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Structural Engineering and Mechanics Volume 81, Number 5, March10 2022 , pages 607-616 DOI: https://doi.org/10.12989/sem.2022.81.5.607 |
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Meshless local Petrov-Galerkin method for rotating Rayleigh beam |
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Vijay Panchore
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| Abstract | ||
| In this work, the free vibration problem of a rotating Rayleigh beam is solved using the meshless Petrov-Galerkin method which is a truly meshless method. The Rayleigh beam includes rotatory inertia in addition to Euler-Bernoulli beam theory. The radial basis functions, which satisfy the Kronecker delta property, are used for the interpolation. The essential boundary conditions can be easily applied with radial basis functions. The results are obtained using six nodes within a subdomain. The results accurately match with the published literature. Also, the results with Euler-Bernoulli are obtained to compare the change in higher natural frequencies with change in the slenderness ratio. The mass and stiffness matrices are derived where we get two stiffness matrices for the node and boundary respectively. The non-dimensional form is discussed as well. | ||
| Key Words | ||
| mechanical vibration; meshless Petrov-Galerkin method; radial basis function; Rotating Rayleigh beam | ||
| Address | ||
| Vijay Panchore: Department of Mechanical Engineering, Maulana Azad National Institute of Technology, Bhopal, 462003, India | ||