Input power to waveguides calculated by a finite element method

This paper considers the power injected into waveguide structures from forces that are concentrated along the waveguide but are otherwise arbitrary. The motion of the structure is described by a set of coupled, linear, one-dimensional wave equations. These equations are, in this work, devised by the waveguide finite element method, which is a versatile tool for describing wave motion in general structures that have uniform properties along one direction. Two separate procedures are derived. The first is based on spatial and frequency averaging of a modal solution. The second procedure is based on a spatial Fourier transform, which by nature assumes the waveguide to be infinite. It is shown that, in the limit of zero damping, the two methods are identical. Subsequently input power to a stiffener in a railway car structure is calculated and compared with an in situ measurement, showing a fair agreement.