本文選題：旋轉(zhuǎn)圓盤(pán) + 變分��； 參考：《東北大學(xué)》2012年碩士論文

【摘要】：圓盤(pán)部件是被廣泛應(yīng)用于航空、航天、造船、土建和機(jī)械等工業(yè)領(lǐng)域的基本結(jié)構(gòu)單元。隨著材料科學(xué)的迅速發(fā)展,新型材料的應(yīng)用日益廣泛,圓盤(pán)類(lèi)部件的在滿足使用強(qiáng)度的要求下厚度逐漸減小,以節(jié)省材料減輕重量。轉(zhuǎn)子轉(zhuǎn)盤(pán)是圓盤(pán)類(lèi)部件的典型代表,現(xiàn)代燃?xì)廨啓C(jī)中帶葉轉(zhuǎn)子,由于技術(shù)水平的進(jìn)步,更薄的轉(zhuǎn)盤(pán)、更高的轉(zhuǎn)動(dòng)速度使得轉(zhuǎn)子的橫向振動(dòng)以及幾何非線性振動(dòng)顯得更加突出。 對(duì)于圓盤(pán)類(lèi)部件的研究,一個(gè)重要方向就是圓盤(pán)的行波振動(dòng)問(wèn)題：另一個(gè)是振動(dòng)響應(yīng)問(wèn)題。本文針對(duì)中心固支旋轉(zhuǎn)圓盤(pán)行波振動(dòng)特性進(jìn)行研究,給出了旋轉(zhuǎn)圓盤(pán)行波振動(dòng)的解析方法、有限元數(shù)值仿真解法以及實(shí)驗(yàn)分析方法。針對(duì)靜止態(tài)中心固支圓盤(pán),給出了強(qiáng)迫振動(dòng)方程,應(yīng)用Galerkin截?cái)喾ㄇ蠼饬藛吸c(diǎn)諧波激勵(lì)、定點(diǎn)響應(yīng)問(wèn)題。采用模態(tài)實(shí)驗(yàn)理論,對(duì)本文采用的解析方法、有限元仿真進(jìn)行對(duì)比驗(yàn)證。 本文的主要研究?jī)?nèi)容大致可以歸為以下幾個(gè)方面： (1)根據(jù)彈性力學(xué)外力功及應(yīng)變能基本理論,建立考慮薄膜應(yīng)力影響的旋轉(zhuǎn)圓盤(pán)動(dòng)能—?jiǎng)菽芊匠?應(yīng)用拉格朗日方程建立旋轉(zhuǎn)圓盤(pán)橫向振動(dòng)控制方程,利用Galerkin截?cái)喾▽?duì)運(yùn)動(dòng)方程離散,求解圓盤(pán)固有頻率隨轉(zhuǎn)動(dòng)速度的變化規(guī)律,繪制Campbell曲線； (2)應(yīng)用有限元軟件ANSYS對(duì)旋轉(zhuǎn)圓盤(pán)振動(dòng)特性進(jìn)行數(shù)值仿真。包括：?jiǎn)卧?lèi)型的選取、材料參數(shù)的輸入、固有頻率、模態(tài)振型的求解方法。繪制了旋轉(zhuǎn)圓盤(pán)的Campbell曲線,與解析方法進(jìn)行對(duì)比,驗(yàn)證兩種方法的吻合度。 (3)對(duì)中心固支圓盤(pán)進(jìn)行單點(diǎn)諧響應(yīng)分析,基于Kirchhoff薄板理論由一點(diǎn)的應(yīng)力狀態(tài)推導(dǎo)彈性薄板的動(dòng)力學(xué)方程,通過(guò)坐標(biāo)變化計(jì)算出彈性圓板的自由振動(dòng)方程。應(yīng)用振型疊加法,將中心固支圓盤(pán)的振型函數(shù)用懸臂梁模型近似替代,將圓盤(pán)振動(dòng)方程轉(zhuǎn)化為多個(gè)單自由度無(wú)阻尼系統(tǒng)振動(dòng)的疊加。采用單點(diǎn)諧響應(yīng)分析理論,計(jì)算了圓盤(pán)定點(diǎn)對(duì)激勵(lì)的響應(yīng)位移,并繪制頻譜圖： (4)介紹了實(shí)驗(yàn)?zāi)B(tài)的理論基礎(chǔ)和實(shí)驗(yàn)?zāi)B(tài)分析的基本過(guò)程。對(duì)中心固支圓盤(pán),進(jìn)行靜止態(tài)實(shí)驗(yàn)?zāi)B(tài)分析與旋轉(zhuǎn)態(tài)振動(dòng)測(cè)量。得到了靜止態(tài)中心固支圓盤(pán)固有頻率、模態(tài)振型及旋轉(zhuǎn)態(tài)圓盤(pán)振動(dòng)時(shí)域曲線,頻響曲線。應(yīng)用激光測(cè)振儀,測(cè)量了旋轉(zhuǎn)圓盤(pán)的響應(yīng),繪制了瀑布圖,確定了轉(zhuǎn)動(dòng)圓盤(pán)的固有頻率,驗(yàn)證了離心剛化效應(yīng)的存在。
[Abstract]:Disc components are widely used in aviation, aerospace, shipbuilding, civil engineering and machinery and other industrial areas of the basic structural units. With the rapid development of material science, the application of new materials is becoming more and more extensive, and the thickness of disc components decreases gradually under the requirement of strength, so as to reduce the weight of materials. Rotor turntable is a typical representative of disc components. Due to the advancement of technology, thinner rotating disk and higher rotation speed, the transverse vibration and geometric nonlinear vibration of the rotor become more prominent. One important direction of the research on disk components is the traveling wave vibration of the disk and the other is the vibration response problem. In this paper, the vibration characteristics of rotating disk with fixed center are studied, and the analytical