發(fā)布時(shí)間：2019-02-11 19:21

【摘要】：自從人類發(fā)現(xiàn)和成功制備碳納米管以來(lái),納米科學(xué)和技術(shù)迅速發(fā)展成為當(dāng)今科學(xué)研究的一個(gè)重要領(lǐng)域,大批專家和學(xué)者開(kāi)展了廣泛而深入的研究。由于納米材料和結(jié)構(gòu)具有出色的化學(xué)、電學(xué)以及力學(xué)等特性,被廣泛應(yīng)用于微納電機(jī)系統(tǒng)(MEMS/NEMS)、生物傳感器、原子力顯微鏡以及場(chǎng)濾波器中。這些元器件的設(shè)計(jì)和制造依賴于納米結(jié)構(gòu)力學(xué)性質(zhì)的研究,因此對(duì)納米結(jié)構(gòu)力學(xué)特性的研究很有意義。本文基于非局部板理論,研究了雙層納米板結(jié)構(gòu)在不同邊界條件下的非線性自由振動(dòng)和主共振性質(zhì),得到了結(jié)構(gòu)非線性振動(dòng)頻率以及幅頻響應(yīng)關(guān)系的表達(dá)式,并且采用全局?jǐn)z動(dòng)方法研究了結(jié)構(gòu)的同宿和混沌動(dòng)力學(xué)特性。主要研究工作如下:研究了雙層納米板結(jié)構(gòu)的非線性彎曲振動(dòng)特性�？紤]結(jié)構(gòu)在振動(dòng)中的幾何大變形,采用非線性應(yīng)變位移關(guān)系建立結(jié)構(gòu)的非線性動(dòng)力學(xué)方程,在簡(jiǎn)支和固支可動(dòng)邊界條件下,利用多尺度法解析地分析求得結(jié)構(gòu)的主共振幅頻響應(yīng)關(guān)系式,以及非線性自由振動(dòng)的解析表達(dá)式,分析討論了非局部效應(yīng)及結(jié)構(gòu)參數(shù)對(duì)幅頻響應(yīng)曲線和非線性振動(dòng)頻率的影響,并發(fā)現(xiàn)雙層納米板結(jié)構(gòu)不存在內(nèi)共振的振動(dòng)形式。研究了嵌入彈性基礎(chǔ)中雙層納米板結(jié)構(gòu)的非線性振動(dòng)特性,同時(shí)比較了四種邊界條件下結(jié)構(gòu)非線性自由振動(dòng)的頻率特性。考慮結(jié)構(gòu)所處彈性介質(zhì)環(huán)境,討論了彈性基礎(chǔ)的剛度系數(shù)對(duì)結(jié)構(gòu)非線性主共振幅頻響應(yīng)曲線和自由振動(dòng)頻率的影響。并且注意到結(jié)構(gòu)非線性振動(dòng)特性與邊界是否可動(dòng)有關(guān),因此在簡(jiǎn)支可動(dòng)、簡(jiǎn)支不可動(dòng)、固支可動(dòng)、固支不可動(dòng)這四種邊界條件下,討論了納米板的長(zhǎng)寬比與結(jié)構(gòu)一階和二階非線性振動(dòng)頻率比的關(guān)系。研究了在面內(nèi)載荷作用下,屈曲雙層納米板結(jié)構(gòu)的同宿和混沌動(dòng)力學(xué)行為。雙層納米板結(jié)構(gòu)在面內(nèi)載荷作用下經(jīng)歷同步屈曲和異步屈曲狀態(tài),在這兩種不同屈曲狀態(tài)下,發(fā)展并利用改進(jìn)的高維Melnikov方法研究了結(jié)構(gòu)的同宿和混沌運(yùn)動(dòng),建立橫截同宿軌道是否存在的判別條件,在異步屈曲條件下,劃分了結(jié)構(gòu)發(fā)生不同混沌運(yùn)動(dòng)和超混沌運(yùn)動(dòng)的參數(shù)區(qū)域,計(jì)算了這些參數(shù)區(qū)域中結(jié)構(gòu)振動(dòng)的Lyapunov指數(shù)和Lyapunov維數(shù)。并且對(duì)比了經(jīng)典連續(xù)介質(zhì)理論和非局部模型的計(jì)算結(jié)果,在兩種屈曲條件下,討論了非局部參數(shù)即小尺度效應(yīng)對(duì)結(jié)構(gòu)發(fā)生同宿和混沌運(yùn)動(dòng)的影響規(guī)律。研究受面內(nèi)靜態(tài)載荷以及橫向簡(jiǎn)諧激勵(lì)的雙層納米板結(jié)構(gòu)的同宿運(yùn)動(dòng)。利用雙模態(tài)Galerkin截?cái)喾椒ń⒔Y(jié)構(gòu)的非線性動(dòng)力學(xué)方程,建模過(guò)程中發(fā)現(xiàn)結(jié)構(gòu)的轉(zhuǎn)動(dòng)慣量可以破壞未擾振動(dòng)系統(tǒng)的Hamilton辛對(duì)稱結(jié)構(gòu),而根據(jù)Reddy和Amabili的文獻(xiàn),在之后的非線性動(dòng)力學(xué)分析中可以忽略轉(zhuǎn)動(dòng)慣量的影響。利用改進(jìn)的高維同宿Melnikov方法討論了結(jié)構(gòu)在四種屈曲狀態(tài)下的同宿現(xiàn)象,給出結(jié)構(gòu)在不同相平面上發(fā)生同宿運(yùn)動(dòng)的解析判定條件,并分析了小尺度效應(yīng)以及邊界條件對(duì)結(jié)構(gòu)同宿運(yùn)動(dòng)的影響。研究參數(shù)激勵(lì)下雙模態(tài)屈曲雙層納米板結(jié)構(gòu)的同宿現(xiàn)象和混沌運(yùn)動(dòng)。在結(jié)構(gòu)一階和二階模態(tài)分別經(jīng)歷同步和異步屈曲的條件下,利用推廣的Melnikov方法在八維相空間中分析了結(jié)構(gòu)的同宿和混沌運(yùn)動(dòng),將分析所得結(jié)果與Lyapunov指數(shù)譜以及公開(kāi)發(fā)表的文獻(xiàn)中采用分子動(dòng)力學(xué)方法的計(jì)算結(jié)果加以對(duì)比,并分析了小尺寸效應(yīng)等因素對(duì)結(jié)構(gòu)同宿運(yùn)動(dòng)等非線性動(dòng)力學(xué)行為的影響規(guī)律。
[Abstract]:Since the discovery and successful preparation of carbon nanotubes, the rapid development of nano-science and technology has become an important field of scientific research in the present day, and a large number of experts and scholars have conducted extensive and in-depth research. Due to the excellent chemical, electrical and mechanical properties of the nano-materials and the structure, it is widely used in the micro-nano-motor system (MEMS/ NEMS), the biosensor, the atomic force microscope and the field filter. The design and manufacture of these components depend on the study of the mechanical properties of the nano-structure, so the research on the mechanical properties of the nano-structure is of great significance. Based on the non-local plate theory, the nonlinear free vibration and the main resonance properties of the two-layer nano-plate structure under different boundary conditions are studied, and the expressions of the nonlinear vibration frequency and the amplitude-frequency response relation of the structure are obtained. The homoclinic and hybrid dynamics of the structure are studied by the global perturbation method. The main research work is as follows: the nonlinear bending vibration characteristics of the double-layer nano-plate structure are studied. considering the geometric large deformation of the structure in the vibration, the nonlinear dynamic