指数型阻尼模型及其在钢筋混凝土结构动力分析中的应用

发布时间：2018-06-26 06:45

本文选题：粘滞阻尼 + 复阻尼　；参考：《北京交通大学》2013年博士论文

【摘要】：摘要：阻尼是振动系统的重要动力特性之一。经过了百余年来的发展,研究者们提出了多种阻尼模型的假设,每种阻尼模型都有各自的动力分析方法和适用范围。在工程实践中,粘滞阻尼模型因其数学上的简便性而广泛地用来描述振动系统中的阻尼特性。然而,该模型假设阻尼力与瞬时速度相关,计算出的每周能量损失与外激励频率成正比,这并不能真实地反映许多工程材料或结构复杂的阻尼耗能特性。因此,深入研究其它形式的阻尼模型及其相应的动力分析方法,以期能够更好地描述振动系统的阻尼特性是土木工程和其它相关领域的重要课题。针对经典的粘滞阻尼理论在描述固体材料的阻尼耗能特性中的局限性,本文引入了一种更加合理的指数型阻尼模型来描述混凝土这种弱粘弹性材料的阻尼耗能特性。在讨论固体材料阻尼耗能机理的基础上,通过理论分析,建立含有指数型阻尼系统的运动学方程,并发展了指数型阻尼系统的动力分析方法以及阻尼参数识别方法。最后通过试验研究,识别出混凝土材料的松弛因子,验证了该模型对描述混凝土材料阻尼特性的适用性。本文的主要内容如下：首先,研究了复阻尼理论在描述固体材料阻尼耗能的特点,讨论了复阻尼系统的动力分析方法以及目前复阻尼理论在数学描述上存在的问题。根据对偶原则,结合高斯积分和精细积分的基本方法,给出了复阻尼系统动力方程的时程积分递推表达式,并对复阻尼动力方程时程积分的稳定性问题做进一步探讨。其次,研究了指数型阻尼系统运动方程的时程分析方法。基于一种无条件稳定的微分求积法,给出了这种非粘滞阻尼系统的逐步积分表达式,得到一种兼顾精度和效率且适用性更强的数值积分方法。第三,研究了指数型阻尼系统频域计算方法。根据离散傅立叶变换(DFT)的基本理论,通过引入拟力法来处理非零初始条件,有效地将DFT/FFT法扩展到指数型阻尼系统中去,得到了更广泛适用的频域分析方法。第四,基于拟变分原理,通过理论推导,建立了含有指数型阻尼系统的运动方程,为后面提出的指数型阻尼模型的阻尼参数识别方法提供了理论支持。第五,针对目前指数型阻尼模型参数识别方法的不足,提出了具有比例阻尼系数矩阵的指数型阻尼模型,并给出了一种新的松弛因子的迭代计算方法。结合有限元模型修正法,通过数值试验验证了本文方法的有效性。最后,对一组钢筋混凝土悬臂梁进行振动测试试验,通过本文提出的指数型阻尼模型的参数识别方法,识别出了适合于描述混凝土材料的阻尼参数。进一步讨论本文提出的指数型阻尼模型对混凝土这种弱粘弹性材料的阻尼特性的描述能力,与此同时也验证了各章算法的有效性和正确性。
[Abstract]:Abstract: damping is one of the most important dynamic characteristics of a vibration system. After more than a hundred years of development, researchers have proposed a variety of damping models. Each damping model has its own dynamic analysis method and scope of application. In engineering practice, the viscous damping model is widely used to describe the vibration because of its mathematical simplicity. However, the model assumes that the damping force is related to the instantaneous velocity, and the calculated energy loss is proportional to the external excitation frequency, which does not truly reflect the complex damping energy dissipation characteristics of many engineering materials or structures. Therefore, the damping models of other forms and their corresponding dynamic analysis methods are studied in depth. In order to better describe the damping characteristics of vibration systems, it is an important topic in civil engineering and other related fields.
In view of the limitation of the classical viscous damping theory in describing the damping energy characteristics of solid materials, a more reasonable exponential damping model is introduced to describe the damping energy dissipation characteristics of the weak viscoelastic material of concrete. On the basis of discussing the damping energy mechanism of solid material, a theoretical analysis is made to establish a reference point. The kinematic equation of the digital damping system is developed, and the dynamic analysis method of the exponential damping system and the identification method of damping parameters are developed. Finally, the relaxation factor of the concrete material is identified by the experiment. The applicability of the model to the damping characteristic of the concrete material is verified. The main contents of this paper are as follows:
First, the characteristics of damping theory of complex damping in describing damping energy of solid materials are studied. The dynamic analysis method of complex damping system and the existing problems in the mathematical description of complex damping theory are discussed. According to the dual principle, the time history integral of the dynamic equation of the complex damping system is given by combining the basic method of Gauss integral and fine integral. The recurrence expression is also discussed, and the stability of the time integration of the complex damping dynamic equation is further discussed.
Secondly, the time history analysis method of the motion equation of an exponential damping system is studied. Based on an unconditionally stable differential quadrature method, the progressive integral expression of this kind of non viscous damping system is given, and a numerical integral square method which gives consideration to the accuracy and efficiency and more applicability is obtained.
Third, the frequency domain calculation method of exponential damping system is studied. According to the basic theory of discrete Fu Liye transform (DFT), by introducing the pseudo force method to deal with the non zero initial conditions, the DFT/FFT method is effectively extended to the exponential damping system, and a more widely applicable frequency domain analysis method is obtained.
Fourth, based on the quasi variational principle, the equation of motion with exponential damping system is established through theoretical deduction, which provides theoretical support for the damping parameter identification method of the exponential damping model.
Fifth, an exponential damping model with proportional damping coefficient matrix is proposed in view of the shortage of parameter identification method of exponential damping model, and an iterative calculation method of a new relaxation factor is given. The validity of this method is verified by numerical experiments.
Finally, the vibration test of a set of reinforced concrete cantilever beam is carried out, and the damping parameters suitable for describing the concrete material are identified by the parameter identification method of the exponential damping model proposed in this paper. The damping characteristic of the weak viscoelastic material, which is proposed by the exponential damping model proposed in this paper, is further discussed. Capability, at the same time, it also verifies the validity and correctness of the algorithms in each chapter.
【学位授予单位】：北京交通大学
【学位级别】：博士
【学位授予年份】：2013
【分类号】：TU375;TU311.3

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