method, finite element numerical simulation method and experimental analysis method are given. In this paper, the forced vibration equation is given for the fixed disk in the center of static state. The problem of single point harmonic excitation and fixed point response is solved by using Galerkin truncation method. The modal experiment theory is used to verify the analytical method and finite element simulation. The main contents of this paper can be classified into the following aspects: 1) according to the basic theory of external force work and strain energy of elastic mechanics, the kinetic energy potential energy equation of rotating disk considering the effect of film stress is established, and the governing equation of lateral vibration of rotating disk is established by using Lagrange equation. The equation of motion is discretized by Galerkin truncation method, and the Campbell curve is drawn by solving the law of the change of the natural frequency of the disk with the rotational velocity. 2) the vibration characteristics of rotating disk are simulated by finite element software ANSYS. It includes the selection of element type, the input of material parameters, the natural frequency and the solution of modal mode. The Campbell curve of the rotating disk is drawn and compared with the analytical method to verify the coincidence of the two methods. The dynamic equations of elastic thin plates are derived from the stress state of one point based on Kirchhoff thin plate theory, and the free vibration equations of elastic circular plates are calculated by coordinate change. By using the mode superposition method, the mode shape function of the center-clamped disk is approximately replaced by the cantilever beam model, and the vibration equation of the disk is transformed into the superposition of the vibration of several single-degree-of-freedom undamped systems. Based on the theory of single point harmonic response, the response displacement of disk fixed point to excitation is calculated, and the spectrum diagram is plotted. The theoretical basis of experimental mode and the basic process of experimental modal analysis are introduced. The static experimental modal analysis and rotational vibration measurement were carried out for the central clamped disc. The time domain and frequency response curves of the fixed disk in the static state are obtained, including the natural frequency, the mode mode and the vibration time domain of the rotating disk. The response of the rotating disk was measured by using the laser vibration measuring instrument, the waterfall diagram was drawn, the natural frequency of the rotating disc was determined, and the existence of the centrifugal stiffening effect was verified.
【學(xué)位授予單位】：東北大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2012
【分類(lèi)號(hào)】：TH113.1

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