發(fā)布時(shí)間：2018-01-03 20:09

  本文關(guān)鍵詞：旋轉(zhuǎn)機(jī)械隨機(jī)參數(shù)動(dòng)力響應(yīng)的概率密度分析方法研究　出處：《河南工業(yè)大學(xué)》2012年碩士論文　論文類型：學(xué)位論文

  更多相關(guān)文章： 隨機(jī)參數(shù)轉(zhuǎn)子系統(tǒng) Riccati 傳遞矩陣法 概率密度 動(dòng)力響應(yīng)

【摘要】：隨機(jī)參數(shù)轉(zhuǎn)子動(dòng)力學(xué)問題正在受到越來越多國(guó)內(nèi)學(xué)者的關(guān)注，已經(jīng)成為轉(zhuǎn)子系統(tǒng)線性和非線性動(dòng)力學(xué)問題之后的重要研究課題。但以往的研究多以求得隨機(jī)參數(shù)結(jié)構(gòu)反應(yīng)的數(shù)值特征值為目標(biāo)，從全面反映隨機(jī)結(jié)構(gòu)反應(yīng)的概率信息的角度考察，這僅是對(duì)隨機(jī)結(jié)構(gòu)反應(yīng)的一種較為宏觀的把握，更為精細(xì)化的反映是對(duì)隨機(jī)參數(shù)結(jié)構(gòu)反應(yīng)概率密度的把握。本文以隨機(jī)攝動(dòng)Riccati傳遞矩陣法導(dǎo)出的隨機(jī)參數(shù)轉(zhuǎn)子系統(tǒng)動(dòng)力學(xué)響應(yīng)與隨機(jī)參數(shù)變量之間的函數(shù)關(guān)系式為基礎(chǔ)，研究了通過數(shù)值積分方法獲得了隨機(jī)參數(shù)轉(zhuǎn)子系統(tǒng)動(dòng)力響應(yīng)的概率密度的方法。主要研究?jī)?nèi)容和成果如下： 1.研究了在已知隨機(jī)參數(shù)變量聯(lián)合概率密度情況下的轉(zhuǎn)子系統(tǒng)動(dòng)力學(xué)響應(yīng)的概率分布的計(jì)算方法，運(yùn)用二次型、雅克比行列式及概率的相關(guān)知識(shí)，導(dǎo)出了用數(shù)值積分法計(jì)算動(dòng)力響應(yīng)概率密度的關(guān)鍵公式。 2.以MATLAB7.0為平臺(tái)，開發(fā)了基于攝動(dòng)Riccati傳遞矩陣法的隨機(jī)參數(shù)轉(zhuǎn)子系統(tǒng)動(dòng)力響應(yīng)概率密度計(jì)算程序。 3.基于該方法，以實(shí)驗(yàn)室的具有隨機(jī)可控電磁支撐的Bentley轉(zhuǎn)子為模型，計(jì)算分析了兩個(gè)隨機(jī)參數(shù)變量轉(zhuǎn)子系統(tǒng)動(dòng)力學(xué)響應(yīng)的概率密度，并與Monte Carlo模擬方法對(duì)比。結(jié)果表明：當(dāng)變異系數(shù)較小時(shí)，該分析方法具有很高的計(jì)算精度，且較隨機(jī)模擬方法具有計(jì)算量小、速度快的優(yōu)點(diǎn)；隨著變異系數(shù)的增大，，該方法的精度有一定的下降；當(dāng)變異系數(shù)達(dá)到0.30時(shí)，仍然保持著較高的精度（在10%以內(nèi)），能夠滿足工程實(shí)際的需要。 4.以鍋爐給水泵轉(zhuǎn)子為例，研究了兩端軸承的四個(gè)主剛度參數(shù)隨機(jī)變化情況下的轉(zhuǎn)子系統(tǒng)動(dòng)力響應(yīng)的概率密度，并與Monte Carlo模擬方法對(duì)比。通過這個(gè)工程實(shí)例，說明了該方法的精度和實(shí)用性。
[Abstract]:The problem of rotor dynamics with random parameters is attracting more and more attention from domestic scholars. It has become an important research topic after the linear and nonlinear dynamic problems of rotor systems, but most of the previous studies are aimed at finding the numerical eigenvalues of the structural responses of random parameters. From the point of view of reflecting the probability information of stochastic structural response, this is only a macroscopic grasp of stochastic structural response. The more detailed reflection is the grasp of the probability density of the random parameter structure response. In this paper, the dynamic response of the stochastic parameter rotor system derived by the stochastic perturbation Riccati transfer matrix method and the random parameter variable. Is based on the functional relationship of. The probability density of the dynamic response of a stochastic parameter rotor system is obtained by numerical integration method. The main contents and results are as follows: 1. The method of calculating the probability distribution of dynamic response of rotor system under the condition of joint probability density of known random parameter variables is studied, and the knowledge of quadratic form, Jacobian determinant and probability is used. The key formulas for calculating the probability density of dynamic response by numerical integration method are derived. 2. Based on the perturbed Riccati transfer matrix method, a program for calculating the probability density of the dynamic response of a stochastic parameter rotor system is developed on the platform of MATLAB7.0. 3. Based on this method, the probability density of dynamic response of two random parameter variable rotor systems is calculated and analyzed using the Bentley rotor with controlled electromagnetic support in the laboratory as the model. Compared with the Monte Carlo simulation method, the results show that the analysis method has high accuracy and less computational complexity than the random simulation method when the coefficient of variation is small. The advantage of speed; With the increase of the coefficient of variation, the precision of the method decreases to a certain extent. When the coefficient of variation reaches 0. 30, the accuracy is still high (less than 10%), which can meet the need of engineering practice. 4. Taking the boiler feedwater pump rotor as an example, the probability density of the dynamic response of the rotor system under the random variation of the four main stiffness parameters of the two ends bearings is studied. The method is compared with Monte Carlo simulation method. The accuracy and practicability of the method are illustrated by an engineering example.
【學(xué)位授予單位】：河南工業(yè)大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2012
【分類號(hào)】：TH113

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