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http://dx.doi.org/10.12989/sem.2017.61.6.765

Quadratic B-spline finite element method for a rotating non-uniform Rayleigh beam  

Panchore, Vijay (Aerospace Engineering, Indian Institute of Science)
Ganguli, Ranjan (Aerospace Engineering, Indian Institute of Science)
Publication Information
Structural Engineering and Mechanics / v.61, no.6, 2017 , pp. 765-773 More about this Journal
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 ($\bar{n}$).
Keywords
Galerkin method; quadratic B-spline basis function; rotating beam; free vibration; conventional finite element method;
Citations & Related Records
Times Cited By KSCI : 4  (Citation Analysis)
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