Nonlinear normal modes, Part II: Toward a practical computation using numerical continuation techniques
暂无分享,去创建一个
Gaëtan Kerschen | Jean-Claude Golinval | Maxime Peeters | Régis Viguié | Guillaume Sérandour | G. Kerschen | J. Golinval | M. Peeters | R. Viguié | G. Serandour
[1] H. Nijmeijer,et al. Dynamics and Bifurcations ofNon - Smooth Mechanical Systems , 2006 .
[2] R. M. Rosenberg,et al. The Normal Modes of Nonlinear n-Degree-of-Freedom Systems , 1962 .
[3] Joseph C. Slater,et al. A numerical method for determining nonlinear normal modes , 1996 .
[4] Alexander F. Vakakis,et al. Normal modes and localization in nonlinear systems , 1996 .
[5] R. Rand,et al. Normal modes and global dynamics of a two-degree-of-freedom non-linear system—I. Low energies , 1992 .
[6] Eric Pesheck,et al. Reduced order modeling of nonlinear structural systems using nonlinear normal modes and invariant manifolds , 2000 .
[7] Rajendra Singh,et al. Analysis of periodically excited non-linear systems by a parametric continuation technique , 1995 .
[8] Christophe Pierre,et al. Normal Modes for Non-Linear Vibratory Systems , 1993 .
[9] Willy Govaerts,et al. Numerical Continuation of Bifurcations of Limit Cycles in MATLAB , 2005, SIAM J. Sci. Comput..
[10] Christophe Pierre,et al. Normal modes of vibration for non-linear continuous systems , 1994 .
[11] Nenad Mihajlovic,et al. Torsional and lateral vibrations in flexible rotor systems with friction , 2005 .
[12] Alexander F. Vakakis,et al. Complicated dynamics of a linear oscillator with a light, essentially nonlinear attachment , 2005 .
[13] Peter Eberhard,et al. Sensitivity analysis for dynamic mechanical systems with finite rotations , 2008 .
[14] Fengxia Wang,et al. Nonlinear normal modes in multi-mode models of an inertially coupled elastic structure , 2006 .
[15] Alexander F. Vakakis,et al. NONLINEAR NORMAL MODES , 2001 .
[16] Bruno Cochelin,et al. Two methods for the computation of nonlinear modes of vibrating systems at large amplitudes , 2006 .
[17] A. Nayfeh,et al. Applied nonlinear dynamics : analytical, computational, and experimental methods , 1995 .
[18] R. Seydel. Practical bifurcation and stability analysis : from equilibrium to chaos , 1994 .
[19] G. C. Gardner. Viscous Flow of a Liquid Over a Rotating Surface With Gas Drag , 1963 .
[20] Alexander F. Vakakis,et al. Nonlinear normal modes, Part I: An attempt to demystify them , 2008 .
[21] M. Géradin,et al. Mechanical Vibrations: Theory and Application to Structural Dynamics , 1994 .
[22] E. Allgower,et al. Introduction to Numerical Continuation Methods , 1987 .
[23] E. J. Doedel,et al. Computation of Periodic Solutions of Conservative Systems with Application to the 3-body Problem , 2003, Int. J. Bifurc. Chaos.
[24] Alexander F. Vakakis,et al. Nonlinear normal modes, Part I: A useful framework for the structural dynamicist , 2009 .
[25] Marco Amabili,et al. Nonlinear normal modes for damped geometrically nonlinear systems: Application to reduced-order modelling of harmonically forced structures , 2006 .
[26] Oleg Gendelman,et al. Energy Pumping in Nonlinear Mechanical Oscillators: Part II—Resonance Capture , 2001 .
[27] R. Seydel. From Equilibrium to Chaos: Practical Bifurcation and Stability Analysis , 1988 .
[28] Leon O. Chua,et al. Practical Numerical Algorithms for Chaotic Systems , 1989 .
[29] Pedro Ribeiro,et al. Non-linear forced vibrations of thin/thick beams and plates by the finite element and shooting methods , 2004 .
[30] Emilio Freire,et al. Continuation of periodic orbits in conservative and Hamiltonian systems , 2003 .
[31] R. Seydel. Practical Bifurcation and Stability Analysis , 1994 .
[32] Laurette S. Tuckerman,et al. Numerical methods for bifurcation problems , 2004 .
[33] Fabrice Thouverez,et al. Presentation of the ECL Benchmark , 2003 .
[34] Alexander F. Vakakis,et al. Irreversible Passive Energy Transfer in Coupled Oscillators with Essential Nonlinearity , 2005, SIAM J. Appl. Math..
[35] P. Sundararajan,et al. An algorithm for response and stability of large order non-linear systems : Application to rotor systems , 1998 .
[36] R. M. Rosenberg,et al. On Nonlinear Vibrations of Systems with Many Degrees of Freedom , 1966 .
[37] Marco Amabili,et al. Reduced-order models for large-amplitude vibrations of shells including in-plane inertia , 2008 .
[38] Christophe Pierre,et al. Non-linear normal modes and invariant manifolds , 1991 .
[39] A. M. Lyapunov. The general problem of the stability of motion , 1992 .
[40] A. Nayfeh,et al. Applied nonlinear dynamics : analytical, computational, and experimental methods , 1995 .
[41] R. M. Rosenberg,et al. Normal Modes of Nonlinear Dual-Mode Systems , 1960 .
[42] Romesh Saigal. Numerical Continuation Methods, An Introduction (Eugene Allgower and Kurt Georg) , 1991, SIAM Rev..
[43] R. Seydel. From equilibrium to chaos , 1988 .
[44] Oleg Gendelman,et al. Energy pumping in nonlinear mechanical oscillators : Part I : Dynamics of the underlying Hamiltonian systems , 2001 .