A combined FD-HB approximation method for steady-state vibrations in large dynamical systems with localised nonlinearities

The approximation of steady-state vibrations within non-linear dynamical systems is well-established in academics and is becoming increasingly important in industry. However, the complexity and the number of degrees of freedom of application-oriented industrial models demand efficient approximation...

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Bibliographic Details
Published in:Computational mechanics 2022-12, Vol.70 (6), p.1241-1256
Main Authors: Kappauf, Jonas, Bäuerle, Simon, Hetzler, Hartmut
Format: Article
Language:English
Subjects:
Approximation
Classical and Continuum Physics
Computational Science and Engineering
Degrees of freedom
Dynamical systems
Engineering
Finite difference method
Harmonic balance method
Nonlinear systems
Nonlinearity
Original Paper
Steady state
Theoretical and Applied Mechanics
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Summary:The approximation of steady-state vibrations within non-linear dynamical systems is well-established in academics and is becoming increasingly important in industry. However, the complexity and the number of degrees of freedom of application-oriented industrial models demand efficient approximation methods for steady-state solutions. One possible approach to that problem are hybrid approximation schemes, which combine advantages of standard methods from the literature. The common ground of these methods is their description of the steady-state dynamics of a system solely based on the degrees of freedom affected directly by non-linearity—the so-called non-linear degrees of freedom. This contribution proposes a new hybrid method for approximating periodic solutions of systems with localised non-linearities. The motion of the non-linear degrees of freedom is approximated using the Finite Difference  method, whilst the motion of the linear degrees of freedom is treated with the Harmonic Balance  method. An application to a chain of oscillators showing stick-slip oscillations is used to demonstrate the performance of the proposed hybrid framework. A comparison with both pure Finite Difference  and Harmonic Balance  method reveals a noticeable increase in efficiency for larger systems, whilst keeping an excellent approximation quality for the strongly non-linear solution parts.
ISSN:0178-7675
1432-0924
DOI:10.1007/s00466-022-02225-3