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.

中文翻译：

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通过波有限元方法预测高耗散元结构的阻尼

为了准确预测高耗散结构（HDS）的全局阻尼损失因子（DLF），当前的研究使用波有限元（WFE）方法。首先推导代表周期性元结构的晶胞 (UC) 的受迫响应。然后它通过功率平衡计算波的 DLF。采用布洛赫展开式。对施加到周期性结构的点力的响应在布里渊区中分解，从而允许通过波空间上的积分进行预测。全局DLF是基于功率输入法(PIM)导出的。从简单的面板到复杂的元结构的几个案例证明了该方法的准确性。对于HDS，将通用层合模型（GLM）的结果用于波DLF，并提供基于有限元法（FEM）数据的PIM作为全局DLF的参考方法。该研究讨论了弯曲波对 HDS 的 DLF 估计的影响。还提供了带有元结构的最终案例研究。后者由主体橡胶中的双周期涂层球体组成，它证明了布洛赫模式的重要性。