本文選題：壓電納米板　切入點：非局部理論　出處：《北京交通大學(xué)》2016年博士論文

【摘要】：壓電材料由于其特有的機-電耦合性能,在傳感技術(shù)、信息技術(shù)、新興的智能材料系統(tǒng)等工程領(lǐng)域中有著廣泛的應(yīng)用。而隨著材料制備技術(shù)的發(fā)展,低維壓電納米結(jié)構(gòu)在微/納米級機電系統(tǒng)中應(yīng)用前景廣闊,因而受到了國內(nèi)外學(xué)者的普遍關(guān)注。大量研究表明,在納米尺度下,壓電納米材料的特性會受到尺度效應(yīng)的影響,與宏觀尺寸下的特性相比會表現(xiàn)出明顯的差異,并導(dǎo)致新特性出現(xiàn)。為準確描述壓電納米結(jié)構(gòu)的尺度效應(yīng),本文將采用Eringen提出的非局部理論建立非局部壓電納米板模型,研究其振動和穩(wěn)定性問題,包括線性振動、非線性振動、屈曲和后屈曲等。在此基礎(chǔ)上,我們將進一步討論磁電彈納米板的非線性振動問題。與壓電納米板相比,磁電彈納米板的機-電-磁耦合特性使其非局部本構(gòu)關(guān)系更為復(fù)雜。研究以理論分析為重點,通過解析和數(shù)值求解,分析非局部系數(shù)、熱-電-機械荷載、邊界條件等不同因素對壓電納米板的線性振動、非線性振動、屈曲和后屈曲等特性的影響,以及對磁電彈納米板非線性振動特性的影響。具體來說,本文的討論分為以下幾個部分:1.文章首先討論的是壓電納米板的自由振動問題。基于非局部本構(gòu)關(guān)系,分別建立Kirchhoff壓電納米板和Mindlin壓電納米板模型,分析其在熱-電-機械荷載作用下的自由振動特性。對于Kirchhoff壓電納米板,僅考慮四周簡支邊界條件的影響;對于Mindlin壓電納米板,考慮不同邊界條件的影響。通過Hamilton原理推導(dǎo)出問題的控制方程和相應(yīng)的邊界條件,再利用解析和數(shù)值方法求解得出壓電納米板的固有頻率和振動模態(tài)。2.在壓電納米板自由振動問題的研究基礎(chǔ)上,進一步研究壓電納米板在熱-電-機械荷載作用下的非線性振動特性。先針對Kirchhoff壓電納米板,僅考慮四周簡支的邊界條件,通過Navier法求解得到非線性頻率的解析解。之后討論在不同邊界條件下,Mindlin壓電納米板的非線性振動問題;利用微分求積法(DQ法)對控制方程進行離散,再利用迭代法求解出非線性頻率和振動模態(tài)的解析解。3.考查在不同邊界條件下Mindlin壓電納米板受到面內(nèi)軸向荷載時的屈曲和后屈曲行為。通過最小勢能原理,可推導(dǎo)出問題的控制方程和相應(yīng)的邊界條件。由于壓電納米板的屈曲問題僅考慮了線性幾何關(guān)系,因而可以直接通過DQ法對控制方程進行離散求解,得出板的臨界屈曲荷載;而對于后屈曲問題,由于考慮了 vonKarman幾何非線性,因而需要通過迭代法求出壓電納米板的后屈曲荷載。4.在前面的研究基礎(chǔ)之上,進一步研究非局部磁電彈納米板的非線性振動問題。與壓電納米材料相比,磁電彈納米材料的非局部本構(gòu)關(guān)系更為復(fù)雜�；贛indlin板理論、非局部本構(gòu)關(guān)系和von Karman非線性幾何關(guān)系,考慮不同邊界條件的影響,分析磁電彈納米板在熱-電-磁-機械荷載作用下的非線性振動特性。本文通過建立了非局部壓電納米板和磁電彈納米板模型,分析了尺度效應(yīng)、多場耦合效應(yīng)等因素對壓電納米板和磁電彈納米板振動和穩(wěn)定特性的影響,為微/納米電子機械器件的設(shè)計提供理論依據(jù)。
[Abstract]:The piezoelectric material due to its unique electro-mechanical coupling performance information technology in sensor technology, has been widely used new intelligent material system in the engineering field. With the development of material preparation technology, low dimensional piezoelectric nanostructures in micro / nano electromechanical system application in Jing Guangkuo, which has been the attention of scholars at home and abroad. A large number of studies show that, in the nanometer scale, the characteristics of piezoelectric nano materials will be affected by the scale effect, compared with the characteristics of the macro dimensions will show obvious differences, and lead to new features. In order to accurately describe the scale effect of piezoelectric nano structure, this paper will the use of Eringen's nonlocal theory to establish the non local piezoelectric nano plate model, study the problems of vibration and stability, including linear vibration, nonlinear vibration, buckling and post buckling. On this basis, we will further discuss The nonlinear vibration problem of magnetoelectroelastic nano plate. Compared with the piezoelectric nano plate, magneto electro elastic nano board machine - electric - magnetic coupling characteristics of the non local constitutive relationship is more complicated. The research on the theoretical analysis for the key, through the analytical and numerical analysis, non local coefficient, thermal electrical mechanical load. Linear vibration, different boundary conditions on piezoelectric nano plate nonlinear vibration, impact buckling characteristics such as buckling and post, and the influence on the nonlinear vibration characteristics of