On the mathematical modelling of beams rotating about a fixed axis (Q2583461)

The authors use four different modeling approaches to study the rotating beam problem. It is assumed that the beam is fixed at one and end is free at the other end. The conventional procedure of Lagrangian mechanics is used to derive the equations of motion. The resulting system of equations is solved numerically. Some problems in satisfying boundary conditions at the free end of the beam are encountered. The authors propose an algebraic constraint at the free end in order to overcome difficulties. Numerical results are presented for a specific choice of (non constant) angular velocity.