Piezoelectric materials have been found to have many electromechanical applications in intelligent devices, generally in the form of the flexible cantilever element; thus, the analysis to the corresponding cantilever is of importance, especially when advanced mechanical properties of piezoelectric materials should be taken into account. In this study, the vibration problem of a piezoelectric cantilever beam with bimodular functionally-graded properties is solved via analytical and numerical methods. First, based on the equivalent modulus of elasticity, the analytical solution for vibration of the cantilever beam is easily derived. By the simplified mechanical model based on subarea in tension and compression, as well as on the layer-wise theory, the bimodular functionally-graded materials are numerically simulated; thus, the numerical solution of the problem studied is obtained. The comparison between the theoretical solution and numerical study is carried out, showing that the result is reliable. This study shows that the bimodular functionally-graded properties may change, to some extent, the dynamic response of the piezoelectric cantilever beam; however, the influence could be relatively small and unobvious.

中文翻译：

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具有双模函数梯度特性的压电悬臂梁的振动分析

压电式 已经发现材料通常以柔性悬臂梁的形式在智能设备中具有许多机电应用。因此，对相应悬臂的分析非常重要，尤其是在应考虑压电材料的先进机械性能时。在这项研究中，通过分析和数值方法解决了具有双模功能梯度特性的压电悬臂梁的振动问题。首先，基于等效弹性模量，可以轻松得出悬臂梁振动的解析解。通过基于拉伸和压缩分区的简化力学模型，以及基于分层理论，对双模功能梯度材料进行了数值模拟。从而，得到了所研究问题的数值解。进行了理论解和数值研究的比较，表明结果是可靠的。这项研究表明，双模功能梯度性质可能会在一定程度上改变压电悬臂梁的动力响应。但是，影响可能相对较小且不明显。