equation of the structure is established by using the nonlinear strain displacement relation, and the main common amplitude frequency response relation of the structure is analyzed by using the multi-scale method under the dynamic boundary conditions of the simple branch and the solid support, The influence of the non-local effect and the structure parameters on the amplitude-frequency response curve and the nonlinear vibration frequency is discussed, and the vibration form of the inner resonance is not found in the double-layer nano-plate structure. The non-linear vibration characteristics of the two-layer nano-plate structure embedded in the elastic foundation are studied, and the frequency characteristics of the nonlinear free vibration of the structure under the four boundary conditions are compared. Considering the elastic medium environment at the structure, the influence of the stiffness coefficient of the elastic foundation on the nonlinear main-amplitude-frequency response curve and the free-vibration frequency of the structure is discussed. The relationship between the aspect ratio of the nano-plate and the structure-order and the second-order non-linear vibration frequency ratio is discussed. In this paper, the behavior of the co-sink and mixed kinetics of the two-layer plate structure with buckling under the effect of internal load is studied. The double-layer nano-structure experiences synchronous buckling and asynchronous buckling under the action of the internal load, and under the two different buckling conditions, the improved high-dimensional Melnikov method is used to study the homoclinic and hybrid motion of the structure, and the judging conditions of the existence of the cross-section and the sink track are established. Under the condition of asynchronous buckling, the parameters of the structure's different mixed motion and the super-mixed motion are divided, and the Lyapunov exponent and the Lyapunov dimension of the structural vibration in these parameters are calculated. The influence of the non-local parameters, i.e. the small-scale effect on the structure and the sink and the hybrid motion, is discussed in the two buckling conditions. In this paper, the homoclinic motion of the two-layer nano-plate structure excited by the static load in the plane and the transverse simple harmonic excitation is studied. The nonlinear dynamic equation of the structure is established by using the double-mode Galerkin truncation method, and the rotational inertia of the structure is found in the modeling process, so that the Hamiltonian symmetries of the unperturbed vibration system can be destroyed, and according to the literature of Reddy and Amabili, The effect of the moment of inertia can be neglected in the subsequent nonlinear dynamics analysis. In this paper, the homoclinic phenomenon of the structure in four kinds of buckling is discussed with the improved high-dimensional and sink Melnikov method, and the analytical judgment condition of the structure on the plane of different phases is given, and the effect of the small-scale effect and the boundary condition on the structure and the sink movement is also analyzed. In this paper, the homoclinic phenomenon and the mixed motion of the double-mode buckling double-layer nano-plate structure under the excitation of the parameters are studied. under the condition of synchronous and asynchronous buckling of the first and second order modes of the structure, the homoclinic and the mixed motion of the structure are analyzed in the eight-dimensional phase space by using the generalized melnikov method, The results of the analysis and the Lyapunov exponent and the published literature are compared with the results of the molecular dynamics method, and the influence of the factors such as the small-size effect on the nonlinear dynamic behavior of the structure and the sink is analyzed.
【學(xué)位授予單位】：哈爾濱工業(yè)大學(xué)
【學(xué)位級(jí)別】：博士
【學(xué)位授予年份】：2016
【分類號(hào)】：O327

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