Stability of a cantilever beam with tip mass subject to axial sinusoidal excitations

Abstract

The equation of motion of a cantilever beam with a tip mass subject to axial sinusoidal excitations at the clamped end is derived based on Hamilton's principle and the assumed mode method. The effects of axial sinusoidal excitation of the axial displacement, velocity or acceleration at the clamped end on the stability of the beam are then examined by using Bolotin's method. The respective regions of instability are determined by converting the resulting equations of boundary frequencies to the standard form of a generalized eigenvalue problem. Instability regions for various combinations of tip mass and amplitudes of the sinusoidal axial excitations in terms of displacement, velocity, and acceleration are presented. © 1995 Academic Press. All rights reserved.