scholarly journals The Harmonic Balance Method for Bifurcation Analysis of Nonlinear Mechanical Systems

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

Finding Periodic Solutions of Forced Systems With Local Nonlinearities: A Mixed Shooting Harmonic Balance Method

2015 ◽  
Author(s):  
Frederic Schreyer ◽  
Remco Leine
Keyword(s):  
Dynamical Systems ◽  
Periodic Solutions ◽  
Harmonic Balance ◽  
Shooting Method ◽  
Mechanical Systems ◽  
Harmonic Balance Method ◽  
Nonlinear Effects ◽  
Balance Method ◽  
Pros And Cons ◽  
Numerical Approaches

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.

A Reduction Method for Stability and Dynamic Response Analysis of Nonlinear Mechanical Systems

1993 ◽  
Author(s):  
An-Nan Jean ◽  
Ting-Nung Shiau
Keyword(s):  
Steady State ◽  
Transient Response ◽  
Reduction Method ◽  
Mechanical Systems ◽  
Harmonic Balance Method ◽  
Response Analysis ◽  
Periodic Response ◽  
Nonlinear Mechanical ◽  
The Stability ◽  
Nonlinear Mechanical Systems

The stability, transient response, and steady state response of nonlinear mechanical systems is studied using reduction method. The steady state periodic response is investigated using the harmonic balance method. An implicit integration method for predicting transient response is proposed. The stability of the steady state periodic response is studied using Floquet theory. A reduction is introduced to analyze the system dynamic behaviors in modal coordinates to reduce the working space. The method reduces the system degrees of freedom to only those coordinates related to the system nonlinear components. The merit of the method is demonstrated by an example of flexible rotor system with nonlinear bearing supports.

scholarly journals A Mixed Shooting – Harmonic Balance Method for Unilaterally Constrained Mechanical Systems

2016 ◽  
Vol 63 (2) ◽  
pp. 297-314 ◽  
Author(s):  
Frederic Schreyer ◽  
Remco I. Leine
Keyword(s):  
Frequency Domain ◽  
Time Domain ◽  
Harmonic Balance ◽  
Degrees Of Freedom ◽  
Shooting Method ◽  
Mechanical Systems ◽  
Harmonic Balance Method ◽  
Balance Method ◽  
Constrained Mechanical Systems ◽  
Nonlinear Force

Abstract In this paper we present a mixed shooting – harmonic balance method for large linear mechanical systems on which local nonlinearities are imposed. The standard harmonic balance method (HBM), which approximates the periodic solution in frequency domain, is very popular as it is well suited for large systems with many degrees of freedom. However, it suffers from the fact that local nonlinearities cannot be evaluated directly in the frequency domain. The standard HBM performs an inverse Fourier transform, then calculates the nonlinear force in time domain and subsequently the Fourier coefficients of the nonlinear force. The disadvantage of the HBM is that strong nonlinearities are poorly represented by a truncated Fourier series. In contrast, the shooting method operates in time-domain and relies on numerical time-simulation. Set-valued force laws such as dry friction or other strong nonlinearities can be dealt with if an appropriate numerical integrator is available. The shooting method, however, becomes infeasible if the system has many states. The proposed mixed shooting-HBM approach combines the best of both worlds.

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