Multi-scale Dynamics and Nonlinear Eigenvalue Problem of Heterogeneous Metastructures Using a Wave Finite Element Scheme and Modal Strain Energy Method

Wave Finite Element (WFE) scheme is developed to reveal the multi-scale dynamics and damping characteristics of heterogeneous metastructures. Firstly, a clarification of high contrast and high dissipation in metastructures is addressed, especially on the multi-scale dynamics of Highly Contrasted Structure (HCS) and rheological damping of Polyvinyl Butyral (PVB) in Highly Dissipative Structures (HDS). The Bending-Shear Coupling effect in HCS is introduced through the dynamics of the monolithic and bi-layer limits. The Nonlinear Eigenvalue Problem (NEP) for wavevectors propagating in different heading angle is tackled by the Contour Integral method, the wavenumbers is identified by Weighted Wave Assurance Criteria accounting for the energetic distribution for pairing the numerically derived wavemodes, the WFE scheme is further developed to handle the wave identification and calculate the Damping Loss Factor (DLF) of metastructures using the Modal Strain Energy Method. For validation, the wavenumbers of the WFE scheme show good agreement with results from the Analytical method, General Laminate Model (GLM), and classical model RKU. The agreement of DLF verifies the feasibility of WFE for HDS, the multi-scale behavior is captured by analyzing the wavenumber and wavemodes. Some useful conclusions are discussed.