TY - GEN
T1 - The harmonic balance method for bifurcation analysis of nonlinear mechanical systems
AU - Detroux, T.
AU - Renson, L.
AU - Masset, L.
AU - Kerschen, G.
PY - 2016
Y1 - 2016
N2 - Because nowadays structural engineers are willing to use or at least understand nonlinearities instead of simply avoiding them, there is a need for numerical tools performing analysis of nonlinear large-scale structures. Among these techniques, the harmonic balance (HB) method is certainly one of the most commonly used to study finite element models with reasonably complex nonlinearities. However, in its classical formulation the HB method is limited to the approximation of periodic solutions. For this reason, the present paper proposes to extend the method to the detection and tracking of codimension-1 bifurcations in the system parameters space. As an application, the frequency response of a spacecraft is studied, together with two nonlinear phenomena, namely quasiperiodic oscillations and detached resonance curves. This example illustrates how bifurcation tracking using the HB method can be employed as a promising design tool for detecting and eliminating such undesired behaviors.
AB - Because nowadays structural engineers are willing to use or at least understand nonlinearities instead of simply avoiding them, there is a need for numerical tools performing analysis of nonlinear large-scale structures. Among these techniques, the harmonic balance (HB) method is certainly one of the most commonly used to study finite element models with reasonably complex nonlinearities. However, in its classical formulation the HB method is limited to the approximation of periodic solutions. For this reason, the present paper proposes to extend the method to the detection and tracking of codimension-1 bifurcations in the system parameters space. As an application, the frequency response of a spacecraft is studied, together with two nonlinear phenomena, namely quasiperiodic oscillations and detached resonance curves. This example illustrates how bifurcation tracking using the HB method can be employed as a promising design tool for detecting and eliminating such undesired behaviors.
KW - Bifurcation tracking
KW - Continuation of periodic solutions
KW - Detached resonance curves
KW - Harmonic balance method
KW - Quasiperiodic oscillations
UR - https://www.scopus.com/pages/publications/84967145634
U2 - 10.1007/978-3-319-15221-9_5
DO - 10.1007/978-3-319-15221-9_5
M3 - Conference Contribution (Conference Proceeding)
AN - SCOPUS:84967145634
SN - 9783319152202
VL - 1
T3 - Conference Proceedings of the Society for Experimental Mechanics Series
SP - 65
EP - 82
BT - Dynamic Behavior of Materials
A2 - Kerschen, Gaëtan
PB - Springer, New York, NY
T2 - 33rd IMAC Conference and Exposition on Structural Dynamics, 2015
Y2 - 2 February 2015 through 5 February 2015
ER -