### Abstract

Experimental modal analysis is often used to estimate the natural frequencies and damping of a material sample. While the geometry of the sample is often arbitrary, thin rectangular samples are easy to manufacture, model and test and therefore are commonly-used for these measurements. The roving hammer approach can be used to collect frequency response functions at a rectangular grid of points located on plate. Once the mode shapes have been estimated for the rectangular sample, the discrete wavenumber transform can be used to find the wavenumber spectrum of each mode. For simply-supported boundary conditions, the relationship between the mode shape and the modal wavenumber can be determined analytically using the length of the plate and the distance between zeros in the wavenumber spectrum. For the more realistic free-free boundary, no simple relationship holds. However, it will be shown that the wavenumber verse frequency curve can still be accurately estimated using thin-plate theory to minimize the error of the modal wavenumber at each of the modes. The wavenumber curve can then be used to obtain the material wavespeed.

Original language | English (US) |
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Title of host publication | Rotating Machinery, Hybrid Test Methods, Vibro-Acoustics and Laser Vibrometry - Proceedings of the 35th IMAC, A Conference and Exposition on Structural Dynamics |

Publisher | Springer New York LLC |

Pages | 41-46 |

Number of pages | 6 |

Volume | 8B |

ISBN (Print) | 9783319546476 |

DOIs | |

State | Published - Jan 1 2017 |

Event | 35th IMAC Conference and Exposition on Structural Dynamics, 2017 - Garden Grove, United States Duration: Jan 30 2016 → Feb 2 2016 |

### Other

Other | 35th IMAC Conference and Exposition on Structural Dynamics, 2017 |
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Country | United States |

City | Garden Grove |

Period | 1/30/16 → 2/2/16 |

### Fingerprint

### All Science Journal Classification (ASJC) codes

- Engineering(all)
- Computational Mechanics
- Mechanical Engineering

### Cite this

*Rotating Machinery, Hybrid Test Methods, Vibro-Acoustics and Laser Vibrometry - Proceedings of the 35th IMAC, A Conference and Exposition on Structural Dynamics*(Vol. 8B, pp. 41-46). Springer New York LLC. https://doi.org/10.1007/978-3-319-54648-3_5

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*Rotating Machinery, Hybrid Test Methods, Vibro-Acoustics and Laser Vibrometry - Proceedings of the 35th IMAC, A Conference and Exposition on Structural Dynamics.*vol. 8B, Springer New York LLC, pp. 41-46, 35th IMAC Conference and Exposition on Structural Dynamics, 2017, Garden Grove, United States, 1/30/16. https://doi.org/10.1007/978-3-319-54648-3_5

**Estimating material wavespeed using the wavenumber transform of rectangular plate mode shapes.** / Shepherd, Micah R.

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

TY - GEN

T1 - Estimating material wavespeed using the wavenumber transform of rectangular plate mode shapes

AU - Shepherd, Micah R.

PY - 2017/1/1

Y1 - 2017/1/1

N2 - Experimental modal analysis is often used to estimate the natural frequencies and damping of a material sample. While the geometry of the sample is often arbitrary, thin rectangular samples are easy to manufacture, model and test and therefore are commonly-used for these measurements. The roving hammer approach can be used to collect frequency response functions at a rectangular grid of points located on plate. Once the mode shapes have been estimated for the rectangular sample, the discrete wavenumber transform can be used to find the wavenumber spectrum of each mode. For simply-supported boundary conditions, the relationship between the mode shape and the modal wavenumber can be determined analytically using the length of the plate and the distance between zeros in the wavenumber spectrum. For the more realistic free-free boundary, no simple relationship holds. However, it will be shown that the wavenumber verse frequency curve can still be accurately estimated using thin-plate theory to minimize the error of the modal wavenumber at each of the modes. The wavenumber curve can then be used to obtain the material wavespeed.

AB - Experimental modal analysis is often used to estimate the natural frequencies and damping of a material sample. While the geometry of the sample is often arbitrary, thin rectangular samples are easy to manufacture, model and test and therefore are commonly-used for these measurements. The roving hammer approach can be used to collect frequency response functions at a rectangular grid of points located on plate. Once the mode shapes have been estimated for the rectangular sample, the discrete wavenumber transform can be used to find the wavenumber spectrum of each mode. For simply-supported boundary conditions, the relationship between the mode shape and the modal wavenumber can be determined analytically using the length of the plate and the distance between zeros in the wavenumber spectrum. For the more realistic free-free boundary, no simple relationship holds. However, it will be shown that the wavenumber verse frequency curve can still be accurately estimated using thin-plate theory to minimize the error of the modal wavenumber at each of the modes. The wavenumber curve can then be used to obtain the material wavespeed.

UR - http://www.scopus.com/inward/record.url?scp=85035082660&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85035082660&partnerID=8YFLogxK

U2 - 10.1007/978-3-319-54648-3_5

DO - 10.1007/978-3-319-54648-3_5

M3 - Conference contribution

AN - SCOPUS:85035082660

SN - 9783319546476

VL - 8B

SP - 41

EP - 46

BT - Rotating Machinery, Hybrid Test Methods, Vibro-Acoustics and Laser Vibrometry - Proceedings of the 35th IMAC, A Conference and Exposition on Structural Dynamics

PB - Springer New York LLC

ER -