A numerical technique to predict periodic and quasi-periodic response of nonlinear dynamic systems

Computers and Structures

Volumn 81, Issue 13, 2003, Pages 1383-1393

  Sarkar, Sunetra ^a   Venkatraman, Kartik ^a  

^a INDIAN INSTITUTE OF SCIENCE   (India)

Author keywords

Bifurcations; Floquet analysis; Fourier Galerkin Newton technique

Indexed keywords

ALGORITHMS; APPROXIMATION THEORY; BIFURCATION (MATHEMATICS); ERROR ANALYSIS; FREQUENCY DOMAIN ANALYSIS; GALERKIN METHODS; INTEGRATION;

FLOQUET ANALYSIS;

NONLINEAR SYSTEMS;

EID: 0037401787     PISSN: 00457949     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0045-7949(03)00012-9     Document Type: Article

References (17)

1. Minorsky N. Nonlinear Oscillations. 1962;D. van Nostrand Company, Inc, Princeton, NJ.
2. Nayfeh A., Mook D. Nonlinear Oscillations. 1979;John Wiley and Sons, New York.
3. Gelb A., Vander Velde W. Multiple-Input Describing Functions and Nonlinear Systems Design. 1968;McGraw-Hill Book Co, New York.
4. Cesari L. Functional analysis and periodic solutions of nonlinear differential equations. Contribut. Differen. Eqs. 1:1963;149-187.
5. Urabe M. Galerkin's procedure for nonlinear periodic systems. Arch. Rational Mech. Anal. 20:1965;120-152.
6. Urabe M., Reiter A. Numerical computations of nonlinear forced oscillations by Galerkin's procedure. J. Math. Anal. Appl. 14:1966;107-140.
7. Lau S., Cheung Y., Wu S. A variable parameter incrementation method for dynamic instability of linear and nonlinear elastic systems. Trans. ASME, J. Appl. Mech. 49:1982;849-853.
8. Lau S., Cheung Y., Wu S. Incremental harmonic balance method with multiple time scales for aperiodic vibration of nonlinear systems. Trans. ASME, J. Appl. Mech. 50:1983;871-876.
9. Ling F., Wu X. Fast Galerkin method and its application to determine periodic solutions of non-linear oscillators. Int. J. Numer. Meth. Eng. 22(2):1987;89-98.
10. Narayanan S., Sekar P. A frequency domain based numeric-analytic method for nonlinear dynamical systems. J. Sound Vib. 211(3):1998;409-424.
11. Narayanan S., Sekar P. Bifurcation and chaos of coupled system by fast incremental harmonic balancing. Thompson J., Bishop S. IUTAM Symposium on Nonlinearity and Chaos in Engineering Dynamics. 1994;365-375 John Wiley and Sons, New York.
12. Cardona A., Coune T., Lerusse A., Geradin M. A multi-harmonic method for nonlinear vibration analysis. Int. J. Numer. Meth. Eng. 37:1994;1593-1608.
13. Ferri A. On the equivalence of the incremental harmonic balance method and the harmonic balance-Newton-Raphson method. Trans. ASME, J. Appl. Mech. 53:1986;455-457.
14. Iooss G., Joseph D. Elementary Stability and Bifurcation Theory. 1980;Springer-Verlag, New York.
15. Sarkar S. Dynamics of flexible structures with nonlinear joints, Master's thesis, Department of Aerospace Engineering, Indian Institute of Science, Bangalore, India, 1999.
16. Friedmann P., Hammond C., Woo T.-H. Efficient numerical treatment of periodic systems with application to stability problems. Int. J. Numer. Meth. Eng. 11:1977;1117-1136.
17. Thompson J., Stewart H. Nonlinear Dynamics and Chaos. 1986;John Wiley and Sons, New York.