Chinese Journal of Theoretical and Applied Mechanics ›› 2020, Vol. 52 ›› Issue (1): 60-72.DOI: 10.6052/0459-1879-19-348

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Qiu Zhiping(),Jiang Nan   

  1. School of Aeronautic Science and Engineering, Beihang University, Beijing 100191, China
  • Received:2019-12-09 Accepted:2020-01-17 Online:2020-01-18 Published:2020-02-23
  • Contact: Qiu Zhiping


With the rapid development of computer technology, there is an urgent need for more efficient and more stable numerical algorithms with more powerful long-term simulation capabilities. Compared with the traditional algorithms, the symplectic algorithms of Hamiltonian systems have significant advantages in stability and long-term simulation. However, a variety of different degrees of uncertainties exist inevitably in the dynamic system, and the impacts of these uncertainties need to be considered in the dynamic analysis to ensure the rationality and effectiveness. Nevertheless, there has been very little research considering parameter uncertainties on the dynamic response analysis of Hamiltonian systems. For this reason, two kinds of uncertain non-homogeneous linear Hamiltonian systems are studied and compared in this paper breaking through the limitations of traditional Hamiltonian systems, where stochastic and interval parameter uncertainties are taken into account, and applied to the evaluation of structural dynamic response. Firstly, for the deterministic non-homogeneous linear Hamiltonian systems, a parameter perturbation method considering deterministic perturbations is proposed. On this basis, the parameter perturbation methods of stochastic and interval non-homogeneous linear Hamiltonian systems are proposed respectively, and the mathematical expressions of the bounds of their response are obtained. Then, the compatibility conclusion that the region of the dynamic response obtained by the interval method contains that obtained by the stochastic one is derived theoretically. Finally, two numerical examples verify the feasibility and effectiveness of the proposed method in structural dynamic response in a smaller time step, and reflect the envelope relationship between the numerical results of the response of stochastic and interval Hamiltonian systems. Also, in a larger time step, the numerical advantages of the symplectic algorithms of Hamiltonian systems are highlighted compared to the traditional algorithms and the accuracy of the proposed method is verified by comparison with the Monte Carlo simulation method.

Key words: Hamiltonian system, uncertainty, parameter perturbation method, dynamic response, comparative study

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