Abstract
A numerical analysis method is developed for the nonlinear bending vibration of a flexible arm which is accelerated to high rotational velocity in a range of the lowest bending vibration period. The derivation of the differential equation of motion and its finite element formulation is carried out for the moving flexible arm, including the nonlinear effect of a center shaft velocity. The time responses of bending vibration of the flexible arm in a rapid access process are numerically calculated and the critical rotational velocity to induce nonlinear behavior is discussed. From the experimental study it is found that the theoretical results agree well with the experimental ones if three nonlinear terms and the external damping term of the surrounding air are taken into account.
