An Iteration Scheme Suitable for Solving Limit Cycles of Nonsmooth Dynamical Systems
Joint Authors
Liu, Q. X.
Liu, J. K.
Chen, Y. M.
Source
Mathematical Problems in Engineering
Issue
Vol. 2013, Issue 2013 (31 Dec. 2013), pp.1-5, 5 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2013-11-12
Country of Publication
Egypt
No. of Pages
5
Main Subjects
Abstract EN
The Mickens iteration method (MIM) is modified to solve self-excited systems containing nonsmooth nonlinearities and/or nonlinear damping terms.
If the MIM is implemented routinely, the unknown frequency and amplitude of limit cycle (LC) would couple to each other in complicated nonlinear algebraic equations at each iteration.
It is cumbersome to solve these algebraic equations, especially for nonsmooth systems.
In the modified procedures, the unknown frequency is substituted by the determined value obtained at the previous iteration.
By this means, the frequency is decoupled from the nonlinear terms.
Numerical examples show that the LCs obtained by the modified MIM agree well with numerical results.
The presented method is very suitable for solving self-excited systems, especially those with nonlinear damping and nonsmooth nonlinearities.
American Psychological Association (APA)
Liu, Q. X.& Chen, Y. M.& Liu, J. K.. 2013. An Iteration Scheme Suitable for Solving Limit Cycles of Nonsmooth Dynamical Systems. Mathematical Problems in Engineering،Vol. 2013, no. 2013, pp.1-5.
https://search.emarefa.net/detail/BIM-1009939
Modern Language Association (MLA)
Liu, Q. X.…[et al.]. An Iteration Scheme Suitable for Solving Limit Cycles of Nonsmooth Dynamical Systems. Mathematical Problems in Engineering No. 2013 (2013), pp.1-5.
https://search.emarefa.net/detail/BIM-1009939
American Medical Association (AMA)
Liu, Q. X.& Chen, Y. M.& Liu, J. K.. An Iteration Scheme Suitable for Solving Limit Cycles of Nonsmooth Dynamical Systems. Mathematical Problems in Engineering. 2013. Vol. 2013, no. 2013, pp.1-5.
https://search.emarefa.net/detail/BIM-1009939
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1009939