發(fā)布時(shí)間：2018-01-17 18:01

  本文關(guān)鍵詞：激光輻照引起非Fourier熱傳導(dǎo)問(wèn)題的理論分析與計(jì)算　出處：《北京科技大學(xué)》2017年博士論文　論文類型：學(xué)位論文

  更多相關(guān)文章： 非Fourier熱傳導(dǎo)問(wèn)題解析解 Laplace-Hankel積分變換 熱波效應(yīng) 瞬態(tài)溫度場(chǎng) 瞬態(tài)熱應(yīng)力

【摘要】：激光作為一種特殊的定向高能束,己被廣泛應(yīng)用于很多工程領(lǐng)域,特別是在材料表面加工處理、生物醫(yī)學(xué)外科等方面.探討由激光輻照材料表面受熱而引起的材料內(nèi)部溫度場(chǎng)的變化以及瞬態(tài)熱應(yīng)力問(wèn)題已成為力學(xué)研究的一個(gè)重要課題.由于解析解要比數(shù)值解更為準(zhǔn)確和有效地直接反映出控制變量與時(shí)空坐標(biāo)以及材料、幾何等參數(shù)之間的關(guān)系,如何求出問(wèn)題的解析解一直以來(lái)是研究者所面臨的挑戰(zhàn)性問(wèn)題.然而,至今為止多限于在變換域上給出的解析解或者是一維空間問(wèn)題的解析解,而對(duì)高維空間問(wèn)題在原時(shí)空域上的解析解所見(jiàn)文獻(xiàn)研究甚少.本文針對(duì)不同傳熱介質(zhì),建立了考慮熱波效應(yīng)的空間軸對(duì)稱非Fourier熱傳導(dǎo)的數(shù)學(xué)模型,采用關(guān)于時(shí)空變量的積分變換方法,特別是以求出相關(guān)問(wèn)題的逆Laplace變換解析式為突破點(diǎn),獲得了所論問(wèn)題在原時(shí)空域內(nèi)的解析解,并且分析了均勻和非均勻材料的溫度場(chǎng)分布、估算了生物(皮膚)介質(zhì)中的熱損傷以及熱沖擊下考慮慣性力效應(yīng)的瞬態(tài)熱應(yīng)力等問(wèn)題,主要研究工作和成果如下：(1)研究了激光輻照在半無(wú)限大固體材料表面的問(wèn)題,建立了突加溫度和瞬時(shí)脈沖熱流兩種不同邊界條件下的非Fourier熱傳導(dǎo)模型,利用Laplace-Hankel變換及其逆變換,關(guān)鍵的突破是構(gòu)造出了相應(yīng)的逆Laplace變換的解析表達(dá)式,從而求得了問(wèn)題在原時(shí)空域上的單積分形式解析解；其解可準(zhǔn)確算出熱波前的位置,并清晰展現(xiàn)出材料內(nèi)部的溫度場(chǎng).還用隱格式差分方法數(shù)值解驗(yàn)證了本文解析求解的正確性.(2)針對(duì)局部圓形區(qū)域的激光輻照半無(wú)限大固體表面的非Fourier熱傳導(dǎo)問(wèn)題,利用積分變換法求得問(wèn)題在原時(shí)空域的精確解析解,并比較分析了溫度分布的云圖、等溫-流線圖及隨時(shí)間的演化規(guī)律.(3)分析了兩種不同加熱情形下激光輻照皮膚表面時(shí)非Fourier熱傳導(dǎo)問(wèn)題.考慮了血流灌注速度的影響,利用積分變換的方法,技巧性的構(gòu)造了相應(yīng)的逆Laplace變換的解析表達(dá)式,從而求出了問(wèn)題的解析解.進(jìn)而估算了皮膚熱損傷區(qū)域并與經(jīng)典熱傳導(dǎo)理論造成的皮膚熱損傷進(jìn)行比較.(4)針對(duì)功能梯度材料的非均質(zhì)性,研究了指數(shù)型功能梯度材料表面受到激光輻照的非Fourier熱傳導(dǎo)問(wèn)題.成功地求出了變系數(shù)的控制方程的初-邊值問(wèn)題在原時(shí)空域上的解析解,給出了溫度隨時(shí)間演化的溫度場(chǎng)云圖,并討論了非均勻參數(shù)對(duì)熱波傳播的影響.(5)研究了熱彈性材料表面受到激光輻照熱沖擊時(shí),非Fourier熱傳導(dǎo)下材料內(nèi)部的瞬態(tài)熱應(yīng)力場(chǎng)的分布問(wèn)題.考慮了動(dòng)態(tài)慣性效應(yīng),分別采用應(yīng)力解法和位移解法得到了均質(zhì)及功能梯度材料內(nèi)部的瞬態(tài)熱應(yīng)力解析解,并討論了瞬態(tài)熱應(yīng)力隨時(shí)間變化的規(guī)律以及材料非均勻性的影響.
[Abstract]:As a kind of special laser directed energy beam has been widely used in many engineering fields, especially in the processing of surface treatment materials, biomedical surgery. To investigate the changes of the heated surface laser irradiation caused by the material internal temperature field and transient thermal stress problem has become an important topic of mechanics. The analytical solution is more accurate than the numerical solution effectively and directly reflect the control variable and the space-time coordinates as well as materials, the relationship between geometric parameters, how to obtain the analytical solution of the problem has been a challenging problem faced by researchers. However, so far limited to give the analytical solutions in transform space or is the analytical solution of one dimensional space, and the high dimensional space to resolve the problem in the original space domain solution by literature research is little. According to the heat transfer medium is established considering The mathematical model of axial symmetric and non Fourier heat conduction of the heat wave effect of the space, by using the integral transform method on the