### Abstract

Recent developments in the holographic investigations of brake noise have produced a wealth of information concerning the vibrations of disc brake systems when high frequency noise (squeal) is being generated. Accurate measurements of the amplitude and phase of the 3D surface displacements of the disc rotor vibrations have been obtained. As well as finding the main frequency(s) and mode of vibration it has been possible to study features such as the in-plane components of the displacement of the disc rotor (often significantly large) and travelling waves moving round the disc at a speed dependent on the frequency and mode order of the vibrations but independent of disc rotational speed. Examining mathematical models that employ a distributed parameter approach (i.e. using a partial differential equation or systems of partial differential equations) to represent disc brake systems, this paper considers the use of numerical methods that are very efficient in computation time. Such methods - known generically as spectral and pseudo-spectral methods - can be used to produce animated solutions of the equations. Thus the parameters used in the models can be easily varied and the partial differential equation(s) solutions compared to the above observed features.

Original language | English |
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Title of host publication | Braking 2004 |

Subtitle of host publication | Vehicle Braking and Chassis Control |

Editors | David Barton, Andrew Blackwood |

Publisher | Wiley |

Pages | 157-165 |

Number of pages | 9 |

ISBN (Print) | 9781860584640 |

Publication status | Published - Oct 2004 |

Event | International Conference on Vehicle Braking and Chassis Control - Leeds, United Kingdom Duration: 7 Jul 2004 → 9 Jul 2004 |

### Publication series

Name | IMechE Event Publications |
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### Conference

Conference | International Conference on Vehicle Braking and Chassis Control |
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Country | United Kingdom |

City | Leeds |

Period | 7/07/04 → 9/07/04 |

### Fingerprint

### Cite this

*Braking 2004: Vehicle Braking and Chassis Control*(pp. 157-165). (IMechE Event Publications). Wiley.

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*Braking 2004: Vehicle Braking and Chassis Control.*IMechE Event Publications, Wiley, pp. 157-165, International Conference on Vehicle Braking and Chassis Control, Leeds, United Kingdom, 7/07/04.

**Pseudo-Spectral Methods Applied to the Mathematical Modelling of Disc Brake Squeal.** / Talbot, C. J.; Fieldhouse, J. D.; Steel, W. P.; Crampton, A.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

TY - GEN

T1 - Pseudo-Spectral Methods Applied to the Mathematical Modelling of Disc Brake Squeal

AU - Talbot, C. J.

AU - Fieldhouse, J. D.

AU - Steel, W. P.

AU - Crampton, A.

PY - 2004/10

Y1 - 2004/10

N2 - Recent developments in the holographic investigations of brake noise have produced a wealth of information concerning the vibrations of disc brake systems when high frequency noise (squeal) is being generated. Accurate measurements of the amplitude and phase of the 3D surface displacements of the disc rotor vibrations have been obtained. As well as finding the main frequency(s) and mode of vibration it has been possible to study features such as the in-plane components of the displacement of the disc rotor (often significantly large) and travelling waves moving round the disc at a speed dependent on the frequency and mode order of the vibrations but independent of disc rotational speed. Examining mathematical models that employ a distributed parameter approach (i.e. using a partial differential equation or systems of partial differential equations) to represent disc brake systems, this paper considers the use of numerical methods that are very efficient in computation time. Such methods - known generically as spectral and pseudo-spectral methods - can be used to produce animated solutions of the equations. Thus the parameters used in the models can be easily varied and the partial differential equation(s) solutions compared to the above observed features.

AB - Recent developments in the holographic investigations of brake noise have produced a wealth of information concerning the vibrations of disc brake systems when high frequency noise (squeal) is being generated. Accurate measurements of the amplitude and phase of the 3D surface displacements of the disc rotor vibrations have been obtained. As well as finding the main frequency(s) and mode of vibration it has been possible to study features such as the in-plane components of the displacement of the disc rotor (often significantly large) and travelling waves moving round the disc at a speed dependent on the frequency and mode order of the vibrations but independent of disc rotational speed. Examining mathematical models that employ a distributed parameter approach (i.e. using a partial differential equation or systems of partial differential equations) to represent disc brake systems, this paper considers the use of numerical methods that are very efficient in computation time. Such methods - known generically as spectral and pseudo-spectral methods - can be used to produce animated solutions of the equations. Thus the parameters used in the models can be easily varied and the partial differential equation(s) solutions compared to the above observed features.

UR - http://www.scopus.com/inward/record.url?scp=15344339618&partnerID=8YFLogxK

UR - https://www.wiley.com/en-gb/Braking+2004%3A+Vehicle+Braking+and+Chassis+Control-p-9781860584640

M3 - Conference contribution

SN - 9781860584640

T3 - IMechE Event Publications

SP - 157

EP - 165

BT - Braking 2004

A2 - Barton, David

A2 - Blackwood, Andrew

PB - Wiley

ER -