基于切比雪夫多项式模型的多自由度结构非线性恢复力时域识别

TIME DOMAIN NONLINEAR-RESTORING FORCE IDENTIFICATION FOR MDOF STRUCTURES WITH CHEBYSHEV POLYNOMIAL MODEL

结构非线性恢复力可直接描述其在动力荷载作用下损伤发生发展过程,传统的基于特征值抽取的结构识别方法严格来讲不适应于振动过程中出现损伤的情况。该文利用结构动力响应时程的切比雪夫多项式表示非线性恢复力,在结构质量等物理参数和恢复力模型未知时,提出利用最小二乘优化算法的多自由度结构在完整及非完整激励下非线性恢复力识别方法。对一个含磁流变阻尼器的多自由度数值模型和一个带磁流变阻尼器的四层框架结构的非线性恢复力进行了识别,在数值模拟中探讨了测量噪声对识别结果的影响,并与基于幂多项式模型的方法的结果进行了对比。结果表明,所提出的非线性恢复力识别方法能对结构的非线性恢复力进行有效识别,识别精度高,可用于工程结构在强动力荷载作用下的损伤发生发展过程的监测与识别,并对结构耗能进行定量评估。

A nonlinear restoring force describes directly the initiation and development procedure of structural damage under dynamic loadings and, strictly speaking, the conventional structural identification approaches based on eigenvalue or eigenvector extraction are not applicable for nonlinear dynamic systems due to the nonlinearity accompanying with the damage initiation and development. In this study, a Chebyshev polynomial model based on structural dynamic response time series is proposed to model the nonlinear restoring forces under complete and incomplete excitation scenarios. Without the use of any assumption on the nonlinear restoring model and mass distribution, the nonlinear restoring force is identified by the least square method under different excitation conditions. The feasibility and robustness of the proposed approaches were illustrated via numerical simulation with a multi-degree-of-freedom(MDOF) structure equipped with a magneto-rheological(MR) damper considering the effect of noise and dynamic test measurements with a 4-story steel frame equipped with two MR dampers to mimic structural nonlinear performance. Identification results are compared with that of the previously proposed power polynominal based approach. The results show that the proposed approach identifies the nonlinear restoring force with higher accuracy and provides a way for the damage initiation and development procedure monitoring and for the quantitative energy consumption evaluation of engineering structures under strong dynamic loadings.