A Galerkin approach for analysing coupling effects in the piezoelectric semiconducting beams
A Galerkin approach for analysing coupling effects in the piezoelectric semiconducting beams
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DOI：
10.1016/j.euromechsol.2023.105145
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发表时间：
2023-09
期刊：
影响因子：
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通讯作者：
Zhaowei Liu;Pei‐Liang Bian;Yilin Qu;Weicheng Huang;Leilei Chen;Jingbo Chen;Prashant Saxena;Tiantang Yu
中科院分区：
文献类型：
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作者：
Zhaowei Liu;Pei‐Liang Bian;Yilin Qu;Weicheng Huang;Leilei Chen;Jingbo Chen;Prashant Saxena;Tiantang Yu
压电半导体结合了压电和半导体材料的特性，使其在各种工程应用中具有很大的前景。本文采用Galerkin方法导出了压电半导体耦合控制方程的一般弱形式。考虑了应变、电场和空穴、电子浓度梯度之间的耦合效应。压电半导体通常以杆和梁的形状部署，因此通常经受轴向和横向载荷。因此，欧拉-伯努利梁理论制定的数值方法来分析这种压电半导体梁的耦合行为。为了满足欧拉-伯努利梁理论的C1连续性要求，而不引入额外的自由度，使用B样条离散。非机械变量，包括电势，空穴和电子浓度，分解成常数，线性和二次项通过系列展开沿着的厚度，这确保了与光束配方兼容。为了验证所提出的方法，首先对正弦分布载荷下的N型压电半导体梁进行了研究，并给出了解析解。随后，复杂的例子，包括一个悬臂梁与广义负载条件和PN结的梁进行了分析，以证明所提出的方法在处理更具挑战性的情况下的能力。
The piezoelectric semiconductor combines the characteristics of both piezoelectric and semiconducting materials, making it highly promising for a variety of engineering applications. The present work adopts a Galerkin approach to derive a general weak form of the coupled governing equations for the analysis of piezoelectric semiconductors. The coupling effect between the strain, the electric field, and the gradients of the concentrations of holes and electrons has been considered. Piezoelectric semiconductors are often deployed in the shape of rods and beams and therefore commonly experience axial and transverse load. Thus, the Euler–Bernoulli beam theory is employed to formulate a numerical approach to analyse the coupling behaviour of such piezoelectric semiconductor beams. In order to satisfy the C 1 continuity requirement of Euler–Bernoulli beam theory without introducing additional degrees of freedom, a discretisation with B-Splines is used. Non-mechanical variables, including electrical potential, holes and electrons concentrations, are decomposed into constant, linear and quadratic terms through series expansion along the thickness, which ensures compatibility with beam formulation. To validate the proposed method, an N-type piezoelectric semiconducting beam under a sinusoidal distributed load, for which an analytical solution is available, is initially examined. Subsequently, complex examples including a cantilever beam with generalised loading conditions and a beam with PN-junction are analysed to demonstrate the capabilities of the proposed method in handling more challenging scenarios.