Interaction of Nonconservative 1D Continuum and Moving MDOF Oscillator

Abstract

This paper presents a method for computing the response of a 1D elastic continuum induced by a multi-degree-of-freedom (MDOF) oscillator traveling over it. The continuum and the oscillator are nonconservative systems with proportional damping. Unlike most studies in the field, the solution method does not address a particular type of continuous structure and oscillator. Instead, a rigorous mathematical formulation is presented that can be applied to a broad class of proportionally damped 1D continua and MDOF oscillators, regardless of boundary conditions. The problem is reduced to the integration of a system of linear differential equations with time-dependent coefficients. These coefficients are found to depend on natural frequencies, damping ratios, and eigenfunctions and eigenvectors of the continuum and the oscillator. The method is tested on numerical examples and results are compared to those available in the literature. As a practical application, the method can be used to analyze vehicle-bridge interaction problems.