减震设计与抗震设计RC框架结构抗地震倒塌能力对比

与传统抗震设计不同,结构的消能减震设计通过在结构上设置减震装置以消耗地震输入能量,达到减轻主体结构地震响应的目的,在满足相同的设计要求下,减震设计结构由于阻尼器的耗能作用,其截面尺寸或配筋较抗震设计结构有一定的优化。根据我国抗震规范,按传统抗震方法和消能减震方法分别设计了一组钢筋混凝土框架结构。采用基于动力增量时程分析方法的结构抗倒塌易损性分析流程,对不同设计方法所设计的框架结构的抗地震倒塌能力和抗倒塌安全储备进行了定量评价,并对计算结果进行了对比分析。根据分析结果提出了提高高烈度区减震设计框架结构抗倒塌能力的相关措施,并通过算例验证了所提措施的有效性。     

弹性DEM方法在杆系结构中的应用研究

基于颗粒离散元方法（DEM）,结合杆系结构的特点,提出了一种适于杆系结构问题分析的DEM模型。对颗粒元相应的质量和转动惯量计算公式进行了修正;通过能量等效原理推导了杆系DEM模型分析时弹簧接触刚度系数表达式;将瑞利阻尼引入到DEM方法之中,给出了阻尼常数计算公式并用算例进行了验证。将该方法应用于杆系结构弹性分析,包括静动力与几何非线性大变形问题的空间框架结构和网壳结构等多个算例,计算结果与有限元方法结果吻合良好。DEM方法的特点是将动力分析和几何非线性分析自动包含在运动方程的计算之中,不用组集刚度矩阵,无需迭代求解。杆系DEM模型非常适宜处理杆系结构大变形及动力非线性问题,尤其是在结构进入强非线性之后的模拟分析。     

索膜结构风振气弹效应的风洞实验研究

提出一种可以考虑索膜结构与风荷载动力耦合作用的简化气弹力学模型方法。以该方法为理论基础,进行了多个鞍形索网和鞍形膜结构的缩尺模型风洞气弹实验。研究内容包括:1)通过对形状相同的刚性模型和弹性模型表面的脉动风压与结构响应观测,探讨了附加气动力对结构响应的影响;2)利用随机减量技术对实验数据进行处理,实现了对气动阻尼、附加质量等参数的识别;3)通过对大量试验数据分析,得到了附加质量和气动阻尼随来流风速、风向、结构刚度和结构振动模态的变化规律。实验结果表明:气动阻尼对结构振动的影响较为显著,特别是对结构的低阶模态,气动阻尼比可达到15%左右;附加质量对结构振动的影响较小,其量级仅为结构质量的1倍―2倍左右。该试验过程中未发现结构出现整体气弹失稳现象,但在某些工况下,在结构局部测点出现气动负阻尼。     

Data based model free hysteresis identification for a nonlinear structure

In the last two decades, the damage detection for civil engineering structures has been widely treated as a modal analysis problem and most of the currently available vibration-based system identification approaches are based on modal parameters, namely the natural frequencies, mode shapes and damping ratios, and/or their derivations, which are suitable for linear systems. Nonlinearity is generic in engineering structures. For example, the initiation and development of cracks in civil engineering structures as typical structural damages are nonlinear process. One of the major challenges in damage detection, early warning and damage prognosis is to obtain reasonably accurate identification of nonlinear performance such as hysteresis which is the direct indicator of damage initiation and development under dynamic excitations. In this study, a general data-based identification approach for hysteretic performance in form of nonlinear restoring force using structural dynamic responses and complete and incomplete excitation measurement time series was proposed and validated with a 4-story frame structure equipped with smart devices of magneto-rheological (MR) damper to simulate nonlinear performance. Firstly, as an optimization method, the least-squares technique was employed to identify the system matrices of an equivalent linear system of the nonlinear structure model basing on the excitation force and the corresponding vibration measurements with impact test when complete and incomplete excitations; and secondly, the nonlinear restoring force of the structure was identified and compared with the test measurements finally. Results show that the proposed data-based approach is capable of identifying the nonlinear behavior of engineering structures and can be employed to evaluate the damage initiation and development of different structure under dynamic loads.     

