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Structural Engineering and Mechanics Volume 61, Number 6, March25 2017 , pages 765-773 DOI: https://doi.org/10.12989/sem.2017.61.6.765 |
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Quadratic B-spline finite element method for a rotating non-uniform Rayleigh beam |
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Vijay Panchore and Ranjan Ganguli
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| Abstract | ||
| The quadratic B-spline finite element method yields mass and stiffness matrices which are half the size of matrices obtained by the conventional finite element method. We solve the free vibration problem of a rotating Rayleigh beam using the quadratic B-spline finite element method. Rayleigh beam theory includes the rotary inertia effects in addition to the Euler- Bernoulli theory assumptions and presents a good mathematical model for rotating beams. Galerkin\'s approach is used to obtain the weak form which yields a system of symmetric matrices. Results obtained for the natural frequencies at different rotating speeds show an accurate match with the published results. A comparison with Euler-Bernoulli beam is done to decipher the variations in higher modes of the Rayleigh beam due to the slenderness ratio. The results are obtained for different values of non-uniform parameter ( n ). | ||
| Key Words | ||
| Galerkin method; quadratic B-spline basis function; rotating beam; free vibration; conventional finite element method | ||
| Address | ||
| Vijay Panchore and Ranjan Ganguli: Aerospace Engineering, Indian Institute of Science, Bangalore, India | ||