Bifurcation tracking by Harmonic Balance Method for performance tuning of nonlinear dynamical systems

[1]  G. G. Stokes.  "J." , 1890, The New Yale Book of Quotations.

[2]  C. D. Boor,et al.  Collocation at Gaussian Points , 1973 .

[3]  R. Seydel.  Numerical computation of branch points in ordinary differential equations , 1979 .

[4]  R. Seydel.  Numerical computation of branch points in nonlinear equations , 1979 .

[5]  G. Moore,et al.  The Calculation of Turning Points of Nonlinear Equations , 1980 .

[6]  M. Crisfield.  A FAST INCREMENTAL/ITERATIVE SOLUTION PROCEDURE THAT HANDLES "SNAP-THROUGH" , 1981 .

[7]  P. Holmes,et al.  Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields , 1983, Applied Mathematical Sciences.

[8]  Andreas Griewank,et al.  The Calculation of Hopf Points by a Direct Method , 1983 .

[9]  A. Griewank,et al.  Characterization and Computation of Generalized Turning Points , 1984 .

[10]  Dirk Roose,et al.  An algorithm for the computation of Hopf bifurcation points in comparison with other methods , 1985 .

[11]  Allan D. Jepson,et al.  Folds in Solutions of Two Parameter Systems and Their Calculation. Part I , 1985 .

[12]  Dirk Roose,et al.  A Direct Method for the Computation of Hopf Bifurcation Points , 1985 .

[13]  C. Felippa.  Traversing Critical Points with Penalty Springs , 1987 .

[14]  Willy Govaerts,et al.  Numerical methods for bifurcations of dynamical equilibria , 1987 .

[15]  Peter Wriggers,et al.  A general procedure for the direct computation of turning and bifurcation points , 1990 .

[16]  R. Seydel.  Practical Bifurcation and Stability Analysis , 1994 .

[17]  S. Strogatz.  Nonlinear Dynamics and Chaos: With Applications to Physics, Biology, Chemistry and Engineering , 1995 .

[18]  Bodo Werner,et al.  Computation of Hopf bifurcation with bordered matrices , 1996 .

[19]  J. A. Kuznecov.  Elements of applied bifurcation theory , 1998 .

[20]  S. Narayanan,et al.  A FREQUENCY DOMAIN BASED NUMERIC–ANALYTICAL METHOD FOR NON-LINEAR DYNAMICAL SYSTEMS , 1998 .

[21]  Anders Eriksson,et al.  Numerical analysis of complex instability behaviour using incremental-iterative strategies , 1999 .

[22]  Alberto Cardona,et al.  Evaluation of simple bifurcation points and post-critical path in large finite rotation problems , 1999 .

[23]  D. Ewins,et al.  The Harmonic Balance Method with arc-length continuation in rotor/stator contact problems , 2001 .

[24]  B. Kendall.  Nonlinear Dynamics and Chaos , 2001 .

[25]  S. Lopez.  Post-critical analysis of structures with a nonlinear pre-buckling state in the presence of imperfections , 2002 .

[26]  Sébastien Baguet,et al.  Stability of thin-shell structures and imperfection sensitivity analysis with the Asymptotic Numerical Method , 2002 .

[27]  Jean-Marc Battini,et al.  Improved minimal augmentation procedure for the direct computation of critical points , 2003 .

[28]  F. Thouverez,et al.  A dynamic Lagrangian frequency–time method for the vibration of dry-friction-damped systems , 2003 .

[29]  Ke Chen,et al.  On Efficient Methods for Detecting Hopf bifurcation with Applications to Power System Instability Prediction , 2003, Int. J. Bifurc. Chaos.

[30]  Willy Govaerts,et al.  MATCONT: A MATLAB package for numerical bifurcation analysis of ODEs , 2003, TOMS.

[31]  Gerald Moore,et al.  Floquet Theory as a Computational Tool , 2004, SIAM J. Numer. Anal..

[32]  Louis A. Romero,et al.  Bifurcation Tracking Algorithms and Software for Large Scale Applications , 2005, Int. J. Bifurc. Chaos.

[33]  Frank Schilder,et al.  Fourier methods for quasi‐periodic oscillations , 2006, International Journal for Numerical Methods in Engineering.

[34]  Claude-Henri Lamarque,et al.  Quasiperiodic energy pumping in coupled oscillators under periodic forcing , 2006 .

[35]  Oleg Gendelman,et al.  Attractors of harmonically forced linear oscillator with attached nonlinear energy sink. II: Optimization of a nonlinear vibration absorber , 2007 .

[36]  Oleg Gendelman,et al.  Quasi-periodic response regimes of linear oscillator coupled to nonlinear energy sink under periodic forcing , 2007 .

[37]  Mikhail Guskov,et al.  Multi-Dimensional Harmonic Balance Applied to Rotor Dynamics , 2008 .

[38]  F. H. Ling,et al.  An Alternating Frequency/Time Domain Method for Calculating the Steady-State Response of Nonlinear Dynamic Systems , 2007 .

[39]  G. Kerschen,et al.  Nonlinear Targeted Energy Transfer in Mechanical and Structural Systems , 2008 .

[40]  Christophe Vergez,et al.  A high-order, purely frequency based harmonic balance formulation for continuation of periodic solutions: The case of non-polynomial nonlinearities , 2008, 0808.3839.

[41]  Jun Jiang,et al.  Determination of the global responses characteristics of a piecewise smooth dynamical system with contact , 2009 .

[42]  J. Sinou,et al.  An adaptive harmonic balance method for predicting the nonlinear dynamic responses of mechanical systems—Application to bolted structures , 2010 .

[43]  Jean-Marc Cadou,et al.  A numerical algorithm coupling a bifurcating indicator and a direct method for the computation of Hopf bifurcation points in fluid mechanics , 2010 .

[44]  Fabrice Thouverez,et al.  On a new harmonic selection technique for harmonic balance method , 2012 .

[45]  Sébastien Baguet,et al.  A comparison of stability computational methods for periodic solution of nonlinear problems with application to rotordynamics , 2013 .

[46]  Gaëtan Kerschen.  Computation of Nonlinear Normal Modes through Shooting and Pseudo-Arclength Computation , 2014 .

[47]  Sébastien Baguet,et al.  Quasi-periodic harmonic balance method for rubbing self-induced vibrations in rotor–stator dynamics , 2014 .

[48]  Behrang Moghaddasie,et al.  Stability boundaries of two-parameter non-linear elastic structures , 2014 .

[49]  Fabrice Thouverez,et al.  A variable-coefficient harmonic balance method for the prediction of quasi-periodic response in nonlinear systems , 2015 .

[50]  Evgeny Petrov,et al.  Analysis of Bifurcations in Multiharmonic Analysis of Nonlinear Forced Vibrations of Gas Turbine Engine Structures With Friction and Gaps , 2015 .

[51]  Luc Masset,et al.  The harmonic balance method for bifurcation analysis of large-scale nonlinear mechanical systems , 2015, 1604.05621.

[52]  L. Xie,et al.  Numerical Tracking of Limit Points for Direct Parametric Analysis in Nonlinear Rotordynamics , 2016 .

[53]  Remco I. Leine,et al.  A Mixed Shooting – Harmonic Balance Method for Unilaterally Constrained Mechanical Systems , 2016 .

[54]  Jörg Wallaschek,et al.  A High-Order Harmonic Balance Method for Systems With Distinct States , 2013, ArXiv.

[55]  N. S.  A FREQUENCY DOMAIN BASED NUMERIC–ANALYTICAL METHOD FOR NON-LINEAR DYNAMICAL SYSTEMS , 2022 .