Vibration and stability of axially moving beam on multiple intermediate elastic supports with transfer matrix method

Abstract

This study delves into the vibration characteristics and stability of an axially moving beam with multiple intermediate elastic supports. Initially, the motion equation of the beam is developed, setting the stage for an in-depth investigation of its free vibration characteristics through the transfer matrix method. This analysis covers the beam’s natural frequencies and critical velocity when moving at a constant velocity. Additionally, the dynamic behavior of the beam is investigated when it is subjected to constant axial movement and a concurrent traveling load. The multi-scale method is used to analyze the instability regions of the axially moving beam on multiple intermediate elastic supports as disturbance of the axial movement approaches subharmonic and sum-type combined resonances. The investigation further considers how alterations in the stiffness and configuration of the elastic supports influence the dynamic behavior and stability of the beam. Unique dynamic characteristics arise when the axially moving beam is supported by multiple elastic elements, contrasting with those observed in beams without such supports. An increase in support stiffness enhances the critical velocity at which the beam axially moves, potentially causing modal transformations of the structure prior to reaching this critical velocity, and diminishing the instability regions associated with sum-type combined resonances under disturbance velocities.