Study of the Dynamics of a Rotating Flexible Beam and a Flexible Pendulum

Abstract

The dynamic of a flexible beam forced by an imposed rotating around an axis perpendicular to its plane is addressed. Three approaches are dealt with, two related with simplified theories, belonging to the Strength of Materials and the third one using Finite Elasticity. Within the Strength of Materials approaches, the governing equations are derived by superposing the deformations and the rigid motion in the first model, and by stating the stationarity of the Lagrangian (including first and second order effects in order to capture the stiffening due to the centrifugal forces) through Hamilton’s principle in the second one. Two actions are considered: gravity forces (pendulum) and prescribed rotation. The stiffening effect due to the centrifugal forces is considered only for the beam rotating at high speeds. Comparison of this too models with the equation of Finite Elasticity is carried out. Energy analysis are performed in order to obtain information about the quality of the numerical solution.