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Wave propagation in mass embedded and pre-stressed hexagonal lattices

机译：大规模嵌入和预应力六边形格子中的波传播

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This paper investigates the elastic wave propagation, mode veering, and in-plane vibration of pre-stressed hexagonal lattice embedded in an elastic medium and composed of axially loaded Timoshenko beams with attached point masses. The frequency band structure of the lattice system is obtained by solving the corresponding eigenvalue problem based on the Bloch theorem and the finite element method. The parametric study is performed by investigating the effects of the pre-stress magnitude, stiffness of elastic medium, and attached point masses on the band structure of a lattice unit cell. For simulating the free vibration behavior of the proposed lattices with different topologies, the Hurty-Craig-Bampton method is introduced to reduce the number of degrees of freedom. Based on the reduced finite element model, the natural frequencies are determined for various boundary conditions. The additional interface reduction technique, called system-level reduction, has been observed to achieve accurate results compared to that of the full model. Numerical experiments demonstrated a significant influence of the additional masses, pre-stress, and stiffness of elastic medium on Bloch waves and eigenvalues of the proposed lattice systems. The effects of different parameters on the emergence of mode veering phenomenon and band gaps are investigated in detail.
机译：本文研究了嵌入弹性介质中的弹性波传播，模式转向和面内振动，并由具有附着点质量的轴向装载的Timoshenko梁组成。通过基于BLOCH定理和有限元方法解决对应的特征值问题而获得晶格系统的频带结构。通过研究晶格单元电池的带结构上的预应力幅度，弹性介质的刚度和附着点质量的效果来执行参数研究。为了模拟具有不同拓扑的提出的格子的自由振动行为，引入了Hurty-Craig-Bampton方法以减少自由度的数量。基于减少的有限元模型，确定各种边界条件的自然频率。已经观察到额外的界面减少技术，称为系统级减少，以实现与完整模型相比的准确结果。数值实验表明，弹性介质的额外质量，预应力和刚度对所提出的晶格系统的特征值的额外质量，预应力和刚度的显着影响。详细研究了不同参数对模式转向现象和带隙的出现的影响。

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