考虑挠曲电效应的压电结构的力学行为分析

发布时间：2019-04-03 10:33

【摘要】：挠曲电性(Flexoelectricity)是由应变梯度或者非均匀变形产生电极化的一种力电耦合效应。挠曲电性不仅可以增强压电材料或结构的有效力电耦合效应,还能使中心对称材料具有压电效应。在纳米尺度下,结构内存在很大的应变梯度,其挠曲电效应对结构的宏观力学行为有非常显著的影响。本文首先针对纳米尺度的压电直梁,利用哈密尔顿变分原理导出考虑挠曲电性的压电直梁的基本方程。分别采用欧拉梁(Euler-Bernoulli beam)和铁木辛柯梁(Timoshenko beam)模型,以电学开路条件下的压电梁为对象,研究了挠曲电效应对两端简支梁的静态弯曲变形和极化强度的影响；其次,针对纳米尺度的压电圆板,利用哈密尔顿变分原理导出考虑挠曲电性的压电圆板的基本方程,采用克希霍夫板(Kirchhoffplate)模型,分别研究了在电学开路和短路条件下,挠曲电效应对外边简支的压电圆板和内外边均简支的压电圆环静态弯曲的影响；最后,针对由压电和压磁材料构成的多铁性磁电双层梁的拉伸和弯曲耦合变形,利用哈密尔顿变分原理导出了考虑挠曲电性的多铁性双层梁的基本方程,研究了其在恒定磁场作用下的磁电效应(Magnetoelectric effect,简称ME效应)。研究结果表明,在纳米尺寸下,挠曲电效应对压电和多铁性磁电复合结构的宏观力学属性有显著影响,这些力学属性具有明显的尺寸依赖性。本文的研究结果,为新型器件的创新与开发提供了有益的指导作用。
[Abstract]:Flexible (Flexoelectricity) is a kind of electro-mechanical coupling effect which is caused by strain gradient or non-uniform deformation. Flexural property can not only enhance the effective electromechanical coupling effect of piezoelectric material or structure, but also make the center symmetric material have piezoelectric effect. In nano-scale, there is a large strain gradient in the structure, and the flexure effect of the structure has a significant effect on the macro-mechanical behavior of the structure. In this paper, the fundamental equations of piezoelectric straight beams with flexible properties are derived by means of Hamilton variational principle for nano-scale piezoelectric straight beams. The effects of flexure effect on static bending deformation and polarization strength of simply supported beams at both ends are studied by using the (Timoshenko beam) model of Euler beam (Euler-Bernoulli beam) and Ferroxinkle beam respectively. The piezoelectric beam under the open circuit condition of electricity is taken as the research object and the effect of the flexure effect on the static bending deformation and polarization strength of the beam is studied. Secondly, for nano-scale piezoelectric circular plates, the fundamental equations of piezoelectric circular plates considering flexure are derived by means of Hamilton variational principle. The Kirchhoff plate (Kirchhoffplate) model is used to study the open circuit and short circuit conditions of piezoelectric circular plates, respectively. The effect of flexure electric effect on the static bending of simply supported piezoelectric circular plate outside and simply supported piezoelectric ring on the inner and outer sides; Finally, according to the tensile and bending coupling deformation of the multi-ferroelectric double-layer beam composed of piezoelectric and piezoelectric materials, the basic equations of the multi-ferroelectric bilayer beam with consideration of flexure are derived by means of Hamilton variational principle. The magnetoelectric effect (Magnetoelectric effect,) under the action of a constant magnetic field (ME effect) is studied. The results show that the flexural effect has a significant effect on the macro-mechanical properties of piezoelectric and polyferroelectric composite structures in nano-scale, and these mechanical properties are size-dependent. The results of this paper provide useful guidance for the innovation and development of new devices.
【学位授予单位】：浙江大学
【学位级别】：硕士
【学位授予年份】：2016
【分类号】：TB303

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