Zhang Xiaoming, Liang Shunli, Han Xiaoming, Li Zhi
School of Mechanical and Power Engineering, Henan Polytechnic University, Jiaozuo 454003, China.
Materials (Basel). 2018 Nov 23;11(12):2363. doi: 10.3390/ma11122363.
Non-propagating waves have great potential for crack evaluation, but it is difficult to obtain the complex solutions of the transcendental dispersion equation corresponding to the non-propagating wave. This paper presents an analytical approach based on the orthogonal function technique to investigate non-propagating Lamb-like waves in a functionally graded piezoelectric spherical curved plate. The presented approach can transform the set of partial differential equations for the acoustic waves into an eigenvalue problem that can give the generally complex wave numbers and the field profiles. A comparison of the obtained results with the well-known ones in plates is provided. The obtained solutions of the dispersion equation are shown graphically in three dimensional frequency-complex wave number space, which aids in understanding the properties of non-propagating waves better. The properties of the guided wave, including real, purely imaginary, and complex branches in various functionally graded piezoelectric spherical curved plates, are studied. The effects of material piezoelectricity, graded fields, and mechanical and electrical boundary conditions on the dispersion characteristics, are illustrated. The amplitude distributions of displacement and electric potential are also discussed, to analyze the specificities of non-propagating waves.
非传播波在裂纹评估方面具有巨大潜力，但要获得与非传播波对应的超越色散方程的复解却很困难。本文提出了一种基于正交函数技术的解析方法，用于研究功能梯度压电球形曲板中的类兰姆非传播波。所提出的方法可以将声波的偏微分方程组转化为一个特征值问题，该问题能够给出一般的复波数和场分布。将所得结果与平板中著名的结果进行了比较。色散方程的所得解在三维频率 - 复波数空间中以图形方式显示，这有助于更好地理解非传播波的特性。研究了各种功能梯度压电球形曲板中导波的特性，包括实部、纯虚部和复部分支。阐述了材料压电性、梯度场以及机械和电气边界条件对色散特性的影响。还讨论了位移和电势的振幅分布，以分析非传播波的特殊性。
