考虑阻尼影响的修正CD-Newmark组合算法数值特性研究

显-隐式组合数值积分算法结合了显式算法无需迭代和隐式算法无条件稳定的各自优点,是结构抗震拟动力试验顺利运行的关键.在对传统显式中央差分法和隐式Newmark β组合算法进行参数修正的基础上,建立了修正CD-Newmark算法,考虑阻尼的影响分析了组合算法的稳定性条件、周期失真率和数值阻尼比,分别得到了试验子结构的稳定性条件和计算子结构无条件稳定的参数合理取值范围,并对计算精度进行了分析.通过算例分析验证了算法的数值特性,从而初步解决了CD-Newmark算法存在稳定性界限过严的问题,为结构抗震拟动力混合试验提供了研究参考.     

等效力控制方法及其在混合试验中的应用

对于大型复杂结构的实时(拟动力)子结构试验,更适宜用无条件稳定的逐步积分方法。隐式逐步积分方法通常是无条件稳定的,然而需要复杂耗时的迭代求解非线性方法。为了避免迭代过程,等效力控制方法用反馈控制求解非线性方程,使隐式逐步积分方法在实时子结构试验中的应用成为可能。本文首先以平均加速度法为例介绍等效力控制方法的原理、关键参数的选取;然后介绍基于等效力控制的能量守恒子结构试验方法和隐式中点法;最后介绍这些方法在以防屈曲支撑阻尼器为试件的单自由度简化结构、以磁流变阻尼器为试件的海洋平台结构的实时子结构试验,以及装配式钢筋混凝土剪力墙结构和框支配筋砌块短肢剪力墙结构拟动力试验中的应用。研究结果表明:这三种等效力控制方法都具有很好的精度,等效力控制方法相对于中心差分法具有更好的稳定性。     

实时子结构实验的研究与应用

最近出现的结构控制装置,其中很多被动控制装置的性能都与速度有关,甚至有的还与加速度有关;采用反馈控制的主动、半主动控制装置,其控制力更是与时间相关,因此无法采用伪动力实验测试这些控制装置的性能或减振效果.实时子结构实验对试件进行实时加载,可以准确反映速度相关型试件的性能.由于试件性能的速度相关性和实验加载的实时性,使得实时子结构实验在逐步积分算法、实验系统累积误差、实验系统的加载控制等方面比伪动力实验更加复杂,另外还会出现系统时间滞后和加载系统与试件相互作用等新问题.根据实时子结构实验研究的关键科学问题介绍其研究进展及其应用,并指出有待进一步研究的问题.     

高阶单步实时动力子结构试验技术研究

结构联机试验可分为两类：拟静力及拟动力试验技术,它们都需要建立一套显式的逐步积分算法。国内外学者在这方面已经进行了许多的研究,取得了很好的成果。随着振动控制技术在结构工程上的应用,一些速度相关型的装置开始用于被控系统,它给原有的实时子结构试验带来了新问题。如何建立更好的高精度、无条件稳定的实时动力子结构试验算法日趋重要。本文在前人早期高阶单步逐步积分算法研究成果的基础上,提出了一种新的高阶单步实时动力子结构试验算法。数值模拟分析表明,新算法不仅是显式的,而且具有高精度、无算法阻尼、无超越现象等算法特点,均比目前所见到的已有算法优越。如果能实现实时子结构试验,就能同时控制位移和速度,则应用本文算法必将取得更好的试验结果。     

隔震桥梁子结构拟动力实验中加载速率的影响因素研究

本研究运用DSP高速数字信号处理器的实时信号处理与控制技术,研究了基于速度控制法、OS数值积分法和相应的实验误差控制法的子结构拟动力实验系统。该试验系统对动力加载装置采用速度控制,在加载过程中考虑了加载速率对实验结果的影响,使隔震橡胶支座的速度相关性能在试验中得到充分体现,同时采用OS数值积分法,充分地减少了试验的时滞误差,提高了试验精度。并通过不同加载速率的子结构拟动力实验研究了天然橡胶支座、高阻尼橡胶隔震支座和超高阻尼橡胶隔震支座对桥梁的隔震效果,在对实验结果进行分析对比后,定量地研究了不同的加载速率对隔震桥梁子结构拟动力实验结果的影响。     

隐式时间积分方法的拟动力实验

本文介绍了采用隐式时间积分方法实现的拟动力实验。目前拟动力实验中所用的时间积分方法是显式条件稳定的，所以时间步Δｔ的选择受到试件刚度和自由度的限制，对于刚度大自由度很多的试件需采用很小的Δｔ，而Δｔ太小将造成实验累积误差增大，实验结果失真。隐式时间积分方法是无条条件稳定的Δｔ的选择不受试件特性的限制，可以比显式算法的稳定极限大很多，从而拓宽了拟动力的应用范围。     

