【摘要】：旋轉(zhuǎn)結(jié)構(gòu)作為獨(dú)立的結(jié)構(gòu)或組合結(jié)構(gòu)的部件,被廣泛應(yīng)用于航空航天、海洋工程、土木工程以及機(jī)械工程等工程應(yīng)用領(lǐng)域,其相關(guān)動(dòng)力學(xué)問(wèn)題的求解一直是工程領(lǐng)域研究的一個(gè)重要內(nèi)容。在傳統(tǒng)求解分析方法中,需要建立不同幾何配置參數(shù)下旋轉(zhuǎn)結(jié)構(gòu)的求解方案,并對(duì)位移容許函數(shù)進(jìn)行修改以適用于各種不同的邊界條件。為了實(shí)現(xiàn)模型的參數(shù)化,本文針對(duì)旋轉(zhuǎn)結(jié)構(gòu),構(gòu)建了一種適用于復(fù)雜邊界條件的統(tǒng)一動(dòng)力學(xué)分析模型,對(duì)工程實(shí)際應(yīng)用領(lǐng)域中旋轉(zhuǎn)結(jié)構(gòu)的設(shè)計(jì)提供必要的理論和技術(shù)支持,并從本質(zhì)上研究結(jié)構(gòu)振動(dòng)特性和聲場(chǎng)的形成機(jī)理。本文圍繞著復(fù)雜邊界條件下旋轉(zhuǎn)結(jié)構(gòu)動(dòng)力學(xué)建模問(wèn)題,開(kāi)展了如下的研究工作:建立了復(fù)雜邊界條件下旋轉(zhuǎn)板(扇形板、環(huán)板和圓板)結(jié)構(gòu)橫向振動(dòng)統(tǒng)一分析模型,采用二維譜幾何法來(lái)描述旋轉(zhuǎn)板結(jié)構(gòu)橫向振動(dòng)位移容許函數(shù)。為了消除位移容許函數(shù)及其空間導(dǎo)數(shù)在邊界處存在的不連續(xù)或跳躍現(xiàn)象,構(gòu)建的位移函數(shù)分量表示為一個(gè)標(biāo)準(zhǔn)的單余弦級(jí)數(shù)與四項(xiàng)正弦函數(shù)之和。在旋轉(zhuǎn)板各邊界上均勻分布具有獨(dú)立剛度系數(shù)的線(xiàn)性和旋轉(zhuǎn)約束彈簧,模擬板結(jié)構(gòu)系統(tǒng)的復(fù)雜邊界條件,通過(guò)修改邊界約束彈簧的剛度系數(shù)值即可求解復(fù)雜邊界條件下旋轉(zhuǎn)板結(jié)構(gòu)的振動(dòng)問(wèn)題。采用基于能量原理的瑞利-里茲法求解位移容許函數(shù)的未知級(jí)數(shù)展開(kāi)系數(shù)。通過(guò)數(shù)值分析對(duì)所構(gòu)建的位移容許函數(shù)和統(tǒng)一分析模型進(jìn)行了驗(yàn)證,對(duì)旋轉(zhuǎn)板橫向振動(dòng)特性影響因素進(jìn)行了研究分析。構(gòu)建了復(fù)雜邊界條件下旋轉(zhuǎn)板結(jié)構(gòu)面內(nèi)振動(dòng)問(wèn)題的統(tǒng)一分析模型。為了確保面內(nèi)振動(dòng)位移容許函數(shù)及其導(dǎo)數(shù)在各邊界處的連續(xù)性,采用二維譜幾何法對(duì)旋轉(zhuǎn)板結(jié)構(gòu)徑向和周向的位移容許函數(shù)進(jìn)行了統(tǒng)一描述。采用沿各邊界均勻分布的切向和法向約束彈簧來(lái)描述面內(nèi)振動(dòng)問(wèn)題的復(fù)雜邊界條件。基于瑞利-里茲法推導(dǎo)了復(fù)雜邊界條件下旋轉(zhuǎn)板結(jié)構(gòu)面內(nèi)振動(dòng)特征方程,并通過(guò)求解一個(gè)標(biāo)準(zhǔn)特征值問(wèn)題來(lái)獲得面內(nèi)自由振動(dòng)特征參數(shù)。通過(guò)將本文數(shù)值計(jì)算結(jié)果與其它分析方法結(jié)果進(jìn)行對(duì)比分析,檢驗(yàn)了本文方法及統(tǒng)一分析模型。提出了一種三維譜幾何法,并建立了復(fù)雜邊界條件下旋轉(zhuǎn)板結(jié)構(gòu)三維振動(dòng)統(tǒng)一分析模型。采用三維譜幾何法將旋轉(zhuǎn)板結(jié)構(gòu)三維振動(dòng)位移容許函數(shù)描述為三重三角級(jí)數(shù)形式,以消除位移容許函數(shù)及其空間導(dǎo)數(shù)在結(jié)構(gòu)各邊界面上可能存在的間斷點(diǎn)。通過(guò)修改各邊界面上三個(gè)方向的邊界約束彈簧剛度系數(shù),模擬各種不同的邊界條件及其任意組合。采用基于能量原理的瑞利-里茲法推導(dǎo)了旋轉(zhuǎn)板結(jié)構(gòu)系統(tǒng)的三維自由振動(dòng)運(yùn)動(dòng)方程,通過(guò)求解該方程獲得結(jié)構(gòu)系統(tǒng)的振動(dòng)特性,即通過(guò)求解同一個(gè)邊值問(wèn)題而獲得不同幾何形狀旋轉(zhuǎn)結(jié)構(gòu)的振動(dòng)特性。通過(guò)對(duì)不同邊界條件下旋轉(zhuǎn)結(jié)構(gòu)自由振動(dòng)特性的求解,并與相關(guān)文獻(xiàn)結(jié)果及有限元法結(jié)果進(jìn)行對(duì)比分析來(lái)驗(yàn)證所提方法及構(gòu)建的統(tǒng)一分析模型。構(gòu)建了復(fù)雜邊界條件/耦合連接條件下旋轉(zhuǎn)板-圓柱殼耦合結(jié)構(gòu)系統(tǒng)動(dòng)力學(xué)問(wèn)題的統(tǒng)一分析模型。采用二維譜幾何法來(lái)描述旋轉(zhuǎn)板和圓柱殼結(jié)構(gòu)的六種位移容許函數(shù),分別對(duì)各自外在的復(fù)雜邊界條件進(jìn)行建模。在連接公共邊,采用具有線(xiàn)性剛度和旋轉(zhuǎn)剛度的三維彈性耦合器來(lái)描述板殼連接的相容性條件。三維彈性耦合器由沿公共邊界分布的四類(lèi)耦合彈簧來(lái)描述,詳盡地考慮了彎矩、橫向剪切、面內(nèi)剪切與縱向剪切的耦合效應(yīng),通過(guò)改變相應(yīng)彈簧剛度值來(lái)實(shí)現(xiàn)結(jié)構(gòu)系統(tǒng)各種不同的耦合連接條件。最后采用瑞利-里茲法求解得到板-殼耦合結(jié)構(gòu)動(dòng)力學(xué)問(wèn)題相應(yīng)的雙重改進(jìn)三角級(jí)數(shù)解。將本文數(shù)值計(jì)算結(jié)果與其它文獻(xiàn)解及有限元法結(jié)果進(jìn)行對(duì)比分析來(lái)檢驗(yàn)構(gòu)建的分析模型。在此基礎(chǔ)上,對(duì)旋轉(zhuǎn)板-圓柱殼耦合結(jié)構(gòu)的強(qiáng)迫振動(dòng)響應(yīng)進(jìn)行了計(jì)算分析,并研究了各種不同耦合連接條件、耦合位置及其它結(jié)構(gòu)參數(shù)對(duì)板-殼耦合結(jié)構(gòu)振動(dòng)響應(yīng)特性的影響。最后,設(shè)計(jì)并搭建了相關(guān)實(shí)驗(yàn)臺(tái)架,對(duì)旋轉(zhuǎn)板(凹角環(huán)扇形板和圓板)以及彈性圓板-圓柱殼耦合結(jié)構(gòu)的振動(dòng)特性開(kāi)展了相關(guān)的實(shí)驗(yàn)研究。通過(guò)將實(shí)驗(yàn)測(cè)試結(jié)果與本文方法的預(yù)測(cè)結(jié)果進(jìn)行對(duì)比分析來(lái)檢驗(yàn)了所提出的分析方法,并對(duì)特殊的實(shí)驗(yàn)現(xiàn)象和實(shí)驗(yàn)誤差原因進(jìn)行了分析。
