- About this Journal ·
- Abstracting and Indexing ·
- Aims and Scope ·
- Annual Issues ·
- Article Processing Charges ·
- Articles in Press ·
- Author Guidelines ·
- Bibliographic Information ·
- Citations to this Journal ·
- Contact Information ·
- Editorial Board ·
- Editorial Workflow ·
- Free eTOC Alerts ·
- Publication Ethics ·
- Reviewers Acknowledgment ·
- Submit a Manuscript ·
- Subscription Information ·
- Table of Contents
Abstract and Applied Analysis
Volume 2013 (2013), Article ID 329638, 3 pages
Comment on “Nonlinear Response of Strong Nonlinear System Arisen in Polymer Cushion”
School of Mathematics and Computer Science, Yangtze Normal University, Chongqing 408100, China
Received 10 April 2013; Accepted 26 May 2013
Academic Editor: Antonio Suárez
Copyright © 2013 Jun Zhou. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
In , (1) is approximated by Taylor’s series for the nonlinear terms: By using Taylor’s expansion function of MATLAB’s symbolic function, the nonlinear terms , , and are expanded to 8th order. After careful calculation, (2) should be corrected as where .
2. Variational Iteration Method
In , the following variational iteration algorithm was constructed: which should be corrected as In order to simplify the solution process, we denote Equation (5) becomes We begin with and use the following relationships: By (7), we have where Consider the following identity: From (10), we obtain where ( = 1~4) are defined above.
3. Discussion and Conclusion
The result of in  should be corrected as that given in (13). In , actually the following variational iteration algorithm is used: which is called the variational iteration algorithm in [8, 9]; for the present problem, the variational iteration algorithm in  is much more effective, which reads The variational iteration method is especially effective in solving nonlinear oscillators.
- J. Wang, L. X. Lu, H. X. Jiang, and Y. Zhu, “Nonlinear response of strong nonlinear system arisen in polymer cushion,” Abstract and Applied Analysis, vol. 2013, Article ID 891914, 3 pages, 2013.
- J. Wang and Z. Wang, “Damage boundary surface of a tangent nonlinear packaging system with critical component,” Journal of Vibration and Shock, vol. 27, no. 2, pp. 166–167, 2008.
- J. Wang, Z. Wang, L. Lu, Y. Zhu, and Y. Wang, “Three-dimensional shock spectrum of critical component for nonlinear packaging system,” Shock and Vibration, vol. 18, no. 3, pp. 437–445, 2011.
- J. Wang, J. Jiang, L. Lu, and Z. Wang, “Dropping damage evaluation for a tangent nonlinear system with a critical component,” Computers and Mathematics with Applications, vol. 61, no. 8, pp. 1979–1982, 2011.
- J. Wang, Y. Khan, R. Yang, L. Lu, Z. Wang, and N. Faraz, “A mathematical modelling of inner-resonance of tangent nonlinear cushioning packaging system with critical components,” Mathematical and Computer Modelling, vol. 54, no. 11-12, pp. 2573–2576, 2011.
- L. Xu, “Dynamics of two-strand yarn spinning in forced vibration,” Nonlinear Analysis, Theory, Methods and Applications, vol. 71, no. 12, pp. e827–e829, 2009.
- R. Yang and S. Wang, “Resonance in a rotor-spun composite yarn spinning process obtained using the variational iteration method,” Computers and Mathematics with Applications, vol. 58, no. 11-12, pp. 2486–2488, 2009.
- J. He and X. Wu, “Variational iteration method: new development and applications,” Computers and Mathematics with Applications, vol. 54, no. 7-8, pp. 881–894, 2007.
- J. H. He, “Some asymptotic methods for strongly nonlinear equations,” International Journal of Modern Physics B, vol. 20, no. 10, pp. 1141–1199, 2006.
- J. H. He, “Asymptotic methods for solitary solutions and compactons,” Abstract and Applied Analysis, vol. 2012, Article ID 916793, 130 pages, 2012.