high-rise tower structure

Guichen Zhang (Department of Engineering Mechanics, Tsinghua University, Beijing, China and School of Electrical and Control Engineering, North China University of Technology, Beijing, China)
Hongtao Zhang (Department of Civil Engineering, North China University of Technology, Beijing, China)
Heng Peng (Department of Engineering Mechanics, Tsinghua University, Beijing, China)
Yinghua Liu (Department of Engineering Mechanics and Key Laboratory of Applied Mechanics, Tsinghua University, Beijing, China)

Engineering Computations

ISSN: 0264-4401

Article publication date: 4 February 2021

Issue publication date: 15 June 2021




High-rise tower structures supported by side frame structure and viscous damper in chemical industry can produce plasticity under dynamic loads, such as wind and earthquake, which will heavily influence the long-term safety operation. This paper aims to systematically study the optimization design of these structures by free vibration and dynamic shakedown analysis.


The transfer matrix method and Euler–Bernoulli beam vibration are used to study the free vibration characteristic of the simplified high-rise tower structure. Then the extended stress compensation method is used to construct the self-equilibrated stress by using the dynamic load vertexes and the lower bound dynamic shakedown analysis for the structure with viscous damper. Using the proposed method, comprehensive parametric studies and optimization are performed to examine the shakedown load of high-rise tower with various supported conditions.


The numerical results show that the supported frame stiffness, attached damper or spring parameters influence the free vibration and shakedown characters of high-rise tower very much. The dynamic shakedown load is lowered down quickly with external load frequency increasing to the fundamental natural frequency of the structure under spring supported condition, while changed little with the damping connection. The optimized location and parameter of support are obtained under dynamical excitations.

Research limitations/implications

In this study, the high-rise tower structure is simplified as a cantilever beam supported by a short cantilever beam and a damper under repeated dynamic load, and linear elasticity for solid is assumed for free vibration analysis. The current analysis does not account for effects such as large deformation, stochastic external load and nonlinear vibration conditions which will inevitably be encountered and affect the load capacity.


This study provides a comprehensive method for the dynamical optimization of high-rise tower structure by combining free vibration and shakedown analysis.



Zhang, G., Zhang, H., Peng, H. and Liu, Y. (2021), "Dynamical shakedown analysis of high-rise tower structure", Engineering Computations, Vol. 38 No. 3, pp. 1432-1451.



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