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

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Abstract

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.
Original languageEnglish
Pages (from-to)(In-press)
JournalProceedings of the Institution of Civil Engineers: Engineering and Computational Mechanics
Volume(In-press)
Early online date14 Oct 2019
DOIs
Publication statusE-pub ahead of print - 14 Oct 2019

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Partial differential equations
Natural frequencies
Materials properties
Calibration
Concretes

Keywords

  • concrete structures
  • dynamics
  • mathematical modelling

Cite this

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title = "On the Coupled, Flexural-Flexural-Torsional Vibrations of an Asymmetric Concrete Beam",
abstract = "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.",
keywords = "concrete structures, dynamics, mathematical modelling",
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AU - Karadelis, John

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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.

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KW - dynamics

KW - mathematical modelling

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