基于力电耦合超材料的圆柱壳类弹性波频率调制

Frequency conversion of elastic wave with cylindrical shell models based on piezoelectric metamaterials

  • 摘要: 目前关于弹性波超材料控制的研究以梁和板类结构居多,针对圆柱壳类结构弹性波超材料控制的研究相对较少。然而,圆柱壳类结构应用广泛,其弹性波的控制对振动研究有重大意义。本文基于力电耦合超材料理论,在圆柱壳上利用“单传感-双驱动”的主动控制方式实现圆柱壳结构中弹性波的频率调制。首先推导圆柱壳结构中的弹性波调控理论,设计力电耦合超材料单元并推导具有时变特性的传递函数。其次,在轴向圆柱壳结构模型中运用仿真技术分析该超材料单元在瞬态研究下弹性波的频率调制功能,并讨论其分析结果。最后制作轴向圆柱壳力电耦合超材料单元的实验分析试样,通过收集弹性波的频域数据用以验证频率的调制功能。圆柱壳力电耦合超材料的仿真结果和实验结果均显著有效,结果表明通过施加力电耦合弹性波超材料单元于圆柱壳表面,可以完成7kHz~12kHz频率范围内的入射波向目标透射波频率的转换,并且修改关键参数可以调制不同频率数值的透射波。研究工作为圆柱壳、曲面壳或球壳结构中弹性波的频率调制提供了理论支持和实验基础。

     

    Abstract: The control of elastic waves in metamaterials has predominantly focused on beam and plate structures, with relatively limited research on cylindrical shell structures. However, cylindrical shell structures are used in various applications where elastic wave modulation plays a crucial role in vibration noise control and vibration energy research. Consequently, this paper achieves frequency conversion of elastic waves in cylindrical shell structures using piezoelectric metamaterials. The study demonstrates that elastic wave frequency conversion can be accomplished through a "single-sensor-dual-actuator" approach, conventional physical law of frequency is not variable can be break by frequency conversion. This work begins with theoretical derivation of the kinetic equation for cylindrical shell structures, along with design of piezoelectric metamaterial cylindrical shells and the development of time-dependent transfer functions. Then, elastic waves frequency conversion is thoroughly analyzed by simulation on axial and circumferential cylindrical shells, these analysis results are investigated and discussed. Finally, frequency conversion function is verified through experiments which are collecting elastic wave parameters in time domain and frequency domain. The experimental results align closely with the simulation outcomes, demonstrating that frequency conversion of incident elastic waves can be successfully achieved in the range of 7 kHz to 9 kHz. Moreover, frequency conversion with different values can be realized by modifying key parameters in the transfer function. This work provides a solid experimental foundation and methodology for achieving elastic waves frequency conversion in curved shell structure, contributing to the broader understanding and application of elastic wave metamaterials.

     

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