Comparison of different harmonic balance based methodologies for computation of nonlinear modes of non-conservative mechanical systems

2019 ◽  
Vol 127 ◽  
pp. 159-171 ◽  
Author(s):  
Martin Jahn ◽  
Sebastian Tatzko ◽  
Lars Panning-von Scheidt ◽  
Jörg Wallaschek
Keyword(s):  
Harmonic Balance ◽  
Mechanical Systems ◽  
Nonlinear Modes

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.

scholarly journals A review on nonlinear modes in conservative mechanical systems

2020 ◽  
Vol 50 ◽  
pp. 49-71
Author(s):  
Alin Albu-Schäffer ◽  
Cosimo Della Santina
Keyword(s):  
Mechanical Systems ◽  
Nonlinear Modes

scholarly journals Nonlinear Modal Analysis of Mechanical Systems With Frictionless Contact Interfaces

2009 ◽  
Author(s):  
Denis Laxalde ◽  
Mathias Legrand ◽  
Christophe Pierre
Keyword(s):  
Large Scale ◽  
Augmented Lagrangian ◽  
Mechanical Systems ◽  
Inequality Constraints ◽  
Rayleigh Quotient ◽  
Contact Forces ◽  
Nonlinear Modes ◽  
Frictionless Contact ◽  
Nonlinear Contact ◽  
Nonlinear Modal Analysis

This paper investigates the nonlinear analysis, in the form of nonlinear modes, of mechanical systems undergoing unilateral frictionless contact. The nonlinear eigenproblem is introduced by a Rayleigh quotient minimization with inequality constraints formulated in the frequency domain. An augmented Lagrangian procedure is used for the calculation of the nonlinear contact forces. The efficiency of the proposed method for large-scale mechanical systems involving non-smooth nonlinear terms is shown. An industrial application consisting of a compressor blade in contact with a rigid casing is proposed. Sensitivity of the nonlinear modal parameters to contact is illustrated.

scholarly journals On the computation of the slow dynamics of nonlinear modes of mechanical systems

2014 ◽  
Vol 42 (1-2) ◽  
pp. 71-87 ◽  
Author(s):  
Malte Krack ◽  
Lars Panning-von Scheidt ◽  
Jörg Wallaschek
Keyword(s):  
Mechanical Systems ◽  
Slow Dynamics ◽  
Nonlinear Modes
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