magneto electro elastic nano plate. Specifically, this paper is divided into the following parts: 1. firstly discussed is the free vibration of piezoelectric nano plate the non local constitutive relation. Based on the established Kirchhoff piezoelectric nano nano plate and Mindlin plate model electric pressure, analysis of its role in the thermo electro mechanical loading. The free vibration characteristics of Kirchhoff piezoelectric nano plate, only consider around Effect of simply supported boundary conditions; for Mindlin piezoelectric nano plate, considering the influence of different boundary conditions. The Hamilton is derived from the principle of the control equations and the corresponding boundary conditions, using the analytical and numerical methods for solving the piezoelectric nano plate natural frequency and vibration mode of.2. based on the piezoelectric nano plate free vibration on the problem of further study on nonlinear vibration characteristics of piezoelectric nano plate in thermal electrical mechanical loads. For Kirchhoff piezoelectric nano plate, only considering the boundary conditions of four simply supported, through the Navier method to obtain analytic solutions of nonlinear frequency. After discussing the various boundary conditions, the nonlinear vibration problem of Mindlin the piezoelectric nano plate; by using differential quadrature method (DQ method) was used to discrete the governing equations, and then solved by the iterative method of nonlinear analytical solution of frequency and vibration modal test in.3. With the boundary conditions of Mindlin piezoelectric nano plates under in-plane buckling and buckling behavior of axial load and by the principle of minimum potential energy can be deduced the governing equations and corresponding boundary conditions. The buckling problems of piezoelectric nano plate only considers the linear relation of geometry, which can direct the discrete control equations are solved by by DQ method, the critical buckling load of the plate; and for the post buckling problems, due to the vonKarman geometric nonlinearity, thus need to through the iterative method to calculate the post buckling load of.4. piezoelectric nano plate based on the above study, further study on the nonlinear vibration problems of non local magnetoelectroelastic nano plate compared with piezoelectric. Nano materials, nano material magnetoelectroelastic non local constitutive relationship is more complicated. Based on Mindlin plate theory, the non local constitutive relation and von Karman nonlinear geometric relationship, considering the different The influence of boundary conditions and nonlinear vibration analysis of effect of magneto electro elastic nano plate in thermal - electric - magnetic - mechanical loads. This paper established the non local piezoelectric nano plate and nano magneto electro elastic plate model, analyzes the influence of scale effect, multi field coupling effect of piezoelectric and magneto electro elastic nano nano plate plate vibration characteristics and stability, to provide the theoretical basis for design of micro / nano electronic and mechanical devices.

【學(xué)位授予單位】：北京交通大學(xué)
【學(xué)位級別】：博士
【學(xué)位授予年份】：2016
【分類號】：O327;TB34

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