Abstract Phononic crystals are widely researched for new kinds of functional composites. However, studies on magneto-elastic PCs at nanoscale that show special superiorities are quite limited. Considering the nonlocal effect and nonlinear magneto-mechanical coupling, this work establishes a theoretical model for size-dependent flexural wave band structure of magneto-elastic PC nanobeams with magnetostrictive materials according to the Euler–Bernoulli beam model and nonlocal theory. The influence of nonlocal parameter, pre-stress and magnetic field on band structure of Titanium/Terfenol-D PC nanobeams is analyzed. The results show that the nonlocal effect has a remarkable weakening impact on the dispersion curve of high order band gap. In addition, band gap exhibits complex nonlinear coupling characteristics due to the consideration of pre-stress and magnetic field. Moreover, geometric parameter plays an important role in determining the size-dependent band structure. Consequently, the research may be helpful for flexible regulation of elastic wave propagation in PC nanobeam-based devices.

中文翻译：

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基于非局域理论的磁弹性声子晶体纳米束弯曲波带结构

摘要 声子晶体作为新型功能复合材料被广泛研究。然而，对具有特殊优势的纳米级磁弹性 PC 的研究非常有限。考虑到非局域效应和非线性磁-机械耦合，本工作根据欧拉-伯努利梁模型和非局域理论，建立了具有磁致伸缩材料的磁弹性PC纳米梁的尺寸相关弯曲波段结构的理论模型。分析了非局部参数、预应力和磁场对Titanium/Terfenol-D PC纳米梁能带结构的影响。结果表明，非局域效应对高阶带隙色散曲线的影响显着减弱。此外，由于考虑了预应力和磁场，带隙表现出复杂的非线性耦合特性。此外，几何参数在确定依赖于尺寸的能带结构中起着重要作用。因此，该研究可能有助于灵活调节基于 PC 纳米束的设备中的弹性波传播。