Isogeometric analysis for in-plane free vibration of centrifugally stiffened beams including Coriolis effects

Abstract

In this paper, in-plane free vibration of a rotating Euler-Bernoulli beam with uniform cross section is studied using a rotation-free isogeometric analysis formulation. Using Hamilton’s principle, the derived equations governing the in-plane bending and axial deformations are coupled by means the Coriolis terms. These two equations are transformed into a one linear gyroscopic eigenvalue problem via a weak formulation. The boundary conditions are enforced by means of Lagrange multipliers. Numerical tests of convergence are conducted and the obtained results are compared to the reference solutions to show the effectiveness and accuracy of the proposed method. Effects on natural frequencies, and mode shapes originated from Coriolis terms, angular speed, slenderness ration, hub radius and boundary conditions are numerically investigated.