축방향 왕복운동을 하는 집중질량을 가진 외팔보의 동적 안정성 해석

Dynamic Stability Analysis of an Axially Oscillating Cantilever Beam with a Concentrated Mass

The effect of a concentrated mass on the regions of dynamic instability of an axially oscillating cantilever beam is investigated in this paper. The equations of motion are derived using Kane's method and the assumed mode method. It is found that the bending stiffness is harmonically varied by axial inertia forces due to oscillating motion. Under the certain conditions between oscillating frequency and the natural frequencies, dynamic instability may occur and the magnitude of the bending vibration increase without bound. By using the multiple time scales method, the regions of dynamic instability are obtained. The regions of dynamic instability are found to be depend on the magnitude of a concentrated mass or its location.