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Abstract and Applied Analysis
Volume 2013 (2013), Article ID 329638, 3 pages
http://dx.doi.org/10.1155/2013/329638
Letter to the Editor

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.

1. Introduction

In [1], the following nonlinear oscillator was studied: Similar nonlinear oscillators arising in packing systems and textile engineering are available in [27].

In [1], (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 [1], 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 [1] should be corrected as that given in (13). In [1], 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 [10] is much more effective, which reads The variational iteration method is especially effective in solving nonlinear oscillators.

References

  1. 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. View at Publisher · View at Google Scholar
  2. 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. View at Scopus
  3. 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. View at Publisher · View at Google Scholar · View at Scopus
  4. 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. View at Publisher · View at Google Scholar · View at Scopus
  5. 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. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  6. 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. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  7. 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. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  8. 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. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  9. J. H. He, “Some asymptotic methods for strongly nonlinear equations,” International Journal of Modern Physics B, vol. 20, no. 10, pp. 1141–1199, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  10. J. H. He, “Asymptotic methods for solitary solutions and compactons,” Abstract and Applied Analysis, vol. 2012, Article ID 916793, 130 pages, 2012. View at Zentralblatt MATH · View at MathSciNet