Damping prediction of highly dissipative meta-structures through a wave finite element methodology

Abstract

Aiming at accurately predicting the global Damping Loss Factor (DLF) for Highly Dissipative Structures (HDS), the current study uses the Wave Finite Element (WFE) methodology. It starts by deriving the forced responses of a Unit Cell (UC) representative of the periodic meta-structure. Then it computes the DLF of the wave via the power balance. The Bloch expansion is employed. The response to a point force applied to the periodic structure is decomposed in the Brillouin zone, allowing the prediction via integration over the wavespace. The global DLF is derived based on the Power Input Method (PIM). The accuracy of the methodology is demonstrated through several cases from simple panels to complex meta-structures. For HDS, results of General Laminated Model (GLM) is exploited for wave DLF and PIM based on Finite Element Method (FEM) data is provided as reference approach for global DLF. The study discusses the influence of bending waves on the DLF estimation for HDS. A final case study with a meta-structure is also offered. The later consists of a doubly periodic coated sphere in a host rubber, it demonstrates the importance of Bloch modes.