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Meshless Local Petrov-Galerkin Method for Rotating Euler-Bernoulli Beam

V. Panchore1, R. Ganguli2, S. N. Omkar3
Ph.D. Student, Department of Aerospace Engineering, Indian Institute of Science, Bangalore, India. E-mail address- vijaypanchore@aero.iisc.ernet.in
Professor, Department of Aerospace Engineering, Indian Institute of Science, Bangalore, India. E-mail address- ganguli@aero.iisc.ernet.in
Chief Research Scientist, Department of Aerospace Engineering, Indian Institute of Science, Bangalore, India. E-mail address- omkar@aero.iisc.ernet.in

Computer Modeling in Engineering & Sciences 2015, 104(5), 353-373. https://doi.org/10.3970/cmes.2015.104.353

Abstract

Free vibration problem of a rotating Euler-Bernoulli beam is solved with a truly meshless local Petrov-Galerkin method. Radial basis function and summation of two radial basis functions are used for interpolation. Radial basis function satisfies the Kronecker delta property and makes it simpler to apply the essential boundary conditions. Interpolation with summation of two radial basis functions increases the node carrying capacity within the sub-domain of the trial function and higher natural frequencies can be computed by selecting the complete domain as a sub-domain of the trial function. The mass and stiffness matrices are derived and numerical results for frequencies are obtained for a fixed-free beam and hinged-free beam simulating hingeless and articulated helicopter blades. Stiffness and mass distribution suitable for wind turbine blades are also considered. Results show an accurate match with existing literature.

Keywords

Petrov-Galerkin Method, Radial Basis Function, Rotating Euler-Bernoulli Beam, Free Vibration.

Cite This Article

Panchore, V., Ganguli, R., Omkar, S. N. (2015). Meshless Local Petrov-Galerkin Method for Rotating Euler-Bernoulli Beam. CMES-Computer Modeling in Engineering & Sciences, 104(5), 353–373.



This work is licensed under a Creative Commons Attribution 4.0 International License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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