Meshfree Galerkin method for a rotating Euler-Bernoulli beam

In this article, we solve the free vibration problem of a rotating Euler-Bernoulli beam using the meshfree Galerkin method. Radial basis functions are used for interpolation. An improved formulation of the rotating Euler-Bernoulli beam free vibration problem with the Galerkin method is explained for the first time, which results into a symmetric stiffness matrix and gives a significant computational advantage over the formulation given in the existing literature. A conventional hp-version of Galerkin finite element method is used for comparison. Results are obtained at different non-dimensional rotating speeds of a rotating beam. Results show excellent agreement with the existing literature.