线弹性系统的动态分布载荷识别研究

Due to the difficulty of performing direct measurements or calculations of the dynamic loads acting on vibrating structures in many practical situations, therefore, the identification technology of distributed dynamic load was proposed. Based on linear elastic theory, the project presents systematic study of identification technology for dynamic load distributed on Bernoulli-Euler beam and elastic thin plate. (1) Deriving the linear relationship between wavelet decomposition coefficients and discrete response values in frequency domain by introducing the wavelet function to discretize distributed load, therefore, simplifying the original identification model. (2) Proposing the piecewise formulation method to identify the load of divided structural intervals, respectively, aiming at solving ill-conditioned problem in boundary load identification. (3) Establishing the methodology of the arrangement of measuring points based on improving the accuracy and the stability of the identified results, by deducing the mathematical formula between the forward problem and the inverse problem, then, revealing the corresponding mechanical meaning. The established methodology can be used in theoretical guidance for multiple sensors placement. (4) Investigating ill-posed problem of the distributed dynamic load identification, pointing out the method to improve the identification accuracy. Meanwhile, summarizing the chief factors of affecting identification accuracy. This study is to improve and develop the theory of dynamical inverse problem and provide the technology support for the potential application of dynamic load identification problem, especially for ship structural engineering.

鉴于实际工程结构所受动载荷往往难以直接测量，动载荷识别技术得以提出。本课题在结构线弹性体系范畴内，以Bernoulli-Euler梁、弹性薄板结构为研究对象，对复杂分布动载荷识别问题展开基础性研究：引入小波函数对分布动载荷离散化，在频域中建立小波分解系数和离散响应信号之间的线性关系，简化了求解难度；针对结构边界区域的载荷识别的病态性，用分段表述的思想对结构进行区域分段，分别进行识别，减小病态性，提高边界载荷识别精度；探索动力学反问题和正问题之间的数学关系，揭示这种关系体现在力学中的涵义，提出基于改善识别结果的精度和稳定性的测量点选取理论，用于指导多传感器的优化配置；探讨分布动载荷识别过程中的不适定问题，研究改善识别精度的方法，同时针对动载荷识别精度的影响因素进行归纳和总结。通过本项研究，旨在从理论上完善和发展动力学反问题，同时为工程上特别船舶结构潜在的动载荷识别问题做技术铺垫。

实际工程结构所受动载荷往往难以直接测量，如力传感器的引入会阻碍结构的工作路径，或改变结构的固有特性等。在此背景下，动载荷识别技术得以提出，也即根据结构部分测量点响应信息和结构系统的动态特性来估计结构所受动载荷。随着现代工程设计的要求不断提高，工程结构上的动载荷识别问题也越来越受到关注。动载荷识别技术属于结构动力学中的第二类反问题，有着广泛的应用前景。结构上单点和多点动载荷的识别技术已日渐成熟，但是结构上连续分布动载荷的识别技术鲜有涉及，还有很长的路要走。本课题对工程结构上动载荷识别问题，分布动载荷识别问题开展了一些应用基础性研究，具体工作如下：对一维Euler-Bernoulli梁结构，提出稳态分布动载荷识别的小波级数分解法。在频域中，对待识别载荷函数进行小波级数分解，构建小波分解系数和频域响应的线性关系。通过挖掘动响应和动载荷的时间和空间上的内在联系，提出并应用基于模态空间分布的响应测量点选取方法。数值仿真表明，梁上分布动载荷识别满足精度要求，尤其在结合提出的测量点选取准则时，对噪声的敏感程度大大降低。