基于Rayleigh-Ritz算法的梁裂缝损伤识别及试验研究

结构动态特性的变化则预示结构出现损伤，基于Ritz线性近似，文中提出一种裂缝损伤识别的方法，用以识别结构裂缝损伤位置及损伤程度。该方法分两步：首先用模态子空间近似关系．消去模态应变能表达式中的整体刚度矩阵和整体质量矩阵，避免模型误差对识别结果的影响。再采用计算向量空间夹角的方法分离损伤位置与损伤程度的耦合影响，进而识别出单元裂缝损伤位置；其次，识别损伤程度采用二次线性规划方法，不再计算特征值灵敏度。线性约束条件保证了二次规划问题的解是唯一的。模拟筒支梁几种裂缝损伤情况进行数值计算与模态试验，利用所得模态参数对该算法程序进行了验证，识别出了裂缝损伤的确切位置及损伤程度，并进行了误差对比。结果表明，该算法由于不用整体结构的数值模型，从而避免了边界条件、连接条件及材料特性参数等因素对识别结果的干扰，识别精度得到提高，将其用于结构损伤识别是可行的。

Damage identification and experimental study on the beam suffered from crack damage by Rayleigh-Ritz algorithm

The change of dynamic characteristics predicts structural damage.Based on Ritz linear approximation,a method is proposed for identifying crack damage location and its severity.With model subspace approximation,model strain energy expression does not include the global stiffness and mass matrices,and model error is eliminated,and the coupling influence of damage location and severity is also separated,and damage location is recognized.Damage severity is identified with the quadratic linear programming,and the linear restrain conditions insure the solution of the quadratic programming problem exclusive. Numerical computation and model experiment are conducted on a simple-supported beam,and has found the exact location and seveity of crack damage,error comparison is implemented.It demonstrates that the method has better identification precision.The global numerical model matrix is not involved in the damage equations.Boundary conditions,joint conditions and material characteristic parametres have no interference on identification results.The method is feasible to structural damage identification.