A Mixed Shooting – Harmonic Balance Method for Unilaterally Constrained Mechanical Systems
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...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Polish Academy of Sciences
2016-06-01
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| Series: | Archive of Mechanical Engineering |
| Subjects: | |
| Online Access: | http://www.degruyter.com/view/j/meceng.2016.63.issue-2/meceng-2016-0017/meceng-2016-0017.xml?format=INT |
| _version_ | 1811258582395518976 |
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| author | Schreyer Frederic Leine Remco I. |
| author_facet | Schreyer Frederic Leine Remco I. |
| author_sort | Schreyer Frederic |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-04-12T18:16:37Z |
| format | Article |
| id | doaj.art-2e6d5b1a2f0f4cc7a5a9314a26ac6864 |
| institution | Directory Open Access Journal |
| issn | 2300-1895 |
| language | English |
| last_indexed | 2024-04-12T18:16:37Z |
| publishDate | 2016-06-01 |
| publisher | Polish Academy of Sciences |
| record_format | Article |
| series | Archive of Mechanical Engineering |
| spelling | doaj.art-2e6d5b1a2f0f4cc7a5a9314a26ac68642022-12-22T03:21:35ZengPolish Academy of SciencesArchive of Mechanical Engineering2300-18952016-06-0163229731410.1515/meceng-2016-0017meceng-2016-0017A Mixed Shooting – Harmonic Balance Method for Unilaterally Constrained Mechanical SystemsSchreyer Frederic0Leine Remco I.1University of Stuttgart, Institute for Nonlinear Mechanics, Pfaffenwaldring 9, 70569 StuttgartUniversity of Stuttgart, Institute for Nonlinear Mechanics, Pfaffenwaldring 9, 70569 StuttgartIn 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.http://www.degruyter.com/view/j/meceng.2016.63.issue-2/meceng-2016-0017/meceng-2016-0017.xml?format=INTShooting method Harmonic Balance Method local nonlinearities periodic solutions nonsmooth dynamics |
| spellingShingle | Schreyer Frederic Leine Remco I. A Mixed Shooting – Harmonic Balance Method for Unilaterally Constrained Mechanical Systems Archive of Mechanical Engineering Shooting method Harmonic Balance Method local nonlinearities periodic solutions nonsmooth dynamics |
| title | A Mixed Shooting – Harmonic Balance Method for
Unilaterally Constrained Mechanical Systems |
| title_full | A Mixed Shooting – Harmonic Balance Method for
Unilaterally Constrained Mechanical Systems |
| title_fullStr | A Mixed Shooting – Harmonic Balance Method for
Unilaterally Constrained Mechanical Systems |
| title_full_unstemmed | A Mixed Shooting – Harmonic Balance Method for
Unilaterally Constrained Mechanical Systems |
| title_short | A Mixed Shooting – Harmonic Balance Method for
Unilaterally Constrained Mechanical Systems |
| title_sort | mixed shooting harmonic balance method for unilaterally constrained mechanical systems |
| topic | Shooting method Harmonic Balance Method local nonlinearities periodic solutions nonsmooth dynamics |
| url | http://www.degruyter.com/view/j/meceng.2016.63.issue-2/meceng-2016-0017/meceng-2016-0017.xml?format=INT |
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