复杂工程结构损伤探测的叠加偏移理论及方法研究

发布时间：2018-09-15 06:52

【摘要】：摘要：基于结构动力学理论的传统结构损伤识别方法已经在工程实际中得到广泛的应用,成为结构损伤识别的主要方法。这种方法尽管较为有效但也存在缺点。首先提取和测量误差经常对结构振动模态数据造成较大的负面影响,其次结构模态振动对于结构的少数低频激振依赖较大。工程经验表明只有当损伤发展到足够大程度时低阶模态参数对于结构损伤的力学响应才足够显著以致于被观测到,而此时结构已经处于极不安全的状态。基于以上原因本文探讨了一种基于偏移成像原理和弹性波传播的结构损伤探测方法。这种方法是局部损伤探测技术中的一种,自上世纪80年代起广泛应用于地球物理勘探领域进行复杂地质构造以及各种矿藏的识别与探测,并取得了良好的识别效果。如果将地球内部空间看做工程结构,将各种地质构造以及不良地质体看做结构内部的各种损伤,就可以将这种方法类似的应用到工程结构损伤识别中。主要研究成果如下： 1由二维标量波动方程推导了基于伪谱法零偏移距成像记录的常速介质中损伤成像公式的解析形式和有限差分形式；根据爆炸反射界面原理用混合法推导了上行波波动方程成像公式的解析与数值表达式；讨论了二维均匀各向同性介质二阶弹性波动方程的规则网格有限差分公式并分析了有限差分格式的稳定性、相容性、收敛性、数值频散性、数值奇异性、各向异性等数值特点；分析了一阶波动方程的交错网格有限差分方法；以板式结构中的单个裂缝损伤作为数值算例用两种方法进行了偏移成像；得到了不同时刻的波场快照图和零偏移距记录；分析了波场振幅、能量、位移、频率、速度、相位、波场应力随着损伤变化的情况；分析了动应力集中系数在损伤周围的变化情况；最后利用叠后零偏移距记录成像方法对不同类型的坝体病害进行探测。 2讨论了能适应相对复杂损伤的叠后成像方法。叠后深度偏移成像包括叠后逆时深度偏移和新的混合法深度偏移；以二阶三维波动方程为例推导了叠后逆时深度偏移波场成像的解析和离散表达式以及稳定性条件；推导了由速度应力表示的一阶三维弹性波动方程的不规则网格差分离散方法；推导了具有四阶空间精度和二阶时间精度的不规则网格差分算子；采用混合法求解ω-x域中的二维单程波方程波场外推的数值形式；分析了数值频散关系、稳定性、传播速度和震源吸收边界处理；以带有裂缝损伤板式结构为例采用叠后深度成像方法得到了波场快照图；分析了波场振幅、能量、位移、频率、速度、相位、波场应力随着损伤变化的情况；分析了动应力集中系数在损伤周围的变化情况；最后将瑞雷波叠后深度成像方法应用于海堤工程检测用以查明海堤内部存在的质量隐患。 3以带空洞损伤的板式结构为例,推导了炮集叠前深度偏移和反射率成像表达式；以五节点四边形网格划分法为例对一维二阶波动方程进行有限差分网格离散化；分析了有限差分格式的数值频散与稳定性；在频率空间域和频率波数域两个空间中采用双平方根算子推导了双程一阶波动方程成像与外推公式；分析了差分格式的数值频散与稳定性；采用裂步Hartley变换推导了一阶二维上行波波动方程外推成像公式；分析了波场振幅、能量、位移、频率、速度、相位、波场应力随着损伤变化的情况；分析了动应力集中系数在损伤周围的变化情况；得到损伤区域的波场快照成像图；最后采用叠前深度偏移对宾馆地基不良地质现象进行探测与识别。 4推导了三种叠前时间偏移成像表达式以及成像条件；分析了实现叠前时间偏移技术的工作步骤、关键技术参数和影响因素；作出了不同时刻波场快照与偏移成像图；分析了波场振幅、能量、位移、频率、速度、相位、波场应力随着损伤变化的情况；得到损伤区域的波场快照图；最后应用叠前逆时偏移方法对隧道不良地质构造进行探测和识别。
[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.
【学位授予单位】：中南大学
【学位级别】：博士
【学位授予年份】：2013
【分类号】：TU317;P631.4

【参考文献】