Energy flow prediction in built-up structures through a hybrid finite element/wave and finite element approach

• Numerical tool for the energy flow evaluation in a periodic substructure from the near-field to the far-field domain.
• The near-field part is then modeled by Finite Element Method (FEM).
• The periodic structure and the far-field part are regarded as waveguides and modeled by an enhanced Wave Finite Element Method (WFEM) where a modal reduction technique is employed to accelerate the calculation..
• A multi-scale strategy is used such that the final matrices dimensions of the built-up structure are largely reduced disorders.
• An application is presented, a structural dynamical system coupled with periodic resistive piezoelectric shunts is discussed.

This paper presents a rapid and accurate numerical tool for the energy flow evaluation in a periodic substructure from the near-field to the far-field domain. Here we suppose that the near-field part contains a point source characterized by the injected power in the structure. The near-field part is then modeled by Finite Element Method (FEM) while the periodic structure and the far-field part are regarded as waveguides and modeled by an enhanced Wave and Finite Element Method (WFEM). Enhancements are made on the eigenvalue scheme, the condensation of the unit cell and the consideration of a reduced wave basis. Efforts are made to adapt substructures modeled by different strategies in a multi-scale manner such that the final matrices dimensions of the built-up structure are largely reduced. The method is then validated numerically and theoretically. An application is presented, where a structural dynamical system coupled with periodic resistive piezoelectric shunts is discussed.