Interaction of nonconservative 1D continuum and moving MDOF oscillator

This paper presents a method for computing the response of a ID elastic con tinuum induced by a multi-degree-of-freedom (MDOF) oscillator traveling ove r it. The continuum and the oscillator are nonconservative systems with pro portional damping. Unlike most studies in the field, the solution method do es not address a particular type of continuous structure and oscillator. In stead, 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 integrat ion of a system of linear differential equations with time-dependent coeffi cients. These coefficients are found to depend on natural frequencies, damp ing ratios, and eigenfunctions and eigenvectors of the continuum and the os cillator. The method is tested on numerical examples and results are compar ed to those available in the literature. As a practical application, the me thod can be used to analyze vehicle-bridge interaction problems.