采用微机开发的拟动力实验

本文介绍了在哈尔滨建筑大学力学与结构实验中心采用微机开发的拟动力实验。将力学与结构实验中心原有的大型电液伺服结构实验系统与微机进行联机，从而实现了多自由度结构的拟动力实验。文中介绍的拟动力实验的试件为某电厂４０米高的筛碎贮仓１：６模型，只取出结构底层的榀，具有两具自由度，所以实难同应用了子结构方法，数值积分方法采用了ＰＣＭ－Ｎｅｗｍａｒｋ法。实验结果与分析结果吻合良好，说明拟动力实验系统的开发是成     

基于振动台的动力子结构试验界面反力获取方法

基于振动台的实时子结构动力试验是一种新型的结构动力试验方法.该试验方法引入了“子结构”这一概念,不仅减小了常规振动台试验对于试验规模的限制,而且克服了拟动力子结构试验中无法考虑加载速率影响的问题.由于该试验方法将整体结构拆分为数值子结构和物理子结构两部分,二者之间通过交界面相互作用力实现实时数据交互,以保证子结构体系与...     

基于Rosenbrock的耦合积分方法及其在实时子结构试验中的应用

作为一种集计算机模拟和物理试验于一体的新型混合试验方法,实时子结构试验在过去20年得到迅速发展.该试验方法的关键在于如何保证数值子结构和试验子结构的实时耦联.对于复杂结构来说,更需要高效的数值积分方法以确保每步计算在一个采样步长内完成.鉴于此,本文在Rosenbrock实时积分方法的基础上,提出了一种具有完全并行计算格式的耦合积分方法,并基于单自由度分离质量模型分析了该方法的收敛性;再通过对三自由度分离质量模型的数值模拟,验证了该方法的收敛性;最后,在多自由度试验平台上完成了两自由度结构的实时子结构试验.理论分析、数值模拟及实时子结构试验表明,该方法具有良好的稳定性和2阶精度,与直接积分方法相比更适用于复杂结构的实时子结构试验.     

子结构地震模拟振动台混合试验原理与实现

为了解决地震模拟振动台承载能力及台面尺寸对大型结构试验的限制,扩展振动台的功能,本文提出了子结构地震模拟振动台混合试验方法、试验过程及实时数值积分方法,并给出了试验子结构边界条件的两种模拟形式.通过一个简单框架结构的地震模拟振动台试验和子结构混合加载试验验证了该方法的可行性,并指出了该试验方法的主要技术问题.混合试验方法通过子结构技术和振动台试验相结合,解决了目前的地震模拟振动台试验和拟动力试验在设备规模和加载速度上的局限性.     

Operator‐splitting method for real‐time substructure testing

It has been shown that the operator‐splitting method (OSM) provides explicit and unconditionally stable solutions for quasi‐static pseudo‐dynamic substructure testing. However, the OSM provides only an explicit target displacement but not an explicit target velocity, so that it is essentially an implicit method for real‐time substructure testing (RST) when the velocity‐dependent restoring force is considered. This paper proposes a target velocity formulation based on the forward difference of the predicted displacements so as to render the OSM explicit for RST. The stability and accuracy of the resulting OSM‐RST algorithm are investigated. It is shown that the OSM‐RST is unconditionally stable so long as the non‐linear stiffness and damping are of the softening type (i.e. the tangent stiffness and damping never exceed the initial values). The stability of the OSM‐RST for structures with infinite tangent damping coefficient or stiffness is also proved, and the stability of the method for MDOF structures with a non‐classical damping matrix is demonstrated by an energy criterion. The effects of actuator delay and compensation are analysed based on the bilinear approximation of the actuator step response. Experiments on damped SDOF and MDOF structures verify that the stability of the OSM‐RST is preserved when the experimental substructure generates velocity‐dependent reaction forces, whereas the stability of real‐time substructure tests based on the central difference method is worsened by the damping of the specimen. Copyright © 2005 John Wiley & Sons, Ltd.     

A family of explicit algorithms for general pseudodynamic testing

A new family of explicit pseudodynamic algorithms is proposed for general pseudodynamic testing. One particular subfamily seems very promising for use in general pseudodynamic testing since the stability problem for a structure does not need to be considered. This is because this subfamily is unconditionally stable for any instantaneous stiffness softening system, linear elastic system and instantaneous stiffness hardening system that might occur in the pseudodynamic testing of a real structure. In addition, it also offers good accuracy when compared to a general second-order accurate method for both linear elastic and nonlinear systems.     

一种基于离散控制理论的无条件稳定显式算法

基于离散控制理论,结合CR法和RST法提岀一种无条件稳定的动力学显式新算法.以算法精度和稳定性为条件,通过离散传递函数推导参数表达式和极点,使得新算法可满足零振幅衰减率和零周期延长率.算法参数α和γ作为传递格式选择参数,当α和γ分别取1时,新算法对应CR法和RST法的位移速度表达式.对新算法的精度和稳定性理论分析表明:...     