[Abstract]:As a component of independent structure or combined structure, the rotating structure is widely used in the application fields of aerospace, ocean engineering, civil engineering and mechanical engineering, and the solution of the related dynamic problems has been an important content in the field of engineering. In the traditional solution analysis method, the solution scheme of the rotation structure under different geometric configuration parameters needs to be established, and the displacement tolerance function can be modified to be suitable for various boundary conditions. In order to parameterize the model, a unified dynamic analysis model for complex boundary conditions is built, and the necessary theory and technical support are provided for the design of the rotating structure in the practical application field of the project. The characteristics of structural vibration and the formation mechanism of sound field are studied from the essence. In this paper, the problem of the dynamic modeling of the rotating structure under complex boundary conditions is studied. The unified analytical model of the transverse vibration of the rotating plate (the sector plate, the ring plate and the circular plate) under the complex boundary conditions is established. A two-dimensional spectral method is used to describe the allowable function of the lateral vibration displacement of the rotating plate structure. In order to eliminate the discontinuity or jumping phenomenon of the displacement tolerance function and its spatial derivative at the boundary, the constructed displacement function component is expressed as a standard single-cosine series and the sum of the four sine functions. The linear and rotational constraint springs with independent stiffness coefficients are uniformly distributed on each boundary of the rotating plate, and the complex boundary conditions of the plate structure system are simulated, and the vibration problem of the rotating plate structure under the complex boundary conditions can be solved by modifying the rigidity coefficient value of the boundary constraint spring. An energy-based Rayleigh-Ritz method is used to solve the unknown series expansion coefficient of the displacement tolerance function. The displacement tolerance function and the unified analytical model are verified by numerical analysis, and the influence factors of the transverse vibration characteristics of the rotating plate are analyzed. The unified analytical model of the in-plane vibration of the rotating plate structure under complex boundary conditions is constructed. In order to ensure the continuity of the in-plane vibration displacement tolerance function and its derivative at each boundary, a two-dimensional spectral geometry method is used to describe the displacement tolerance function in the radial and circumferential direction of the rotating plate structure. The complex boundary conditions of the in-plane vibration problem are described by tangential and normal constraint springs which are uniformly distributed along the boundary. In this paper, the in-plane vibration characteristic equation of a rotating plate structure under complex boundary conditions is derived based on the Rayleigh-Ritz method, and a standard characteristic value problem is solved to obtain the in-plane free vibration characteristic parameters. In this paper, the numerical results of this paper and other analytical methods are compared and analyzed, and the method and the unified analytical model of this paper are examined. In this paper, a three-dimensional spectral geometry method is proposed, and a three-dimensional vibration unified analysis model of the rotating plate structure under complex boundary