A multi-scale model-order reduction strategy for vibration analysis of coupled structures with local inhomogeneities

Although the wave finite-element method (WFEM) is an efficient numerical technique to analyze wave propagation characteristics and forced response of waveguides at medium and high frequencies, its application to large-scale and complex structures is still a challenge. In this paper, we introduce a model-order reduction (MOR) strategy for the WFEM to rapidly investigate the dynamics of coupled elastic systems involving one-dimensional waveguides with local inhomogeneities, such as steel bridges, fuselages and pipeline systems. The proposed method combines the advantages of mode-based component mode synthesis (CMS) and wave-based WFEM. A reduced modal basis is first established to describe the internal degrees of freedom using CMS. Subsequently, a reduced solution subspace considering the contribution of propagating and evanescent waves is constructed by the duality of Bloch's formulations for the waveguide part, while wave scattering characteristics of the coupled element are used to quantify the influence of fixed-interface modes determined by CMS. Structural dynamic response can be then efficiently calculated using a dynamic stiffness matrix method. The performance of the MOR method in dispersion analysis and forced-response calculation is elaborately illustrated via an example of a steel beam with a diaphragm. The influence of the diaphragm on structural dynamic response is explained from the perspective of wave-propagation characteristics. Finally, the method is applied to a real steel-concrete composite girder, and the effects of the number and thickness of diaphragms on the vibration of each plate of the girder are discussed to provide some suggestions on vibration control.