【摘要】：撓曲電性(Flexoelectricity)是由應(yīng)變梯度或者非均勻變形產(chǎn)生電極化的一種力電耦合效應(yīng)。撓曲電性不僅可以增強(qiáng)壓電材料或結(jié)構(gòu)的有效力電耦合效應(yīng),還能使中心對(duì)稱材料具有壓電效應(yīng)。在納米尺度下,結(jié)構(gòu)內(nèi)存在很大的應(yīng)變梯度,其撓曲電效應(yīng)對(duì)結(jié)構(gòu)的宏觀力學(xué)行為有非常顯著的影響。本文首先針對(duì)納米尺度的壓電直梁,利用哈密爾頓變分原理導(dǎo)出考慮撓曲電性的壓電直梁的基本方程。分別采用歐拉梁(Euler-Bernoulli beam)和鐵木辛柯梁(Timoshenko beam)模型,以電學(xué)開路條件下的壓電梁為對(duì)象,研究了撓曲電效應(yīng)對(duì)兩端簡支梁的靜態(tài)彎曲變形和極化強(qiáng)度的影響；其次,針對(duì)納米尺度的壓電圓板,利用哈密爾頓變分原理導(dǎo)出考慮撓曲電性的壓電圓板的基本方程,采用克希霍夫板(Kirchhoffplate)模型,分別研究了在電學(xué)開路和短路條件下,撓曲電效應(yīng)對(duì)外邊簡支的壓電圓板和內(nèi)外邊均簡支的壓電圓環(huán)靜態(tài)彎曲的影響；最后,針對(duì)由壓電和壓磁材料構(gòu)成的多鐵性磁電雙層梁的拉伸和彎曲耦合變形,利用哈密爾頓變分原理導(dǎo)出了考慮撓曲電性的多鐵性雙層梁的基本方程,研究了其在恒定磁場作用下的磁電效應(yīng)(Magnetoelectric effect,簡稱ME效應(yīng))。研究結(jié)果表明,在納米尺寸下,撓曲電效應(yīng)對(duì)壓電和多鐵性磁電復(fù)合結(jié)構(gòu)的宏觀力學(xué)屬性有顯著影響,這些力學(xué)屬性具有明顯的尺寸依賴性。本文的研究結(jié)果,為新型器件的創(chuàng)新與開發(fā)提供了有益的指導(dǎo)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.
【學(xué)位授予單位】：浙江大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2016
【分類號(hào)】：TB303

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