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Meshless local Petrov-Galerkin method for rotating Rayleigh beam using Chebyshev and Legendre polynomials

Vijay Panchore

Archive of Mechanical Engineering | 2022 | vol. 69 | No 2 | 301-318 | DOI: 10.24425/ame.2022.140416

Keywords meshless local Petrov-Galerkin method mechanical vibrations orthogonal polynomials Finite Element Method (FEM) rotating beams

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Abstract

The numerical solutions are obtained for rotating beams; the inclusion of centrifugal force term makes it difficult to get the analytical solutions. In this paper, we solve the free vibration problem of rotating Rayleigh beam using Chebyshev and Legendre polynomials where weak form of meshless local Petrov-Galerkin method is used. The equations which are derived for rotating beams result in stiffness matrices and the mass matrix. The orthogonal polynomials are used and results obtained with Chebyshev polynomials and Legendre polynomials are exactly the same. The results are compared with the literature and the conventional finite element method where only first seven terms of both the polynomials are considered. The first five natural frequencies and respective mode shapes are calculated. The results are accurate when compared to literature.

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Authors and Affiliations

Vijay Panchore

Department of Mechanical Engineering, Maulana Azad National Institute of Technology, Bhopal, India