temporal variables, especially in order to calculate the inverse Laplace transform formula related problems as the breakthrough point, and obtain the analytical theory of problem in the original time domain solution, and analyzes the temperature field distribution in homogeneous and heterogeneous materials the estimated biological (skin) problem of transient thermal inertia effect stress considering medium heat injury and heat shock, the main research work and results are as follows: (1) study on the laser irradiation in a semi infinite solid material surface, a non Fourier heat conduction model of sudden temperature and the instantaneous heat pulse under two different boundary conditions, using the Laplace-Hankel transform and its inverse transform, the key breakthrough is to construct the analytical expression of inverse Laplace transform to obtain the corresponding problems in the original. Single integral form of analytical space-time domain solution; the solution can accurately calculate the wave front position, and shows the temperature field inside the material. Using implicit difference method of numerical solutions are verified analytically. (2) according to the local laser irradiation circular area of semi infinite non thermal Fourier the large conduction solid surfaces, by using the integral transform method to obtain accurate analytical problems in the original time domain solution, and analyzed the temperature distribution nephogram, isothermal streamlines and evolution with time. (3) analysis of the Fourier heat conduction problem of non laser irradiation on skin surface of two different heating conditions. Considering the effect of blood perfusion rate, using the method of integral transform, construction techniques of analytical expression of inverse Laplace transform accordingly, so as to obtain analytic solutions of the problem. We have estimated the skin thermal damage zone and the The skin damage caused by thermal classical heat conduction theory are compared. (4) according to the heterogeneity of functionally graded materials, studied the surface index of functionally graded materials by non Fourier heat conduction problem of laser irradiation successfully. The analytic problem in the original time-space domain boundary value equation with variable coefficients of the initial control - the temperature field nephogram and the temperature evolution over time, and discussed the effect of non-uniform parameters on thermal wave propagation. (5) studied the thermal elastic material surface irradiated by the laser thermal shock, the transient thermal stress field distribution inside the material non Fourier heat conduction should be considered. The dynamic inertia effect. Using the stress method and the displacement method to get the transient heat inside homogeneous and functionally graded materials stress analytic solution, and discussed the transient thermal stress changing with time and the effect of material inhomogeneity.

【學(xué)位授予單位】：北京科技大學(xué)
【學(xué)位級(jí)別】：博士
【學(xué)位授予年份】：2017
【分類號(hào)】：O551.3;TN249

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