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A trigonometric interval method for dynamic response analysis of uncertain nonlinear systems

一种不确定非线性系统动力学响应分析的三角区间方法

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  • Dynamics and Control
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Abstract

This paper proposes a new non-intrusive trigonometric polynomial approximation interval method for the dynamic response analysis of nonlinear systems with uncertain-but-bounded parameters and/or initial conditions. This method provides tighter solution ranges compared to the existing approximation interval methods. We consider trigonometric approximation polynomials of three types: both cosine and sine functions, the sine function, and the cosine function. Thus, special interval arithmetic for trigonometric function without overestimation can be used to obtain interval results. The interval method using trigonometric approximation polynomials with a cosine functional form exhibits better performance than the existing Taylor interval method and Chebyshev interval method. Finally, two typical numerical examples with nonlinearity are applied to demonstrate the effectiveness of the proposed method.

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Authors and Affiliations

  1. School of Aerospace, Tsinghua University, Beijing, 100084, China

    ZhuangZhuang Liu, TianShu Wang & JunFeng Li

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  1. ZhuangZhuang Liu
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  2. TianShu Wang
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  3. JunFeng Li
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Correspondence to TianShu Wang.

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Contributed by LI JunFeng (Associate Editor)

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Liu, Z., Wang, T. & Li, J. A trigonometric interval method for dynamic response analysis of uncertain nonlinear systems. Sci. China Phys. Mech. Astron. 58, 1–13 (2015). https://doi.org/10.1007/s11433-014-5641-8

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  • DOI: https://doi.org/10.1007/s11433-014-5641-8

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