The guided wave technique is commonly used in the health monitoring of thin-walled structures because the guided waves can propagate far in the structures without much energy loss. However, understanding of the wave propagation in bounded layered structures is still lacking. In this study, the Lamb wave field of single- and multi-layer plates excited by surface-mounted piezoelectric wafer active sensors is theoretically analyzed using the normal mode expansion method, which is based on the elastodynamic reciprocity relation and utilizes the orthogonality relations of the Lamb wave modes. The mode participation factors of Lamb wave in single- and multi-layer isotropic plates are derived. The time domain responses are obtained through the inverse Fourier transform of the structural response spectrum, which is obtained by multiplying the transfer function with the excitation frequency spectrum. The developed normal mode expansion method is first applied to an aluminum single-layer plate. The obtained analytical tuning curves and out-of-plane velocity of the plate are in good agreement with the numerical and experimental results. Finally, the analytical wave responses of an aluminum–adhesive–steel triple-layer plate are verified through comparison with the finite element analysis and experiment. The proposed normal mode expansion method provides a reliable and accurate calculation of the wave field in single- and multi-layer plates.

中文翻译：

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单层和多层各向同性板中圆顶兰姆波场的常模展开理论计算

导波技术通常用于薄壁结构的健康监测，因为导波可以在结构中传播很远而没有太多能量损失。然而，对有界层状结构中波传播的理解仍然缺乏。在本研究中，基于弹性动力学互易关系并利用压电晶片有源传感器激发的单层和多层板的兰姆波场，采用常模展开法从理论上分析了表面贴装压电晶片有源传感器激发的兰姆波场。兰姆波模式。推导出了单层和多层各向同性板中兰姆波的模态参与因子。时域响应通过结构响应谱的逆傅立叶变换获得，这是通过将传递函数与激励频谱相乘获得的。所开发的常模扩展方法首先应用于铝单层板。获得的解析调谐曲线和板面外速度与数值和实验结果吻合良好。最后，通过与有限元分析和实验的比较，验证了铝-胶-钢三层板的解析波响应。所提出的法向模式扩展方法为单层和多层板中的波场提供了可靠和准确的计算。获得的解析调谐曲线和板面外速度与数值和实验结果吻合良好。最后，通过与有限元分析和实验的比较，验证了铝-胶-钢三层板的解析波响应。所提出的法向模式扩展方法为单层和多层板中的波场提供了可靠和准确的计算。获得的解析调谐曲线和板面外速度与数值和实验结果吻合良好。最后，通过与有限元分析和实验的比较，验证了铝-胶-钢三层板的解析波响应。所提出的法向模式扩展方法为单层和多层板中的波场提供了可靠和准确的计算。