Vibration analysis of rotating 3D beams by the p-version finite element method

Abstract

Moderately nonlinear vibrations of 3D beams with rectangular cross section and that rotate about a fixed axis are investigated by the p-version finite element method. Two types of nonlinearity are taken into account: one comes from the nonlinear strain–displacement relation, the other appears because of the inertia forces due to the rotation of the beam. The beam may experience longitudinal deformations, torsion and non-planar bending. The beam model is based on Timoshenko's theory for bending and Saint-Venant's for torsion, i.e. it is assumed that the cross section rotates about the longitudinal axis as a rigid body but may deform in longitudinal direction due to warping; furthermore torsion is not constrained to be constant. All inertia forces due to the rotation are included in the inertia terms in the equation of motion, which is derived by the principle of virtual work. The influence of the speed of rotation on the bending linear modes of vibration is presented. Then, nonlinear forced vibrations of rotating beams are investigated in the time domain, using direct integration of the equation of motion and considering constant and non-constant speed of rotation. Impulsive type and harmonic external forces are considered.