Optimal Vibration Suppression in Modal Space for Flexible Beams Subjected to Moving Loads

Yih-Hwang Lin

doi:10.1155/1997/825978

Abstract

Optimal independent modal space control for vibration suppression of beam structures traversed by a moving concentrated force was examined. Two control methodologies, optimal linear quadratic tracking and an optimal linear quadratic regulator, were utilized, with the former approach taking into account the disturbance due to the moving load and the latter one simply ignoring that disturbance. One single actuator placed at the beam center was found to be sufficient to suppress excessive vibration of a beam traversed by the moving load with a reasonable amount of control input. This study shows that excessive vibration of the beam structure induced by the moving load can be more effectively suppressed using the tracking control approach than using the regulator design, even with ±50% variation of the moving load magnitude or speed from that designed for the tracking control system.

Highlights

The dynamic analysis of structures subjected to moving loads has attracted much attention from engineers and scientists since the 19th century (Stokes, 1883)
When a supported beam was subjected to a moving force traveling at constant velocity, the maximum dynamic beam displacement was found to be about 50% greater than that of the static case when the concentrated force was moving at a velocity corresponding to the first resonant beam mode (Timoshenko, 1955)
It has been shown that when an elastic beam is subjected to a moving concentrated force, the dynamic response of the system is dominated by the fundamental mode with a very small contribution from the higher modes (Timoshenko, 1955)

Summary

Introduction

The dynamic analysis of structures subjected to moving loads has attracted much attention from engineers and scientists since the 19th century (Stokes, 1883). When a supported beam was subjected to a moving force traveling at constant velocity, the maximum dynamic beam displacement was found to be about 50% greater than that of the static case when the concentrated force was moving at a velocity corresponding to the first resonant beam mode (Timoshenko, 1955). Besides the original concerns for dynamic analysis of railway bridges and highway structures subjected to moving vehicle loads, the case of a rotating beam subjected to deflection-dependent moving forces, pertinent for the study of lathe machining operation, was studied (Katz et al, 1987). A general treatment for various moving load problems and application to a high speed industrial precision drilling machine were reported by Lin and Trethewey (1990) and Lin et al (1990)

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