A Collocation Approach for Finite Element Basis Functions for Euler-Bernoulli Beams Undergoing Rotation and Transverse Bending Vibration

Abstract

New basis functions are obtained by satisfying the static homogeneous governing differential equation of a rotating beam at one and two collocation points within the beam element. These new basis functions depend on rotation speed, position of element in the beam, and the position of collocation point. They show faster convergence for lower modes at high rotating speeds compared to the conventional Hermite cubic functions. This approach for developing basis functions closer to the problem physics is particularly suited for problems where the governing differential equations do not have exact solutions, which is the case with many realistic problems.

Keywords:

• Rotating cantilever beam
• Collocation method
• Finite element method
• Frequency
• Convergence