Model reduction schemes for the wave and finite element method using the free modes of a unit cell

The wave and finite element method (WFEM) is an efficient numerical tool for analysing wave propagation characteristics and forced response at intermediate and high frequencies. In this work, we introduce free-interface component modal synthesis (CMS) methods into WFEM to accelerate the calculation while maintaining the accuracy. Several free-interface CMS methods with different approximations of the residual effects are implemented and compared. A new eigenvalue scheme based on the dynamic compliance matrix is proposed. A periodic open thin-wall structure is considered as an application for which both free-wave characteristics and forced responses are computed. Aspects such as accuracy, efficiency, and convergence of the proposed method are discussed and compared with those of the Craig-Bampton fixed-interface CMS method. The methods and main findings are further verified by using another more complex periodic structure. Among the implemented models, the minimum model size is achieved by the exact CMS method. The exact CMS method only requires the modes below the maximum analysing frequency, thereby reducing the model size of the open thin-wall structure from 4416 to 16. The most numerically efficient model for WFEM is MacNeal's CMS method, where the CPU time of free-wave analysis can be reduced by 97% for the open thin-wall structure.