Abstract

The problem of an elastic distributed system coupled with a moving oscillator, often referred to as the “moving-oscillator” problem, is studied in this chapter. The problem is formulated using a “relative displacement” model. It is shown that, in the limiting case, the moving-mass problem is recovered. The coupled equations of motion are recast into an integral equation, which is amenable to solution by both iterative and direct numerical procedures. The response of a string with a moving oscillator is studied using the direct numerical method.

Introduction

Perspective

The prediction of the dynamic response of a distributed elastic system that supports one or more translating elastic subsystems has been a fundamental problem of interest for well over a century. Interest in this problem originates in structural engineering for the design of railroad tracks, railroad bridges, and highway bridges, wherein the accurate calculation of loads is essential for reliable design and accurate life prediction (Stokes, 1883; Ting and Yener, 1983; Tan and Shore, 1968). It has been observed that, as a structure is subjected to moving loads, the dynamic deflection and stresses can be significantly higher than those observed in the static case. Hence, strict design criteria are now required as structural engineers become more aggressive in the use of long, flexible spans in cable-stayed and suspension bridges and compliant bearings in highway bridges to accommodate environmental loads.