Solutions of a Dynamics Nonlinear In-Plane Vibration of Suspended Cable Investigated by the Mixed Averaging Method

Article Preview

Abstract:

In this paper, the continuation technique is used to investigate the non-linear response of a suspended cable under harmonic excitation. A modified iteration procedure is applied to the nonlinear oscillator containing a quadratic term. From the formulated mathematical model of the suspended cable, the solution for the cable is obtained by means of the mixed averaging method. Also we can give the frequency simple with the modified iteration procedure. Moreover, the results obtained by this method and the numerical integration are compared. Also the offset is studied. Finally, the effects of the amplitude of the harmonic excitation on the suspended cable and the stability of the system are investigated.

You might also be interested in these eBooks

Info:

Periodical:

Pages:

869-882

Citation:

Online since:

January 2013

Export:

Price:

Permissions CCC:

Permissions PLS:

Сopyright:

© 2013 Trans Tech Publications Ltd. All Rights Reserved

Share:

Citation:

[1] Benedettini F, Rega G. Planar non-linear oscillations of elastic cables under planar excitation. International Journal of Non-linear Mechanics 1987; 22: 497–509.

DOI: 10.1016/0020-7462(87)90039-4

Google Scholar

[2] Irvine HM. Cable Structures, The MIT Press, Cambridge, MA: (1981).

Google Scholar

[3] Wang LH, Zhao YY. Nonlinear interactions and chaotic dynamics of suspended cables with th- ree-to-one internal resonances. Int J Solids Struct 2006; 43: 7800-7819.

DOI: 10.1016/j.ijsolstr.2006.04.006

Google Scholar

[4] Zhao YY, Wang LH. On the symmetric modal interaction of the suspended cable: Three-to-one internal resonance. J Sound and Vib 2006; 294: 1073-1093.

DOI: 10.1016/j.jsv.2006.01.004

Google Scholar

[5] Wang LH, Zhao YY. Multiple internal resonances and non-planar dynamics of shallow suspen- ded cables to the harmonic excitation. J Sound and Vib 2009; 319: 1-14.

DOI: 10.1016/j.jsv.2008.08.020

Google Scholar

[6] Wagg, David/ Neild, Simon. Nonlinear Vibration with Control. Springer Verlag, MA: (2010).

Google Scholar

[7] R.E. Mickens, Quadratic non-linear oscillators, Journal of Sound and Vibration 270 (2004) 427–432.

DOI: 10.1016/s0022-460x(03)00481-4

Google Scholar

[8] H. Hu, J.H. Tang. A classical iteration procedure valid for certain strongly nonlinear oscillators. re valid for certain strongly nonlinear oscillators. Journal Sound Vibration, 2007, 299: 397–402.

DOI: 10.1016/j.jsv.2006.07.017

Google Scholar

[9] S.J. Liao. Beyond Perturbation: Introduction to the Homotopy Analysis Method. CRC Press, Boca Raton, Chapman and Hall, (2003).

Google Scholar

[10] Zhao YY, Wang LH, Liu WC, Zhou HB. Direct treatment and discretizations of non-linear d- ynamics of suspended cables. Acta Mechanica Sinica 2005; 37: 329–38 [in Chinese].

Google Scholar

[11] Mickens, R.E. Iteration method solutions for conservative and limit-cycle x1/3 force oscilla- tors. Journal of Sound and Vibration. 2006, 292: 964–968.

DOI: 10.1016/j.jsv.2005.08.020

Google Scholar

[12] Rega G, Benedettini F. Planar non-linear oscillations of elastic cables under subharmonic ex- citation. Journal of Sound and Vibration 1989; 132: 367–81.

DOI: 10.1016/0022-460x(89)90631-7

Google Scholar

[13] Benedettini F, Rega G. Planar non-linear oscillations of elastic cablesunder superharmonic ex- citation. Journal of Sound and Vibration 1989; 132: 353–66.

DOI: 10.1016/0022-460x(89)90630-5

Google Scholar

[14] Zhao Y, Wang L. On the symmetrical modal interaction of the suspendedcable: Three-to-one internal resonance. Journal of Sound and Vibration2006; 294: 1073–93.

Google Scholar

[15] Srinil N, Rega G, Chucheepsaul S. Large amplitude three-dimensionalfree vibration of inclined sagged elastic cable. Nonlinear Dynamics 2003; 33: 129–46.

Google Scholar

[16] H. Hu. A classical perturbation technique that works even when the linear part of restoring for- ce is zero. Journal of Sound and Vibration, 2004, 269: 409–412.

DOI: 10.1016/s0022-460x(03)00653-9

Google Scholar

[17] R.E. Mickens. Comments on the method of harmonic-balance. Journal of Sound and Vibration, 1984 94 : 456–460.

DOI: 10.1016/s0022-460x(84)80025-5

Google Scholar

[18] Beléndez A, Hernández A, Beléndez T, Álvarez M L, Gallego S, Ortuño M, Neipp C. Application of the harmonic balance method to a nonlinear oscillator typified by a mass attached to a stretched wire. Journal of Sound and Vibration 2007, 302: 1018–1029.

DOI: 10.1016/j.jsv.2006.12.011

Google Scholar

[19] Mickens R E. Harmonic balance and iteration calculations of periodic solutions to. Journal of Sound and Vibration 2007, 306: 968–972.

DOI: 10.1016/j.jsv.2007.06.010

Google Scholar

[20] El-Attar M, Ghobarah A, Aziz TS. Non-linear cable response to multiplesupport periodic excitation. Engineering Structures 2000; 22: 1301–12.

DOI: 10.1016/s0141-0296(99)00065-6

Google Scholar

[21] H. Hu. Solutions of a quadratic nonlinear oscillator: Iteration procedure. Journal of Sound and Vibration 2006; 298: 1159–1165.

DOI: 10.1016/j.jsv.2006.06.005

Google Scholar