【摘要】：摘要：基于結(jié)構(gòu)動力學(xué)理論的傳統(tǒng)結(jié)構(gòu)損傷識別方法已經(jīng)在工程實際中得到廣泛的應(yīng)用,成為結(jié)構(gòu)損傷識別的主要方法。這種方法盡管較為有效但也存在缺點。首先提取和測量誤差經(jīng)常對結(jié)構(gòu)振動模態(tài)數(shù)據(jù)造成較大的負(fù)面影響,其次結(jié)構(gòu)模態(tài)振動對于結(jié)構(gòu)的少數(shù)低頻激振依賴較大。工程經(jīng)驗表明只有當(dāng)損傷發(fā)展到足夠大程度時低階模態(tài)參數(shù)對于結(jié)構(gòu)損傷的力學(xué)響應(yīng)才足夠顯著以致于被觀測到,而此時結(jié)構(gòu)已經(jīng)處于極不安全的狀態(tài)。基于以上原因本文探討了一種基于偏移成像原理和彈性波傳播的結(jié)構(gòu)損傷探測方法。這種方法是局部損傷探測技術(shù)中的一種,自上世紀(jì)80年代起廣泛應(yīng)用于地球物理勘探領(lǐng)域進行復(fù)雜地質(zhì)構(gòu)造以及各種礦藏的識別與探測,并取得了良好的識別效果。如果將地球內(nèi)部空間看做工程結(jié)構(gòu),將各種地質(zhì)構(gòu)造以及不良地質(zhì)體看做結(jié)構(gòu)內(nèi)部的各種損傷,就可以將這種方法類似的應(yīng)用到工程結(jié)構(gòu)損傷識別中。主要研究成果如下： 1由二維標(biāo)量波動方程推導(dǎo)了基于偽譜法零偏移距成像記錄的常速介質(zhì)中損傷成像公式的解析形式和有限差分形式；根據(jù)爆炸反射界面原理用混合法推導(dǎo)了上行波波動方程成像公式的解析與數(shù)值表達式；討論了二維均勻各向同性介質(zhì)二階彈性波動方程的規(guī)則網(wǎng)格有限差分公式并分析了有限差分格式的穩(wěn)定性、相容性、收斂性、數(shù)值頻散性、數(shù)值奇異性、各向異性等數(shù)值特點；分析了一階波動方程的交錯網(wǎng)格有限差分方法；以板式結(jié)構(gòu)中的單個裂縫損傷作為數(shù)值算例用兩種方法進行了偏移成像；得到了不同時刻的波場快照圖和零偏移距記錄；分析了波場振幅、能量、位移、頻率、速度、相位、波場應(yīng)力隨著損傷變化的情況；分析了動應(yīng)力集中系數(shù)在損傷周圍的變化情況；最后利用疊后零偏移距記錄成像方法對不同類型的壩體病害進行探測。 2討論了能適應(yīng)相對復(fù)雜損傷的疊后成像方法。疊后深度偏移成像包括疊后逆時深度偏移和新的混合法深度偏移；以二階三維波動方程為例推導(dǎo)了疊后逆時深度偏移波場成像的解析和離散表達式以及穩(wěn)定性條件；推導(dǎo)了由速度應(yīng)力表示的一階三維彈性波動方程的不規(guī)則網(wǎng)格差分離散方法；推導(dǎo)了具有四階空間精度和二階時間精度的不規(guī)則網(wǎng)格差分算子；采用混合法求解ω-x域中的二維單程波方程波場外推的數(shù)值形式；分析了數(shù)值頻散關(guān)系、穩(wěn)定性、傳播速度和震源吸收邊界處理；以帶有裂縫損傷板式結(jié)構(gòu)為例采用疊后深度成像方法得到了波場快照圖；分析了波場振幅、能量、位移、頻率、速度、相位、波場應(yīng)力隨著損傷變化的情況；分析了動應(yīng)力集中系數(shù)在損傷周圍的變化情況；最后將瑞雷波疊后深度成像方法應(yīng)用于海堤工程檢測用以查明海堤內(nèi)部存在的質(zhì)量隱患。 3以帶空洞損傷的板式結(jié)構(gòu)為例,推導(dǎo)了炮集疊前深度偏移和反射率成像表達式；以五節(jié)點四邊形網(wǎng)格劃分法為例對一維二階波動方程進行有限差分網(wǎng)格離散化；分析了有限差分格式的數(shù)值頻散與穩(wěn)定性；在頻率空間域和頻率波數(shù)域兩個空間中采用雙平方根算子推導(dǎo)了雙程一階波動方程成像與外推公式；分析了差分格式的數(shù)值頻散與穩(wěn)定性；采用裂步Hartley變換推導(dǎo)了一階二維上行波波動方程外推成像公式；分析了波場振幅、能量、位移、頻率、速度、相位、波場應(yīng)力隨著損傷變化的情況；分析了動應(yīng)力集中系數(shù)在損傷周圍的變化情況；得到損傷區(qū)域的波場快照成像圖；最后采用疊前深度偏移對賓館地基不良地質(zhì)現(xiàn)象進行探測與識別。 4推導(dǎo)了三種疊前時間偏移成像表達式以及成像條件；分析了實現(xiàn)疊前時間偏移技術(shù)的工作步驟、關(guān)鍵技術(shù)參數(shù)和影響因素；作出了不同時刻波場快照與偏移成像圖；分析了波場振幅、能量、位移、頻率、速度、相位、波場應(yīng)力隨著損傷變化的情況；得到損傷區(qū)域的波場快照圖；最后應(yīng)用疊前逆時偏移方法對隧道不良地質(zhì)構(gòu)造進行探測和識別。
[Abstract]:Abstract: Traditional structural damage identification methods based on structural dynamics theory have been widely used in engineering practice and become the main method of structural damage identification.Although this method is more effective, it also has some shortcomings.Firstly, extraction and measurement errors often have a negative impact on structural vibration modal data. Structural modal vibration depends heavily on a few low-frequency excitations of the structure. Engineering experience shows that the mechanical response of low-order modal parameters to structural damage is significant enough to be observed only when the damage is large enough, and the structure is already in a state of extreme insecurity. A structural damage detection method based on migration imaging principle and elastic wave propagation is proposed. This method is one of the local damage detection techniques. It has been widely used in geophysical exploration since the 1980s to identify and detect complex geological structures and various mineral deposits, and has achieved good results. Internal space is regarded as engineering structure, and all kinds of geological structures and unfavorable geological bodies are regarded as various kinds of damage in the structure. This method can be applied to identifying the damage of Engineering structure.
