基于二重切比雪夫多项式的多自由度系统SMA非线性恢复力识别

SMA nonlinear restoring force identification for MDOF structures under dynamic loadings with double Chebyshev polynomial

针对真实结构在动力荷载作用下恢复力模型难以用准确参数化形式描述问题,将结构非线性恢复力作为结构损伤及非线性行为的直接描述,提出基于二重切比雪夫多项式模型的多自由度体系非线性恢复力时域识别方法,实现结构质量信息完全未知及激励完整、非完整两种情况下多自由度系统非线性恢复力识别。通过带理想双旗形恢复力模型形状记忆合金(SMA)阻尼器两自由度数值模型的数值模拟与安装SMA阻尼器的钢框架模型动力实验结果验证该方法的识别效果,并与基于幂多项式模型方法进行对比。数值模拟验证中同时考虑测量噪声对识别结果影响。结果表明,该方法能对结构质量分布及在动力荷载作用下非线性恢复力进行有效识别,为结构在动力荷载作用下损伤发生、发展过程监测及结构耗能的定量评估提供方法。

The initiation and development of damage in an engineering structure under dynamic loadings is a typical nonlinear process. Due to the uniqueness of nonlinearity of different engineering structures,it is difficult to express the restoring force in a parametric form and it is highly desired to develop a general structural nonlinearity identification approach for structural damage detection in both qualitative and quantitative ways. A double Chebyshev polynomial model was employed to model the nonlinear restoring force and a time domain nonlinear shape memory alloy（ SMA） restoring force identification approach was proposed for MDOF structures under dynamic loadings when the mass distribution of the structure is unknown and the structure is completely or incompletely excited. The feasibility and robustness of the proposed approaches were illustrated via the numerical simulation of a MDOF structure equipped with a SMA damper with double flag-shaped nonlinear model considering the effect of noise and also via the dynamic test of a 4-story steel frame equipped with a SMA damper to mimic structural nonlinear performance. The numerical results were compared with those by the previously proposed power polynominal based approach. The results show that the proposed approaches are capable of identifying the nonlinearity and the mass distribution of the structure and are applicable for monitoring damage initiation and propagation process and quantitatively evaluating energy consuming during vibration of engineering structures under dynamic excitations.