Computation of the simplest normal form for the singularity of two non-semisimple double zero eigenvalues - Details

Author：

Chen, Shuping (Chen, Shuping.) | Zhang, Wei (Zhang, Wei.) | Yao, Minghui (Yao, Minghui.)

Indexed by：

EI Scopus

Abstract：

In　this　paper　a　method　is　presented　for　computing　the　simplest　normal　form　for　a　vector　field　associated　with　the　singularity　of　two　non-semisimple　double　zero　eigenvalues.　The　method　developed　here　uses　the　lower　order　nonlinear　terms　in　the　normal　form　for　the　simplifications　of　higher　order　terms.　An　explicit　formulae　are　derived,　which　can　be　used　to　compute　the　coefficients　of　the　simplest　normal　form　and　the　associated　nonlinear　transformation.　The　theoretical　model　for　the　nonlinear　oscillation　of　a　simply　supported　rectangular　thin　plate　is　given　to　demonstrate　the　computational　efficiency　of　the　method.　©　2011　IEEE.

Keyword：

Computational efficiency Eigenvalues and eigenfunctions Dynamics Mathematical transformations

Author Community：

[ 1 ] [Chen, Shuping]College of Mechanical Engineering, Beijing University of Technology, Beijing, 100124, China
[ 2 ] [Chen, Shuping]College of Mathematics and Information Engineering, Taizhou University, Linhai, 317000, China
[ 3 ] [Zhang, Wei]College of Mechanical Engineering, Beijing University of Technology, Beijing, 100124, China
[ 4 ] [Yao, Minghui]College of Mechanical Engineering, Beijing University of Technology, Beijing, 100124, China