Chebyshev collocation method for the free vibration analysis of geometrically exact beams with fully intrinsic formulation

Pedram Khaneh Masjedi, Alireza Maheri

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Abstract

A Chebyshev collocation method is presented for the free vibration analysis of geometrically exact nonlinear beams with fully intrinsic formulation. The intrinsic formulation of the governing equations of the beam contains neither displacement nor rotation variables. The proposed collocation discretization technique is based on the Chebyshev points as the collocation points and the orthogonal Chebyshev polynomials as the trial functions. This method is successfully applied to the eigenvalue analysis of the linearized intrinsic governing equations of a nonlinear beam. A number of test cases have been considered for either straight or pretwisted beams and the obtained results are compared to the analytical, numerical as well as experimental results. In order to show the applicability of current approach for real-life engineering problems, a composite wind turbine rotor blade with non-uniform distribution of properties is also considered. In all test cases a very good concordance has been observed. The proposed method bypasses the integrations common in finite element based methods and difficulties associated with finite rotations interpolation and while exhibiting a very good accuracy compared to the finite element results, it is computationally more efficient and simpler to implement in a computer programming cod
Original languageEnglish
Pages (from-to)329-340
Number of pages12
JournalEuropean Journal of Mechanics A/Solids
Volume66
Early online date4 Aug 2017
DOIs
Publication statusPublished - Nov 2017

Fingerprint

collocation
free vibration
Vibration analysis
formulations
Computer programming
Wind turbines
Turbomachine blades
Interpolation
Rotors
computer programming
Polynomials
rotor blades
wind turbines
bypasses
Composite materials
interpolation
polynomials
eigenvalues
engineering
composite materials

Keywords

  • Chebyshev collocation method
  • Geometrically exact beam
  • Intrinsic formulation
  • Free vibration
  • Pretwisted beam
  • Composite rotor blade
  • Composite beam

Cite this

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title = "Chebyshev collocation method for the free vibration analysis of geometrically exact beams with fully intrinsic formulation",
abstract = "A Chebyshev collocation method is presented for the free vibration analysis of geometrically exact nonlinear beams with fully intrinsic formulation. The intrinsic formulation of the governing equations of the beam contains neither displacement nor rotation variables. The proposed collocation discretization technique is based on the Chebyshev points as the collocation points and the orthogonal Chebyshev polynomials as the trial functions. This method is successfully applied to the eigenvalue analysis of the linearized intrinsic governing equations of a nonlinear beam. A number of test cases have been considered for either straight or pretwisted beams and the obtained results are compared to the analytical, numerical as well as experimental results. In order to show the applicability of current approach for real-life engineering problems, a composite wind turbine rotor blade with non-uniform distribution of properties is also considered. In all test cases a very good concordance has been observed. The proposed method bypasses the integrations common in finite element based methods and difficulties associated with finite rotations interpolation and while exhibiting a very good accuracy compared to the finite element results, it is computationally more efficient and simpler to implement in a computer programming cod",
keywords = "Chebyshev collocation method, Geometrically exact beam, Intrinsic formulation, Free vibration, Pretwisted beam, Composite rotor blade, Composite beam",
author = "Masjedi, {Pedram Khaneh} and Alireza Maheri",
year = "2017",
month = "11",
doi = "10.1016/j.euromechsol.2017.07.014",
language = "English",
volume = "66",
pages = "329--340",
journal = "European Journal of Mechanics A/Solids",
issn = "0997-7538",
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TY - JOUR

T1 - Chebyshev collocation method for the free vibration analysis of geometrically exact beams with fully intrinsic formulation

AU - Masjedi, Pedram Khaneh

AU - Maheri, Alireza

PY - 2017/11

Y1 - 2017/11

N2 - A Chebyshev collocation method is presented for the free vibration analysis of geometrically exact nonlinear beams with fully intrinsic formulation. The intrinsic formulation of the governing equations of the beam contains neither displacement nor rotation variables. The proposed collocation discretization technique is based on the Chebyshev points as the collocation points and the orthogonal Chebyshev polynomials as the trial functions. This method is successfully applied to the eigenvalue analysis of the linearized intrinsic governing equations of a nonlinear beam. A number of test cases have been considered for either straight or pretwisted beams and the obtained results are compared to the analytical, numerical as well as experimental results. In order to show the applicability of current approach for real-life engineering problems, a composite wind turbine rotor blade with non-uniform distribution of properties is also considered. In all test cases a very good concordance has been observed. The proposed method bypasses the integrations common in finite element based methods and difficulties associated with finite rotations interpolation and while exhibiting a very good accuracy compared to the finite element results, it is computationally more efficient and simpler to implement in a computer programming cod

AB - A Chebyshev collocation method is presented for the free vibration analysis of geometrically exact nonlinear beams with fully intrinsic formulation. The intrinsic formulation of the governing equations of the beam contains neither displacement nor rotation variables. The proposed collocation discretization technique is based on the Chebyshev points as the collocation points and the orthogonal Chebyshev polynomials as the trial functions. This method is successfully applied to the eigenvalue analysis of the linearized intrinsic governing equations of a nonlinear beam. A number of test cases have been considered for either straight or pretwisted beams and the obtained results are compared to the analytical, numerical as well as experimental results. In order to show the applicability of current approach for real-life engineering problems, a composite wind turbine rotor blade with non-uniform distribution of properties is also considered. In all test cases a very good concordance has been observed. The proposed method bypasses the integrations common in finite element based methods and difficulties associated with finite rotations interpolation and while exhibiting a very good accuracy compared to the finite element results, it is computationally more efficient and simpler to implement in a computer programming cod

KW - Chebyshev collocation method

KW - Geometrically exact beam

KW - Intrinsic formulation

KW - Free vibration

KW - Pretwisted beam

KW - Composite rotor blade

KW - Composite beam

U2 - 10.1016/j.euromechsol.2017.07.014

DO - 10.1016/j.euromechsol.2017.07.014

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EP - 340

JO - European Journal of Mechanics A/Solids

JF - European Journal of Mechanics A/Solids

SN - 0997-7538

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