1. The analytical form and finite difference form of damage imaging formula in constant velocity medium based on pseudospectral zero offset imaging record are deduced from two-dimensional scalar wave equation; the analytical and numerical expressions of the imaging formula of upstream wave equation are deduced by hybrid method according to the principle of explosive reflection interface; and the two-dimensional homogeneous isotropy is discussed. Regular grid finite difference formulas for second-order elastic wave equations in media are presented and the numerical characteristics of the finite difference schemes, such as stability, compatibility, convergence, numerical dispersion, numerical singularity and anisotropy, are analyzed. Numerical examples are used to migrate images by two methods; snapshots and zero offset records of wave field at different times are obtained; amplitude, energy, displacement, frequency, velocity, phase and stress of wave field are analyzed as the damage changes; dynamic stress concentration factor around the damage changes are analyzed; finally, zero offset after stack is used. The migration distance recording method is used to detect different types of dam diseases.
2. The post-stack imaging method which can adapt to relatively complex damage is discussed. The post-stack depth migration imaging includes poststack reverse-time depth migration and new hybrid depth migration. The irregular mesh difference discretization method for the first-order three-dimensional elastic wave equation is presented; the irregular mesh difference operator with fourth-order spatial accuracy and second-order temporal accuracy is derived; the numerical form of wave field extrapolation for two-dimensional one-way wave equation in_-x domain is solved by the hybrid method; the numerical dispersion relation, stability and propagation velocity are analyzed. The amplitude, energy, displacement, frequency, velocity, phase and stress of wave field change with damage, and the variation of dynamic stress concentration factor around damage are analyzed. The Rayleigh wave post-stack depth imaging method is applied to the detection of seawall engineering to find out the hidden quality hazards in the seawall.
3. Taking the plate structure with cavity damage as an example, the formulas of prestack depth migration and reflectivity imaging are deduced; the one-dimensional second-order wave equation is discretized by finite-difference mesh method with five-node quadrilateral mesh generation method; the numerical dispersion and stability of finite-difference scheme are analyzed; the frequency-space domain and frequency-wave number are analyzed. The imaging and extrapolation formulas of two-way first-order wave equation are derived by using double square-root operator in two spaces in the domain; the numerical dispersion and stability of the difference scheme are analyzed; the extrapolation imaging formulas of first-order two-dimensional wave equation are derived by using split-step Hartley transform; the amplitude, energy, displacement, frequency, velocity, phase and wave field are analyzed. The variation of field stress with damage is analyzed; the variation of dynamic stress concentration factor around damage is analyzed; the snapshot image of wave field in the damage area is obtained; and the bad geological phenomena of hotel foundation are detected and identified by prestack depth migration.
Fourthly, three pre-stack time migration imaging expressions and imaging conditions are deduced; the working steps, key technical parameters and influencing factors of pre-stack time migration technology are analyzed; snapshots and migration imaging maps of wave field at different times are made; amplitude, energy, displacement, frequency, velocity, phase and stress of wave field change with damage are analyzed. Finally, the pre-stack reverse-time migration method is used to detect and identify the bad geological structure of the tunnel.
【學(xué)位授予單位】：中南大學(xué)
【學(xué)位級別】：博士
【學(xué)位授予年份】：2013
【分類號】：TU317;P631.4

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