On the equivalence of dynamic relaxation and the Newton‐Raphson method

Dynamic relaxation is an iterative method to solve nonlinear systems of equations, which is frequently used for form finding and analysis of structures that undergo large displacements. It is based on the solution of a fictitious dynamic problem where the vibrations of the structure are traced by means of a time integration scheme until a static equilibrium is reached. Fictitious values are used for the mass and damping parameters. Heuristic rules exist to determine these values in such a way that the time integration procedure converges rapidly without becoming unstable. Central to these heuristic rules is the assumption that the highest convergence rate is achieved when the ratio of the highest and lowest eigenfrequency of the structure is minimal. This short communication shows that all eigenfrequencies become identical when a fictitious mass matrix proportional to the stiffness matrix is used. If, in addition, specific values are used for the fictitious damping parameters and the time integration step, the dynamic relaxation method becomes completely equivalent to the Newton‐Raphson method. The Newton‐Raphson method can therefore be regarded as a specific form of dynamic relaxation. This insight may help to interpret and improve nonlinear solvers based on dynamic relaxation and/or the Newton‐Raphson method.     

Structural dynamic modifications via models

Structural dynamic modification techniques attempt to reduce dynamic design time and can be implemented beginning with spatial models of structures, dynamic test data or updated models. The models assumed in this discussion are mathematical models, namely mass, stiffness, and damping matrices of the equations of motion of a structure. These models are identified/ extracted from dynamic test data viz. frequency response functions (FRFs). Alternatively these models could have been obtained by adjusting or updating the finite element model of the structure in the light of the test data. The methods of structural modification for getting desired dynamic characteristics by using modifiers namely mass, beams and tuned absorbers are discussed.     

Structural dynamic modification using additive damping

In order to control dynamic response in structures and machines, modifications using additive viscoelastic damping materials are highlighted. The techniques described for analysis include analytical methods for structural elements, FEM and perturbation methods for reanalysis or structural dynamic modification for complex structures. Optimisation techniques used for damping effectiveness include multi-parameter optimisation techniques and a technique using dynamic sensitivity analysis and structural dynamic modification. These have been applied for optimum dynamic design of structures incorporating viscoelastic damping. Some current trends for vibration control are also discussed.     

TWO SIMPLE FAST INTEGRATION METHODS FOR LARGE-SCALE DYNAMIC PROBLEMS IN ENGINEERING

A new simple explicit two-step method and a new family of predictor–corrector integration algorithms are developed for use in the solution of numerical responses of dynamic problems. The proposed integration methods avoid solving simultaneous linear algebraic equations in each time step, which is valid for arbitrary damping matrix and diagonal mass matrix frequently encountered in practical engineering dynamic systems. Accordingly, computational speeds of the new methods applied to large system analysis can be far higher than those of other popular methods. Accuracy, stability and numerical dissipation are investigated. Linear and nonlinear examples for verification and applications of the new methods to large-scale dynamic problems in railway engineering are given. The proposed methods can be used as fast and economical calculation tools for solving large-scale nonlinear dynamic problems in engineering.     

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

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。     

多自由度一般积分型粘弹性阻尼减震结构的 随机响应与等效阻尼

该文对任意多自由度带支撑一般积分型粘滞和粘弹性阻尼器减震结构的随机响应与等效阻尼比的解析分析法进行了系统研究。首先建立了结构一般运动方程;然后将运动方程化为振型广义坐标的微分和积分混合地震响应方程组;继而基于多自由度随机平均法理论,获得了结构随机平均Itô方程组的解析式,推导出耗能结构各振型振子的振幅与相位瞬态联合概率密度函数、位移与速度瞬态联合概率密度函数、位移与速度瞬态响应方差的一般解析解;最后,基于与多自由度随机平均法分析完全相同的等效准则,建立了耗能结构各振型等效阻尼比的一般解析式,并根据CQC和SRSS组合方法,建立了耗能结构随机地震响应方差的解析式,给出了带支撑广义Maxwell阻尼器和广义微分模型阻尼器减震结构随机响应和各振型等效阻尼比的一般解析式,通过与一些典型问题的模态应变能法的计算精度对比分析,表明了所提方法的有效性,使耗能结构可直接应用反应谱法进行设计,从而建立了带支撑任意线性粘滞和粘弹性阻尼器一般耗能结构随机响应与特性等效阻尼分析的完备解析解法。     

