### Abstract

In the present contribution, a practical and non-destructive method for the identification of a single crack in a beam resting on elastic foundation is presented. The beam is modelled by differential quadrature method, and the location and depth of crack are predicted by bees algorithm. The crack is assumed to be open and is simulated by torsional spring which divides all parts through cracked beam into two segments. Then, the differential quadrature method is applied to the governing differential equation of motion of each segment and the corresponding boundary and continuity conditions. An eigenvalue analysis is performed on the resulting system of algebraic equations to obtain the natural frequencies of the cracked beam on elastic foundation. Then, the location and depth of cracks are determined by bees algorithm optimization technique. The formulation of thin-walled beams theory is used for the crack detection in this research. To insure the integrity and robustness of the presented algorithm, the finite element analysis is performed on the set of cantilever beams, with different crack lengths and locations. The results show that the presented algorithm predicts location and depth of crack well and can be effectively employed for crack detection in other structures.

Original language | English |
---|---|

Title of host publication | Lecture Notes in Mechanical Engineering |

Publisher | Pleiades Publishing |

Pages | 439-460 |

Number of pages | 22 |

DOIs | |

Publication status | Published - 2018 Jan 1 |

Externally published | Yes |

### Publication series

Name | Lecture Notes in Mechanical Engineering |
---|---|

Volume | PartF3 |

ISSN (Print) | 2195-4356 |

ISSN (Electronic) | 2195-4364 |

### Fingerprint

### Keywords

- Bees algorithm
- Crack detection
- Differential quadrature method
- Vibration analysis

### ASJC Scopus subject areas

- Automotive Engineering
- Aerospace Engineering
- Mechanical Engineering
- Fluid Flow and Transfer Processes

### Cite this

*Lecture Notes in Mechanical Engineering*(pp. 439-460). (Lecture Notes in Mechanical Engineering; Vol. PartF3). Pleiades Publishing. https://doi.org/10.1007/978-981-10-7149-2_30

**Crack detection in a beam on elastic foundation using differential quadrature method and the bees algorithm optimization.** / Khademi Zahedi, R.; Alimouri, P.; Nguyen-Xuan, Hung; Rabczuk, Timon.

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

*Lecture Notes in Mechanical Engineering.*Lecture Notes in Mechanical Engineering, vol. PartF3, Pleiades Publishing, pp. 439-460. https://doi.org/10.1007/978-981-10-7149-2_30

}

TY - CHAP

T1 - Crack detection in a beam on elastic foundation using differential quadrature method and the bees algorithm optimization

AU - Khademi Zahedi, R.

AU - Alimouri, P.

AU - Nguyen-Xuan, Hung

AU - Rabczuk, Timon

PY - 2018/1/1

Y1 - 2018/1/1

N2 - In the present contribution, a practical and non-destructive method for the identification of a single crack in a beam resting on elastic foundation is presented. The beam is modelled by differential quadrature method, and the location and depth of crack are predicted by bees algorithm. The crack is assumed to be open and is simulated by torsional spring which divides all parts through cracked beam into two segments. Then, the differential quadrature method is applied to the governing differential equation of motion of each segment and the corresponding boundary and continuity conditions. An eigenvalue analysis is performed on the resulting system of algebraic equations to obtain the natural frequencies of the cracked beam on elastic foundation. Then, the location and depth of cracks are determined by bees algorithm optimization technique. The formulation of thin-walled beams theory is used for the crack detection in this research. To insure the integrity and robustness of the presented algorithm, the finite element analysis is performed on the set of cantilever beams, with different crack lengths and locations. The results show that the presented algorithm predicts location and depth of crack well and can be effectively employed for crack detection in other structures.

AB - In the present contribution, a practical and non-destructive method for the identification of a single crack in a beam resting on elastic foundation is presented. The beam is modelled by differential quadrature method, and the location and depth of crack are predicted by bees algorithm. The crack is assumed to be open and is simulated by torsional spring which divides all parts through cracked beam into two segments. Then, the differential quadrature method is applied to the governing differential equation of motion of each segment and the corresponding boundary and continuity conditions. An eigenvalue analysis is performed on the resulting system of algebraic equations to obtain the natural frequencies of the cracked beam on elastic foundation. Then, the location and depth of cracks are determined by bees algorithm optimization technique. The formulation of thin-walled beams theory is used for the crack detection in this research. To insure the integrity and robustness of the presented algorithm, the finite element analysis is performed on the set of cantilever beams, with different crack lengths and locations. The results show that the presented algorithm predicts location and depth of crack well and can be effectively employed for crack detection in other structures.

KW - Bees algorithm

KW - Crack detection

KW - Differential quadrature method

KW - Vibration analysis

UR - http://www.scopus.com/inward/record.url?scp=85042876161&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85042876161&partnerID=8YFLogxK

U2 - 10.1007/978-981-10-7149-2_30

DO - 10.1007/978-981-10-7149-2_30

M3 - Chapter

AN - SCOPUS:85042876161

T3 - Lecture Notes in Mechanical Engineering

SP - 439

EP - 460

BT - Lecture Notes in Mechanical Engineering

PB - Pleiades Publishing

ER -