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

作　　者：LIU ZhuangZhuang WANG TianShu LI JunFeng 

机构地区：[1]School of Aerospace, Tsinghua University

出　　处：《Science China(Physics,Mechanics & Astronomy)》2015年第4期45-57,共13页中国科学：物理学、力学、天文学（英文版）

摘　　要：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.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 polyno- mials 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 trigonomet- ric 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.

关 键 词：non-intrusive interval method dynamic response analysis uncertain nonlinear systems trigonometric polynomial ap-proximation interval arithmetic 

分 类 号：O415[理学—理论物理]