scholarly journals Nonlinear dynamics of mechanical systems with friction contacts: Coupled static and dynamic Multi-Harmonic Balance Method and multiple solutions

2014 ◽  
Vol 333 (3) ◽  
pp. 916-926 ◽  
Author(s):  
Stefano Zucca ◽  
Christian Maria Firrone
Keyword(s):  
Nonlinear Dynamics ◽  
Harmonic Balance ◽  
Multiple Solutions ◽  
Mechanical Systems ◽  
Harmonic Balance Method ◽  
Balance Method

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.

Study on Nonlinear Dynamics of Planetary Reducer

2013 ◽  
Vol 756-759 ◽  
pp. 4616-4620
Author(s):  
Xue Feng Han ◽  
Yang Bai ◽  
Ming Li ◽  
Hong Guang Jia
Keyword(s):  
Nonlinear Dynamics ◽  
Harmonic Balance ◽  
Optimization Design ◽  
Harmonic Balance Method ◽  
Balance Method ◽  
Lumped Mass ◽  
Lumped Mass Method ◽  
Nonlinear Dynamics Model ◽  
Response Variation ◽  
Motor Drive System

Based on nonlinear vibration theory and synthesizing harmonic balance method, numerical analysis method and reducer vibration test, the paper studies the characteristics of traditional systematic nonlinear dynamics. Based on harmonic balance method, the paper deduces the frequency response equation in the range of the whole frequency and studies magnitude-frequency characteristic. The accuracy of the model is verified by comparing with traditional model. Lumped mass method is used to construct nonlinear dynamics model of 2K-H planetary reducer drive mechanism in new hybrid cars double motor drive system. And the paper makes detailed and deeper analysis on response variation rules of the system and meshing stock state of gear pair with different parameters. Through the analysis of the relevant parameters, the planetary reducer is to have a more profound understanding, laid the foundation for future optimization design.

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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