Meshless Local Petrov-Galerkin Method for Rotating Euler-Bernoulli Beam
V. Panchore, R. Ganguli and S. N. Omkar

doi:10.3970/cmes.2015.104.353
Source CMES: Computer Modeling in Engineering & Sciences, Vol. 104, No. 5, pp. 353-373, 2015
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Keywords Petrov-Galerkin Method, Radial Basis Function, Rotating Euler-Bernoulli Beam, Free Vibration.
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.

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