conditions is established. The three-dimensional vibration displacement tolerance function of the rotating plate structure is described by the three-dimensional spectral geometry as a triple triangular series form, so as to eliminate the discontinuity points that the displacement tolerance function and the space derivative may exist on each boundary surface of the structure. Various boundary conditions and any combination thereof are simulated by modifying the boundary constraint spring rate coefficient of the three directions on each boundary surface. The three-dimensional free-vibration motion equation of a rotating plate structure system is derived by the energy-based Rayleigh-Ritz method, and the vibration characteristics of the structure system are obtained by solving the equation, that is, by solving the same boundary value problem, the vibration characteristics of the rotating structure of different geometric shapes are obtained. By solving the free vibration characteristics of the rotating structure under different boundary conditions, and comparing with the results of the relevant literature and the results of the finite element method, the proposed method and the unified analysis model of the proposed method are verified. A unified analytical model of the dynamics of a rotating plate-cylindrical shell coupled structure under complex boundary conditions/ coupling conditions is constructed. The six displacement tolerance functions of the rotating plate and the cylindrical shell structure are described by the two-dimensional spectral method, and the complex boundary conditions of the rotating plate and the cylindrical shell are respectively modeled. A three-dimensional elastic coupler with a linear stiffness and a rotational stiffness is used to describe the compatibility condition of the plate-shell connection prior to connecting the common side. The three-dimensional elastic coupler is described by four kinds of coupling springs distributed along the common boundary, and the coupling effect of bending moment, transverse shearing, in-plane shearing and longitudinal shearing is considered in detail, and various coupling conditions of the structural system can be realized by changing the value of the corresponding spring. In the end, the method of Rayleigh-Ritz method is used to solve the double-modified triangular solution of the dynamic problem of the plate-shell coupling structure. The numerical results of this paper are compared with other literature and the results of the finite element method to test and construct the analytical model. In this paper, the forced vibration response of the coupling structure of the rotating plate and the cylindrical shell is calculated and analyzed, and the effects of various coupling conditions, coupling positions and other structural parameters on the vibration response of the plate-shell coupling structure are studied. Finally, the relevant experimental bench is designed and built, and the vibration characteristics of the rotating plate (the concave-angle ring sector plate and the circular plate) and the elastic circular plate-cylindrical shell coupling structure are studied. The results of the experiment and the prediction results of this method are compared and analyzed to verify the proposed analytical method, and the special experimental phenomena and the cause of the experimental error are analyzed.
【學(xué)位授予單位】：哈爾濱工程大學(xué)
【學(xué)位級(jí)別】：博士
【學(xué)位授予年份】：2014
【分類(lèi)號(hào)】：TH113
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本文編號(hào)：2492852