### Abstract

Structures such as beams and plates can produce unwanted noise and vibration. An emerging technique can reduce noise and vibration without any additional weight or cost. This method focuses on creating two dimples in the same and opposite direction on a beam's surface where the effect of dimples on its natural frequencies is the problem of interest. The change in the natural frequency between both cases have a different trend. The strategic approach to calculate natural frequencies is as follows: first, a boundary value model (BVM) is developed for a beam with two dimples and subject to various boundary conditions using Hamilton's Variational Principle. Differential equations describing the motion of each segment are presented. Beam natural frequencies and mode shapes are obtained using a numerical solution of the differential equations. A finite element method (FEM) is used to model the dimpled beam and verify the natural frequencies of the BVM. Both methods are also validated experimentally. The experimental results show a good agreement with the BVM and FEM results. A fixed-fixed beam with two dimples in the same and opposite direction is considered as an example in order to compute its natural frequencies and mode shapes. The effect of dimple locations and angles on the natural frequencies are investigated. The natural frequencies of each case represent a greater sensitivity to change in dimple angle for dimples placed at high modal strain energy regions of a uniform beam.

Original language | English (US) |
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Title of host publication | Acoustics, Vibration and Phononics |

Publisher | American Society of Mechanical Engineers (ASME) |

Volume | 13 |

ISBN (Electronic) | 9780791858486 |

DOIs | |

State | Published - Jan 1 2017 |

Event | ASME 2017 International Mechanical Engineering Congress and Exposition, IMECE 2017 - Tampa, United States Duration: Nov 3 2017 → Nov 9 2017 |

### Other

Other | ASME 2017 International Mechanical Engineering Congress and Exposition, IMECE 2017 |
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Country | United States |

City | Tampa |

Period | 11/3/17 → 11/9/17 |

### Fingerprint

### All Science Journal Classification (ASJC) codes

- Mechanical Engineering

### Cite this

*Acoustics, Vibration and Phononics*(Vol. 13). American Society of Mechanical Engineers (ASME). https://doi.org/10.1115/IMECE2017-70631

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*Acoustics, Vibration and Phononics.*vol. 13, American Society of Mechanical Engineers (ASME), ASME 2017 International Mechanical Engineering Congress and Exposition, IMECE 2017, Tampa, United States, 11/3/17. https://doi.org/10.1115/IMECE2017-70631

**Development of an analytical model for beams with two dimples in opposing direction.** / Ghazwani, Mofareh; Myers, Kyle R.; Naghshineh, Koorosh.

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

TY - GEN

T1 - Development of an analytical model for beams with two dimples in opposing direction

AU - Ghazwani, Mofareh

AU - Myers, Kyle R.

AU - Naghshineh, Koorosh

PY - 2017/1/1

Y1 - 2017/1/1

N2 - Structures such as beams and plates can produce unwanted noise and vibration. An emerging technique can reduce noise and vibration without any additional weight or cost. This method focuses on creating two dimples in the same and opposite direction on a beam's surface where the effect of dimples on its natural frequencies is the problem of interest. The change in the natural frequency between both cases have a different trend. The strategic approach to calculate natural frequencies is as follows: first, a boundary value model (BVM) is developed for a beam with two dimples and subject to various boundary conditions using Hamilton's Variational Principle. Differential equations describing the motion of each segment are presented. Beam natural frequencies and mode shapes are obtained using a numerical solution of the differential equations. A finite element method (FEM) is used to model the dimpled beam and verify the natural frequencies of the BVM. Both methods are also validated experimentally. The experimental results show a good agreement with the BVM and FEM results. A fixed-fixed beam with two dimples in the same and opposite direction is considered as an example in order to compute its natural frequencies and mode shapes. The effect of dimple locations and angles on the natural frequencies are investigated. The natural frequencies of each case represent a greater sensitivity to change in dimple angle for dimples placed at high modal strain energy regions of a uniform beam.

AB - Structures such as beams and plates can produce unwanted noise and vibration. An emerging technique can reduce noise and vibration without any additional weight or cost. This method focuses on creating two dimples in the same and opposite direction on a beam's surface where the effect of dimples on its natural frequencies is the problem of interest. The change in the natural frequency between both cases have a different trend. The strategic approach to calculate natural frequencies is as follows: first, a boundary value model (BVM) is developed for a beam with two dimples and subject to various boundary conditions using Hamilton's Variational Principle. Differential equations describing the motion of each segment are presented. Beam natural frequencies and mode shapes are obtained using a numerical solution of the differential equations. A finite element method (FEM) is used to model the dimpled beam and verify the natural frequencies of the BVM. Both methods are also validated experimentally. The experimental results show a good agreement with the BVM and FEM results. A fixed-fixed beam with two dimples in the same and opposite direction is considered as an example in order to compute its natural frequencies and mode shapes. The effect of dimple locations and angles on the natural frequencies are investigated. The natural frequencies of each case represent a greater sensitivity to change in dimple angle for dimples placed at high modal strain energy regions of a uniform beam.

UR - http://www.scopus.com/inward/record.url?scp=85040933593&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85040933593&partnerID=8YFLogxK

U2 - 10.1115/IMECE2017-70631

DO - 10.1115/IMECE2017-70631

M3 - Conference contribution

VL - 13

BT - Acoustics, Vibration and Phononics

PB - American Society of Mechanical Engineers (ASME)

ER -