[1] R. M. Rosenberg, On nonlinear vibrations of systems with many degrees of freedom,Advances in Applied Mechanics, 9 (1966), 155-242. [2] R. H. Rand, Nonlinear normal modes in two degree of freedom systems, Journal ofApplied Mechanics, 38, 2 (1971), 561. [3] S. W. Shaw and C. Pierre, Normal modes for nonlinear vibratory systems, Journal of Sound and Vabration, 164, 1 (1993), 85-124. [4] S. W. Shaw and C. Pierre, Normal modes of vibration for nonlinear continuous systems,Journal of Sound and Vibration, 169, 3 (1994), 319-347. [5] L. Jezequel and C. H. Lamarque, Analysis of nonlinear dynamical systems by the normalform theory, Journal of Sound and Vibration, 149, 3 (1991), 429-459. [6] Liu Liansheng, Huo Quanzhong and Huang Kelei, A method of finding the principlemodes of nonlinear vibration systems and their stabilites, Applied Mathematics andMechanics (English Ed.), 8, 6 (1987), 523-532. [7] Liu Dongshen and Huang Kelei, A method of modal analysis using nonlinear vibrationsystems, Acta Mechanca Sinica, 20, 1 (1988), (in Chinese). [8] Chen Yushu, The Modern Methods in Non-Linear Dynamics, Science Press (1992). (inChinese). [9] J. Cars, Applications of Centre Manifold Theory, Springer-Verlag New York (1981). [10] Al Kelley, On the Lyapunov subcentre manifold, Journal of Mathematical Analysis andApplications, 18, 3 (1967), 472-478. [11] M. Hirsch and S. Smale, Differential Equations, Dynamical Systems and Linear Algebra,Academic Press, New York (1974). [12] V. I. Arnold, Geometrical Method in foe Theory of Ordinary Differential Equations,Springer-Verlag, New York (1988). [13] J. Guckenheimer and P. Holmes, Nonlinear Oscillations, Dynamical Systems andBifurcations of Vector Fields, Springer-Verlag, New York (1986). |