孔隙材料頻散特性之探討

Abstract

本研究針對六角與三角蜂巢結構，建立彈性動態模型與頻率帶隙模型。彈性動態模型基於固體力學的四級理論架構，納入材料組成律、變形機制與幾何特性，並考慮尺寸效應；頻率帶隙模型則透過傳遞矩陣法與Bloch理論建構，用以識別特定頻率範圍內的帶隙區域。此外，亦進行參數化分析，探討相對密度、傾角與牆厚等幾何參數對動態響應與帶隙行為的影響。為佐證理論模型，本研究亦自製哈金森衝擊桿測試儀，並以3D列印製作試體，實際觀察不同微結構配置下之波傳行為。透過理論與實驗結合之方式，建立了一套分析蜂巢材料動態行為的完整架構，可作為未來設計高強度、高韌性與具消能潛力之蜂巢結構材料的基礎。

This study develops elastodynamic models and frequency bandgap models for hexagonal and triangular honeycomb structures. The elastodynamic model is constructed based on a four-level solid mechanics framework, incorporating constitutive behavior, deformation mechanisms, and geometric features, while accounting for size effects. The frequency bandgap model is formulated using the transfer matrix method and Bloch's theorem to identify the bandgap regions across a specified frequency range. Parametric studies are conducted to evaluate the effects of microstructural parameters, such as relative density, inclined angle, and wall thickness, on the dynamic response and bandgap characteristics. To support the theoretical analysis, a Hopkinson bar apparatus is constructed, and 3D-printed specimens are prepared to experimentally investigate wave propagation in cellular structures with various geometries. This integrated modeling and testing framework provides a foundation for designing lightweight, high-strength, and energy-dissipative cellular materials.