Modified state–space procedures for pseudodynamic testing

The existing on‐line numerical integration algorithms are derived from the Newmark method, which is based on an approximation of derivatives in the differential equation. The state–space procedure (SSP), based on an interpolation of the discrete excitation signals for piecewise convolution integral, has been confirmed as more reliable than the Newmark method in terms of numerical accuracy and stability. In an attempt to enhance the pseudodynamic test, this study presents an on‐line integration algorithm (referred to as the OS–SSP method) via an integration of the state–space procedure with Nakashima's operator‐splitting concept. Numerical stability and accuracy assessment of the proposed algorithm in addition to the explicit Newmark method and the OS method were investigated via an eigenvalue, frequency‐domain and time‐domain analysis. Of the on‐line integration algorithms investigated, the OS–SSP method is demonstrated as the most accurate method with an acceptable stability (although not unconditionally stable) characteristic. Therefore, the OS–SSP method is the most desirable method for pseudodynamic testing if the numerical stability criterion (Δt/T⩽0.5) is ensured for every vibration mode involved. Copyright © 2001 John Wiley & Sons, Ltd.     

Implicit time integration for pseudodynamic tests

The use of unconditionally stable implicit time integration techniques for pseudodynamic tests has been recently proposed and advanced by several researchers. Inspired by such developments, a pseudodynamic test scheme based on an unconditionally stable implicit time integration algorithm and dual displacement control is presented in this paper. The accuracy of the proposed scheme is proved with error-propagation analysis. It is shown by numerical examples and verification tests that the error-correction method incorporated can eliminate the spurious higher-mode response, which can often be excited by experimental errors. The practicality of the proposed scheme lies in the fact that the implementation is as easy as that of explicit schemes and that the convergence criteria required are compatible with the accuracy limits of ordinary test apparatus.     

Energy-consistent integration method and its application to hybrid testing

The time-integration algorithm is an indispensable element to determine response of the boundary of the numerical as well as physical parts in a hybrid test. Instability of the time-integration algorithm may directly lead to failure of the test, so stability of an integration algorithm is particularly important for hybrid testing. The explicit algorithms are very popular in hybrid testing, because iteration is not needed. Many unconditionally stable explicit-algorithms have been proposed for hybrid testing. However, the stability analysis approaches used in all these methods are valid only for linear systems. In this paper, a uniform formulation for energy-consistent time integrations, which are unconditionally stable, is proposed for nonlinear systems. The solvability and accuracy are analyzed for typical energy-consistent algorithms. Some numerical examples and the results of a hybrid test are provided to validate the effectiveness of energy-consistent algorithms.     

On the accuracy of an implicit algorithm for pseudodynamic tests

The error-propagation characteristics of an implicit time integration algorithm in pseudodynamic testing are examined. It is shown that the implicit algorithm is superior to explicit integration algorithms in terms of experimental error amplification. The influence of systematic experimental errors is studied and methods for controlling these errors are examined. In spite of the fact that the implicit algorithm is unconditionally stable, it is shown that the integration time interval in a pseudodynamic test is limited by the calibration range of the electronic hardware as well as the degree of participation of the higher modes. Furthermore, the tolerance for experimental errors decreases as the integration time interval increases.     

Stability and accuracy analysis of the central difference method for real‐time substructure testing

The central difference method (CDM) that is explicit for pseudo‐dynamic testing is also believed to be explicit for real‐time substructure testing (RST). However, to obtain the correct velocity dependent restoring force of the physical substructure being tested, the target velocity is required to be calculated as well as the displacement. The standard CDM provides only explicit target displacement but not explicit target velocity. This paper investigates the required modification of the standard central difference method when applied to RST and analyzes the stability and accuracy of the modified CDM for RST. Copyright © 2005 John Wiley & Sons, Ltd.     

Pseudodynamic testing of strain-softening systems with adaptive time steps

A structure may exhibit a severe strain-softening behaviour when subjected to strong earthquake excitation. Pseudodynamic testing of such structures using an implicit time-integration algorithm may be conceived of as a problem, since the Newton-type iterations, which are often required when structural non-linearity develops, may not converge under these circumstances. An unconditionally stable implicit time-integration algorithm implemented with Newton-type iterations is analysed to provide an insight into this problem. A simple convergence condition is derived to detect possible divergence. The condition is shown to be a sufficient criterion for convergence for general multiple-degree-of-freedom structures, and it is used later on to develop an adaptive time-stepping strategy to avoid divergence under severe strain-softening conditions. The implementation of this technique for pseudodynamic testing is presented. As demonstrated by numerical examples, the algorithm proves to be effective and reliable.     

A two-step unconditionally stable explicit method with controllable numerical dissipations

A family of unconditionally stable direct integration algorithm with controllable numerical dissipations is proposed. The numerical properties of the new algorithms are controlled by three parameters α, β and γ. By the consistent and stability analysis, the proposed algorithms achieve the second-order accuracy and are unconditionally stable under the condition that α≥-0.5, β≤ 0.5 and γ≥-(1+α)/2. Compared with other unconditionally stable algorithms, such as Chang's algorithms and CR algorithm, the proposed algorithms are found to be superior in terms of the controllable numerical damping ratios. The unconditional stability and numerical damping ratios of the proposed algorithms are examined by three numerical examples. The results demonstrate that the proposed algorithms have a superior performance and can be used expediently in solving linear elastic dynamics problems.