Coupled-Nonlinear Elastic Structure: An Innovative Parameterization Scheme of the Motion Equations
Abstract: In this paper, I applied the Euler-Lagrange equations in order to obtain the coupled-nonlinear motion equations for an elastic structure. The model is composed of six coupled and strongly nonlinear ordinary differential equations. The new contribution of this work arises from the fact that a convenient and innovative parameterization of the motion equations for the elastic system was developed with all mathematical nonlinearities taken into account, without the usage of any simplifying linearization procedure, as found in most of the works presented in the literature. The results can be used as a source for conducting experiments and can be useful for a better understanding and control of such nonlinear elastic systems.
Cite this paper: David, S. (2014) Coupled-Nonlinear Elastic Structure: An Innovative Parameterization Scheme of the Motion Equations. Applied Mathematics, 5, 3460-3473. doi: 10.4236/am.2014.521324.
References

[1]   Goldstein, H. (1981) Classical Mechanics. 2nd Edition, Addison Wesley Publishing Company, Reading.

[2]   Nayfeh, A. and Mook, D.T. (1979) Nonlinear Oscillations. Wiley & Sons, New York.

[3]   Andrianov, I.V. and Weichert, D. (2009) Modeling, Simulation and Control of Nonlinear Engineering Dynamical Systems: State-of-the-Art, Perspectives and Applications. Springer, Berlin.

[4]   Balthazar, J.M. and Fenili, A. (2009) Some Remarks on Nonlinear Vibrations of Ideal and Nonideal Slewing Flexible Structures. Journal of Sound and Vibration, 282, 543-552.

[5]   Batra, R.C. (2006) Elements of Continuum Mechanics. AIAA Education Series, USA.

[6]   Hagedorn, P. (1984) Oscilações Não Lineares. Editora Edgard Blucher LTDA, São Paulo. (In Portuguese)

[7]   Nayfeh, A.H. and Pai, P.F. (2004) Linear and Nonlinear Structural Mechanics. John Wiley & Sons, Inc., New York.
http://dx.doi.org/10.1002/9783527617562

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