- About this Journal ·
- Abstracting and Indexing ·
- Advance Access ·
- 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
Journal of Applied Mathematics
Volume 2012 (2012), Article ID 531480, 22 pages
Approximate Super- and Sub-harmonic Response of a Multi-DOFs System with Local Cubic Nonlinearities under Resonance
1Department of Engineering Mechanics, Tsinghua University, Beijing 100084, China
2Traction Power State Key Laboratory, Southwest Jiaotong University, Chengdu 610031, China
Received 15 June 2012; Accepted 1 October 2012
Academic Editor: Livija Cveticanin
Copyright © 2012 Yang CaiJin. 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.
- M. K. Yazdi, H. Ahmadian, A. Mirzabeigy, and A. Yildirim, “Dynamic analysis of vibrating systems with nonlinearities,” Communications in Theoretical Physics, vol. 57, pp. 183–187, 2012.
- I. Kovacic and M. J. Brennan, The Duffing Equation: Nonlinear Oscillators and Their Behaviour, John Wiley & Sons, 2011.
- A. I. Manevich and L. I. Manevitch, The Mechanics of Nonlinear Systems with Internal Resonances, Imperial College Press, 2005.
- J. C. Ji and C. H. Hansen, “On the approximate solution of a piecewise nonlinear oscillator under super-harmonic resonance,” Journal of Sound and Vibration, vol. 283, no. 1-2, pp. 467–474, 2005.
- A. M. Elnaggar and A. F. El-Basyouny, “Harmonic, subharmonic, superharmonic, simultaneous sub/super harmonic and combination resonances of self-excited two coupled second order systems to multi-frequency excitation,” Acta Mechanica Sinica, vol. 9, no. 1, pp. 61–71, 1993.
- M. Eissa and A. F. El-Bassiouny, “Analytical and numerical solutions of a non-linear ship rolling motion,” Applied Mathematics and Computation, vol. 134, no. 2-3, pp. 243–270, 2003.
- T. C. Kim, T. E. Rook, and R. Singh, “Super- and sub-harmonic response calculations for a torsional system with clearance nonlinearity using the harmonic balance method,” Journal of Sound and Vibration, vol. 281, no. 3–5, pp. 965–993, 2005.
- C. Duan and R. Singh, “Super-harmonics in a torsional system with dry friction path subject to harmonic excitation under a mean torque,” Journal of Sound and Vibration, vol. 285, no. 4-5, pp. 803–834, 2005.
- R. W. Hamming, Numerical Methods for Scientists and Engineers, Dover Publications, 1987.
- B. W. Bader, Tensor-Krylov Methods for Solving Large-scale Systems of Nonlinear Equations, University of Colorado, 2003.
- Z. C. Zheng, “On the intrinsic simple connection of linear with nonlinear system-the quantity and qualitative analysis of large scale multiple DOF nonlinear systems,” in Proceedings of the National Structure Dynamics Conference, pp. 1–13, Nanchang, China, 2008.
- M. I. Friswell, J. E. T. Penny, and S. D. Garvey, “Using linear model reduction to investigate the dynamics of structures with local non-linearities,” Mechanical Systems and Signal Processing, vol. 9, no. 3, pp. 317–328, 1995.
- R. H. B. Fey, D. H. van Campen, and A. de Kraker, “Long term structural dynamics of mechanical systems with local nonlinearities,” Journal of Vibration and Acoustics, vol. 118, no. 2, pp. 147–153, 1996.