Dynamic model for free vibration and response analysis of rotating beams

Abstract

A new modeling method for the vibration analysis of a rotating cantilever beam is proposed and compared to the other modeling methods. Applying the Hamilton principle, the equations for the axial, chordwise and flapwise motions are derived. During the derivation of these equations, the nonlinear von Karman strain and the corresponding linear stress are used to consider the stiffening effect due to rotation. The derived equations of motion obtained from the proposed method are analytically and numerically compared to equations from the previous modeling methods. Computations of the natural frequencies and time responses show that the described equations of motion are more reliable than the equations of the other modeling methods.