阶梯型截面Timoshenko梁边界支承的线性静力识别方法

Linear Static Identification Method of Boundary Support of Stepped Cross-Section Timoshenko Beam

研究了阶梯型截面Timoshenko梁边界支承刚度的挠度识别法和挠度-应变识别方法.利用Heaviside函数,得到了任意载荷作用下阶梯型截面Timoshenko梁弯曲变形的解析通解,并利用解析通解中的待定常数给出了梁边界支承刚度的表达式.基于阶梯型截面Timoshenko梁挠度和梁表面轴向应变的测量值,利用最小二乘法,得到确定弯曲通解中待定常数的线性代数方程组,进而分别建立了挠度识别法和挠度-应变识别方法,分析了测量点数目和位置以及梁变截面位置等对两种识别方法误差敏感度的影响,给出了挠度或轴向应变的最佳测量方案.通过数值试验,考察了两种识别方法的可靠性和适用性,结果表明:挠度-应变识别方法对系统测量误差具有较好的鲁棒性,适用于实际工程中梁构件边界支承刚度的识别.

The methods of deflection-based identification and deflection-strain-based identification of the boundary supporting rigidities of the stepped cross-section Timoshenko beam are investigated, respectively. Based on the Heaviside function, the general analytical solutions of bending deformation of the stepped cross-section Timoshenko beam subjected to arbitrary transversal load are obtained, and the supporting rigidities of the beam boundary are expressed analytically by the undetermined constants of the general analytical solution. Based on the measured values of the deflections and axial strains on the surfaces of the stepped cross-section Timoshenko beam, the linear algebraic equations for determining the undetermined constants of the general analytical solution are given with the least square method, and the deflection-based identification and deflection-strain-based identification of the boundary supporting rigidities of the stepped cross-section Timoshenko beam are established. The influences of the number and location of the measurement points as well as the locations where the beam cross-section changes on the error sensitivities of the two identification methods are analyzed, and the best measurement scheme is presented. The reliabilities and suitabilities of the two identification methods are examined with the numerical experiments, and it is revealed that the deflection-strain-based identification method possesses better robustness on measurement error of system and can be employed for boundary supporting rigidity identification in practices.