A new approach for computing the normal forms of high dimensional nonlinear systems - Details

Author：

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

Indexed by：

EI Scopus

Abstract：

Normal　form　theory　is　very　useful　for　direct　bifurcation　and　stability　analysis　of　nonlinear　differential　equations　modeled　in　real　life.　This　paper　develops　a　new　computation　method　for　obtaining　a　significant　refinement　of　the　normal　forms　for　high　dimensional　nonlinear　systems.　The　method　developed　here　uses　the　lower　order　nonlinear　terms　in　the　normal　form　for　the　simplifications　of　higher　order　terms.　In　the　theoretical　model　for　the　nonplanar　nonlinear　oscillation　of　a　cantilever　beam,　the　computation　method　is　applied　to　compute　the　coefficients　of　the　normal　forms　for　the　case　of　two　non-semisimple　double　zero　eigenvalues.　The　normal　forms　of　the　averaged　equations　and　their　coefficients　for　non-planar　non-linear　oscillations　of　the　cantilever　beam　under　combined　parametric　and　forcing　excitations　are　calculated.©　2010　by　ASME.

Keyword：

Nanocantilevers Computation theory Cantilever beams Differential equations Nonlinear systems Nonlinear equations Oscillators (mechanical) Eigenvalues and eigenfunctions

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