### Abstract

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

Pages (from-to) | (In-press) |

Journal | Proceedings of the Institution of Civil Engineers: Engineering and Computational Mechanics |

Volume | (In-press) |

Early online date | 14 Oct 2019 |

DOIs | |

Publication status | E-pub ahead of print - 14 Oct 2019 |

### Fingerprint

### Keywords

- concrete structures
- dynamics
- mathematical modelling

### Cite this

**On the Coupled, Flexural-Flexural-Torsional Vibrations of an Asymmetric Concrete Beam.** / Karadelis, John.

Research output: Contribution to journal › Article

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TY - JOUR

T1 - On the Coupled, Flexural-Flexural-Torsional Vibrations of an Asymmetric Concrete Beam

AU - Karadelis, John

PY - 2019/10/14

Y1 - 2019/10/14

N2 - This article presents the analytical solution of an L-shaped cross-section asymmetric beam (concrete terrace unit) undergoing triple coupling that is, flexural vibration in two mutually perpendicular planes (vertical and horizontal) plus torsional vibration about an axis passing through its shear centre, using the classical approach. Essentially, the procedure involved the development of three governing, coupled, partial differential equations based on Euler-Bernoulli theory for beams with isotropic material properties, from which the exact solution was extracted. The warping effect was considered in the torsional equation. A comparison between the analytical solution and corresponding numerical and experimental results obtained earlier was attempted and similarity and accuracy were discussed. It is reasonable to state that the analytical method in calculating the natural frequencies of a system is the most reliable, compared to experimental (needs skills and experience) and numerical (calibration, updating, validation, etc). However, even the analytical solution may not be as accurate as expected, as it depends on several factors/parameters beyond the full control of the investigator. Some useful comments and conclusions are drawn.

AB - This article presents the analytical solution of an L-shaped cross-section asymmetric beam (concrete terrace unit) undergoing triple coupling that is, flexural vibration in two mutually perpendicular planes (vertical and horizontal) plus torsional vibration about an axis passing through its shear centre, using the classical approach. Essentially, the procedure involved the development of three governing, coupled, partial differential equations based on Euler-Bernoulli theory for beams with isotropic material properties, from which the exact solution was extracted. The warping effect was considered in the torsional equation. A comparison between the analytical solution and corresponding numerical and experimental results obtained earlier was attempted and similarity and accuracy were discussed. It is reasonable to state that the analytical method in calculating the natural frequencies of a system is the most reliable, compared to experimental (needs skills and experience) and numerical (calibration, updating, validation, etc). However, even the analytical solution may not be as accurate as expected, as it depends on several factors/parameters beyond the full control of the investigator. Some useful comments and conclusions are drawn.

KW - concrete structures

KW - dynamics

KW - mathematical modelling

U2 - 10.1680/jencm.18.00035

DO - 10.1680/jencm.18.00035

M3 - Article

VL - (In-press)

SP - (In-press)

JO - Proceedings of the Institution of Civil Engineers: Engineering and Computational Mechanics

JF - Proceedings of the Institution of Civil Engineers: Engineering and Computational Mechanics

SN - 1755-0777

ER -