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A Monte Carlo simulation method for non-random vibration analysis

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Abstract

In recent years, the authors developed a non-random vibration analysis method for structural dynamic analysis under uncertain excitations. In non-random vibration analysis, the interval process model is employed to describe the uncertain dynamic load rather than the traditional stochastic process model, and the structural dynamic response is obtained in the form of upper and lower bounds, rather than its precise probability distribution. Since the probability distribution information is not required, the non-random vibration analysis generally could decrease the dependence on large experimental sample number; meanwhile, the bounds of dynamic response are easy to understand conceptually and convenient to use in practical structural reliability or safety design. On the basis of our previous work, this paper further proposes a Monte Carlo simulation method, aiming to provide a general way for non-random vibration analysis and also offer a reference solution for other non-random vibration analysis methods proposed in the future. Firstly, a sampling approach is presented to realize the precise sampling of the single interval process and the multi-dimensional interval process vector. Then, based on the sampling approach, a calculation procedure of non-random vibration analysis is constructed to obtain the structural dynamic response bounds under uncertain dynamic load. Finally, the proposed method is not only applied to single-degree-of-freedom and multi-degree-of-freedom linear vibration systems, but also to more complex vibration systems such as nonlinear systems and continuum structures.

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Authors and Affiliations

  1. State Key Laboratory of Advanced Design and Manufacturing for Vehicle Body, Key Laboratory of Advanced Design and Simulation Technology for Special Equipments Ministry of Education, Hunan University, Changsha City, 410082, People’s Republic of China

    C. Jiang, N. Y. Liu & B. Y. Ni

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  1. C. Jiang
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  2. N. Y. Liu
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  3. B. Y. Ni
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Correspondence to C. Jiang.

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Jiang, C., Liu, N.Y. & Ni, B.Y. A Monte Carlo simulation method for non-random vibration analysis. Acta Mech 228, 2631–2653 (2017). https://doi.org/10.1007/s00707-017-1842-3

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  • DOI: https://doi.org/10.1007/s00707-017-1842-3

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