Keywords: rotating beam, dynamic, flexure, analog equation method, bar, beam, boundary element method.

In this paper beams under rotation are analyzed. More specifically, an Euler-Bernoulli beam having at its left end a rigid element (wind turbine rigid hub) is examined. The left end of the aforementioned rigid element can rotate about a transverse axis. The beam is a prismatic one having an arbitrary cross section and is subjected to an arbitrary time dependent loading. Two degrees of freedom are assumed, namely the displacement of the centroid and the angle of rotation. The material is linearly elastic. The Hamilton principle is employed in order to obtain the equations of equilibrium, the boundary conditions and the initial conditions of the problem. The obtained initial boundary value problem is numerically solved employing the analog equation method, a boundary element based method.

Numerical applications are presented to examine the efficiency and accuracy of the prescribed system beam element-rigid hub. Two types of numerical examples are examined. The first one considers the calculation of natural frequencies and the modeshapes of the beam for multiple constant values of angular velocity, while the second one considers the calculation of time histories of the kinematical components of the problem for specific loading.

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