# Quadratic B-spline finite element method for a rotating nonuniform Euler–Bernoulli beam

Panchore, V and Ganguli, R (2018) Quadratic B-spline finite element method for a rotating nonuniform Euler–Bernoulli beam. In: International Journal for Computational Methods in Engineering Science and Mechanics, 19 (5). pp. 340-350.

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Official URL: https://doi.org/10.1080/15502287.2018.1520757

## Abstract

In this article, we solve the free vibration problem of a rotating non-uniform Euler-Bernoulli beam using the quadratic B-spline finite element method. The Galerkin method is used to obtain the weak form of the problem. The quadratic B-spline approximation provides the required C1 continuity. This approximation yields the mass and stiffness matrices, which are half the size of the matrices obtained by the conventional finite element approximation. The resulting polynomials are quadratic while the Hermite polynomials are cubic. The mass and the stiffness matrix are derived. Results are matched with the published literature and compared with the conventional finite element results. A non-uniform approximation is used as well to observe an impact of the centrifugal force in numerical solution. Results are found to be more accurate with the non-uniform B-spline approximation for the first three natural frequencies of a rotating beam. Since the centrifugal force makes a difference to the first few modes, it is a desirable outcome.

Item Type: Journal Article International Journal for Computational Methods in Engineering Science and Mechanics Bellwether Publishing, Ltd. The copyright for this article belongs to the Bellwether Publishing, Ltd. Computer aided analysis; Computer aided design; Galerkin methods; Interpolation; Numerical analysis; Polynomials; Stiffness; Stiffness matrix; Vibration analysis, Beams; blades; Centrifugal Forces; Finite element approximations; Free vibration problem; Hermite polynomials; Nonuniform B spline; Quadratic B-splines, Finite element method Division of Mechanical Sciences > Aerospace Engineering(Formerly Aeronautical Engineering) 05 Aug 2022 10:52 05 Aug 2022 10:52 https://eprints.iisc.ac.in/id/eprint/75385