A harmonic balance approach for designing compliant mechanical systems with nonlinear periodic motions

Several numerical approaches have been developed to capture nonlinear effects of dynamical systems. In this paper we present a mixed shooting-harmonic balance method to solve large mechanical systems with local nonlinearities efficiently. The Harmonic Balance Method as well as the shooting method have both their pros and cons. The proposed mixed shooting-HBM approach combines the efficiency of HBM and the accuracy of the shooting method and has therefore advantages of both.

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The Harmonic Balance Method for Bifurcation Analysis of Nonlinear Mechanical Systems

Nonlinear Dynamics, Volume 1 - Conference Proceedings of the Society for Experimental Mechanics Series ◽

10.1007/978-3-319-15221-9_5 ◽

2016 ◽

pp. 65-82

Author(s):

T. Detroux ◽

L. Renson ◽

L. Masset ◽

G. Kerschen

Keyword(s):

Bifurcation Analysis ◽

Harmonic Balance ◽

Mechanical Systems ◽

Harmonic Balance Method ◽

Balance Method ◽

Nonlinear Mechanical ◽

Nonlinear Mechanical Systems

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Bifurcations of limit cycles in periodically forced nonlinear systems: the harmonic balance approach

IEEE Transactions on Circuits and Systems I Fundamental Theory and Applications ◽

10.1109/81.285687 ◽

1994 ◽

Vol 41 (4) ◽

pp. 315-320 ◽

Cited By ~ 39

Author(s):

C. Piccardi

Keyword(s):

Nonlinear Systems ◽

Limit Cycles ◽

Harmonic Balance ◽

Balance Approach

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Time delay effects on oscillation profiles in cyclic gene regulatory networks: Harmonic balance approach

Proceedings of the 2011 American Control Conference ◽

10.1109/acc.2011.5990877 ◽

2011 ◽

Cited By ~ 5

Author(s):

Yutaka Hori ◽

Shinji Hara

Keyword(s):

Time Delay ◽

Gene Regulatory Networks ◽

Harmonic Balance ◽

Regulatory Networks ◽

Balance Approach ◽

Delay Effects ◽

Cyclic Gene ◽

Gene Regulatory

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Harmonic Balance Approach for an Airfoil with a Freeplay Control Surface

AIAA Journal ◽

10.2514/1.10973 ◽

2005 ◽

Vol 43 (4) ◽

pp. 802-815 ◽

Cited By ~ 72

Author(s):

Liping Liu ◽

Earl H. Dowell

Keyword(s):

Harmonic Balance ◽

Control Surface ◽

Balance Approach

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Signal space - an implementation of the harmonic balance approach for microwave nonlinear network analysis

10.1109/euma.1996.337638 ◽

1996 ◽

Cited By ~ 2

Author(s):

Dan Elad ◽

Asher Madjar

Keyword(s):

Network Analysis ◽

Harmonic Balance ◽

Signal Space ◽

Nonlinear Network ◽

Balance Approach

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Analytical Periodic Motions in a Periodically Forced, Damped Duffing Oscillator

Volume 4: Dynamics, Control and Uncertainty, Parts A and B ◽

10.1115/imece2012-86077 ◽

2012 ◽

Author(s):

Albert C. J. Luo ◽

Jianzhe Huang

Keyword(s):

Numerical Simulations ◽

Analytical Solutions ◽

Harmonic Balance ◽

Duffing Oscillator ◽

Harmonic Balance Method ◽

Approximate Solutions ◽

Balance Method ◽

Periodic Motions ◽

Conditions Of Stability ◽

Generalized Harmonic Balance Method

The analytical solutions of the period-1 motions for a hardening Duffing oscillator are presented through the generalized harmonic balance method. The conditions of stability and bifurcation of the approximate solutions in the oscillator are discussed. Numerical simulations for period-1 motions for the damped Duffing oscillator are carried out.

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