Normal Form for High-Dimensional Nonlinear System and Its Application to a Viscoelastic Moving Belt
This paper is concerned with the computation of the normal form and its application to a viscoelastic moving belt. First, a new computation method is proposed for significantly refining the normal forms for high-dimensional nonlinear systems. The improved method is described in detail by analyzing t...
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| Format: | Article |
| Language: | English |
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Wiley
2014-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2014/879564 |
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| author | S. P. Chen Y. H. Qian |
| author_facet | S. P. Chen Y. H. Qian |
| author_sort | S. P. Chen |
| collection | DOAJ |
| description | This paper is concerned with the computation of the normal form and its application to a viscoelastic moving belt. First, a new computation method is proposed for significantly refining the normal forms for high-dimensional nonlinear systems. The improved method is described in detail by analyzing the four-dimensional nonlinear dynamical systems whose Jacobian matrices evaluated at an equilibrium point contain three different cases, that are, (i) two pairs of pure imaginary eigenvalues, (ii) one nonsemisimple double zero and a pair of pure imaginary eigenvalues, and (iii) two nonsemisimple double zero eigenvalues. Then, three explicit formulae are derived, herein, which can be used to compute the coefficients of the normal form and the associated nonlinear transformation. Finally, employing the present method, we study the nonlinear oscillation of the viscoelastic moving belt under parametric excitations. The stability and bifurcation of the nonlinear vibration system are studied. Through the illustrative example, the feasibility and merit of this novel method are also demonstrated and discussed. |
| format | Article |
| id | doaj-art-f1b224fda02643dc8682c5ac880b4d01 |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-f1b224fda02643dc8682c5ac880b4d012025-02-03T01:30:12ZengWileyAbstract and Applied Analysis1085-33751687-04092014-01-01201410.1155/2014/879564879564Normal Form for High-Dimensional Nonlinear System and Its Application to a Viscoelastic Moving BeltS. P. Chen0Y. H. Qian1College of Mathematics, Xiamen University of Technology, Xiamen 361024, ChinaCollege of Mathematics, Physics and Information Engineering, Zhejiang Normal University, Jinhua, Zhejiang 321004, ChinaThis paper is concerned with the computation of the normal form and its application to a viscoelastic moving belt. First, a new computation method is proposed for significantly refining the normal forms for high-dimensional nonlinear systems. The improved method is described in detail by analyzing the four-dimensional nonlinear dynamical systems whose Jacobian matrices evaluated at an equilibrium point contain three different cases, that are, (i) two pairs of pure imaginary eigenvalues, (ii) one nonsemisimple double zero and a pair of pure imaginary eigenvalues, and (iii) two nonsemisimple double zero eigenvalues. Then, three explicit formulae are derived, herein, which can be used to compute the coefficients of the normal form and the associated nonlinear transformation. Finally, employing the present method, we study the nonlinear oscillation of the viscoelastic moving belt under parametric excitations. The stability and bifurcation of the nonlinear vibration system are studied. Through the illustrative example, the feasibility and merit of this novel method are also demonstrated and discussed.http://dx.doi.org/10.1155/2014/879564 |
| spellingShingle | S. P. Chen Y. H. Qian Normal Form for High-Dimensional Nonlinear System and Its Application to a Viscoelastic Moving Belt Abstract and Applied Analysis |
| title | Normal Form for High-Dimensional Nonlinear System and Its Application to a Viscoelastic Moving Belt |
| title_full | Normal Form for High-Dimensional Nonlinear System and Its Application to a Viscoelastic Moving Belt |
| title_fullStr | Normal Form for High-Dimensional Nonlinear System and Its Application to a Viscoelastic Moving Belt |
| title_full_unstemmed | Normal Form for High-Dimensional Nonlinear System and Its Application to a Viscoelastic Moving Belt |
| title_short | Normal Form for High-Dimensional Nonlinear System and Its Application to a Viscoelastic Moving Belt |
| title_sort | normal form for high dimensional nonlinear system and its application to a viscoelastic moving belt |
| url | http://dx.doi.org/10.1155/2014/879564 |
| work_keys_str_mv | AT spchen normalformforhighdimensionalnonlinearsystemanditsapplicationtoaviscoelasticmovingbelt AT yhqian normalformforhighdimensionalnonlinearsystemanditsapplicationtoaviscoelasticmovingbelt |