Vibration Analysis of a Beam Translating over Supports in Vertical Motion

수직운동하는 지지대 상에서 직진운동하는 보의 진동해석

Vibration of a beam translating over supports in vertical motion is investigated in this paper. Equations of motion are formulated using the virtual work principle by regarding the supports as kinematical constraints imposed on an unrestrained beam and by discretizing the beam via the assumed mode method. Differential-algebraic equations of motion are derived and reduced to differential equations in independent generalized coordinates by the generalized coordinate partitioning method. Geometric stiffness of the beam due to translating motion is considered and how the geometric stiffness of beam affects dynamic stability is also investigated. Instability of the beam. in various conditions is also investigated using Floquet theory and then the results are verified through the dynamic response analysis. Results of numerical simulation are presented for various prescribed motions of the beam.