Spectral Finite Element Analysis of Stationary Vibrations in a beam-plate structure

摘要

A spectral finite element method for predicting structure borne sound transmission in beam-plate structures is presented. A variational principle similar to the principle of virtual work but one that is stationary for true motion, even for non conservative systems, is the basis for the FE formulation. The base functions are exponential functions and general algorithms are presented by which the local dynamic stiffness matrices for such elements are calculated efficiently and systematically, by standard matrix algebra. Thereby, such functions are used in FE formulations, with not much more effort than that needed for standard polynomial base functions. The element formulations are based on a wave guide description of the displacements. For the investigated structure, approximate cross sectional mode shapes are found, considering the levels of the plates in-plane dynamic stiffness is very high, while the levels for bending and rotational displacements in the beams are smaller, yet much higher than those for bending of the plates. Numerical experiments are performed to validate and investigate the approximations made. Stationary vibrations in a half section of a railway car base frame are calculated and the results are compared to those of a standard FE calculation. The bending vibrations of the beams and plates are found to differ, for third octave bands, with no more than a few dB.