In this paper, the effects of nonlinear constitutive relation on the electro-elastic coupling behaviors in non-uniform piezoelectric semiconductor beams are investigated. On the basis of three-dimensional theory for piezoelectric semiconductor and double power series, one-dimensional bending model is developed. In order to deal with the nonlinear problem, a differential quadrature method based iteration procedure is proposed. Comparing with the results from finite element method, the proposed method has good convergence and high accuracy. In numerical analysis, the effects of nonlinearity and non-uniformity in piezoelectric semiconductor are discussed thoroughly. It is found the introduction of nonlinearity induces the loss of symmetric for all electrical field quantities but little changes the mechanical quantities. While the reduction of width along the length direction produces larger mechanical and electrical responses. Importantly, the effects of nonlinearity on the electrical field quantities are more evident in a piezoelectric semiconductor beam with rapidly varied cross section. Besides, we designed the piezoelectric semiconductor beams subject to double shear forces and a beam with locally varied cross section. In the designed structures, the potential barriers and wells are realized, which provide new approaches adjusting the electro-elastic behaviors in piezoelectric semiconductors. The study in this paper could be the guidance designing high performance electronic devices.

中文翻译：

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变截面弯曲压电半导体梁电弹耦合特性的非线性分析


本文研究了非线性本构关系对非均匀压电半导体梁电弹性耦合行为的影响。在压电半导体三维理论和双幂级数理论的基础上，建立了一维弯曲模型。为了处理非线性问题，提出了一种基于微分求积法的迭代过程。与有限元法的结果相比，该方法收敛性好，精度高。在数值分析中，深入讨论了压电半导体中非线性和不均匀性的影响。研究发现，非线性的引入导致所有电场量失去对称性，但对机械量几乎没有变化。而沿长度方向宽度的减小会产生更大的机械和电气响应。重要的是，非线性对电场量的影响在横截面快速变化的压电半导体梁中更加明显。此外，我们还设计了承受双剪切力的压电半导体梁和局部变化横截面的梁。在设计的结构中，实现了势垒和势阱，为调节压电半导体的电弹性行为提供了新的方法。本文的研究可为高性能电子器件的设计提供指导。