利用部分加速度测量的结构滞回特性免模型识别

结构非线性恢复力与位移的关系即滞回特性是强动力荷载作用下结构损伤发生发展过程的直接表征,可直接用于结构耗能的定量评估。该文提出一种仅部分自由度受到激励且只有部分自由度上加速度响应测量已知时结构非线性恢复力和质量识别方法。无需结构恢复力参数化模型,利用切比雪夫多项式来描述非线性恢复力,结合无迹卡尔曼滤波算法（Unscented Kalman Filter, UKF）,在结构刚度、阻尼、质量未知情况下,实现非线性恢复力和结构质量识别。在一个多自由度数值模型中引入磁流变阻尼器模拟非线性构件,通过数值模拟验证该方法的识别效果。结果表明,该方法在仅部分自由度受激励且仅部分自由度上加速度响应时程已知时,可对结构非线性恢复力和质量进行有效识别。该方法对工程结构在强动力荷载作用下损伤发展过程的识别及耗能的定量评估具有重要意义。     

Nonlinear time heteronymous damping in nonlinear parametric planetary systems

The analysis of dynamics of time heteronymous weakly and strongly nonlinear planetary transmission systems with kinematic couplings–gears constitutes a study of complicated function of many parameters including the material of gears, damping properties and damping viscous properties of lubricating oil film in the gear mesh. The purpose of this theoretical preexperimental study is to educe the methodology that makes possible to analyse the influence of all parameter variants in the area of linear and nonlinear systems with constant and time variable damping on internal dynamics. More precise dynamic analysis of such systems leads to mathematical–physical models, whose motions are described by ordinary deterministic nonlinear time heteronymous differential equations at the application of mass discretization. Their solution leads to the method of transformation of the nonlinear boundary problem of differential equations into the equivalent problem of solving integro-differential systems of equations by the method of decomposition of solving kernels of Green’s type and by the method of successive approximations. The structures with lightening holes in cog wheel discs are characterized by time variable damping in gear meshes. In this paper, the examples of resonance bifurcation characteristics in the gear mesh give a comparison between two variants with lightening wheel discs and the variant with full wheel disc, i.e. two variants with time variable quadratic damping and the variant with the constant one.     

用矩阵广义逆和灵敏度分析修正阻尼结构动力学模型

本文基于矩阵广义逆和灵敏度分析,提出了一种阻尼结构动力学模型的修正方法。该方法以实测结构模态参数为基准修正结构初始质量、刚度和阻尼矩阵,从而使计算和实测结构模态参数更为吻合。方法的修正过程分两步:首先,利用复模态理论的正交关系和特征关系对结构初始质量、刚度和阻尼矩阵作第一次修正;其次,利用复频率灵敏度分析对质量、刚度和阻尼矩阵作再次修正。数值算例和应用实例均表明,本文方法具有较高的修正精度,是一种简便有效的结构动力学模型修正方法。     

粘滞流体阻尼墙对平面不规则结构的扭转效应控制研究

平面不规则结构由于平扭耦联会使边界处的位移较规则结构增大很多,而给结构配置阻尼器是减小平面不规则结构边界位移的有效途径,该文将耗能效率较高的粘滞流体阻尼墙应用于控制平面不规则结构的扭转响应,研究阻尼墙控制结构扭转效应的机理及控制结构扭转的优化布置。将减震系统刚度矩阵转换到结构的质量中心,将配置阻尼墙后形成阻尼中心的阻尼矩阵转换到质量中心,从而建立可以考虑扭转效应和附加阻尼位置效应的非线性运动控制方程,并根据响应结果推导出结构位移比的表达式;利用运动方程研究阻尼中心的位置、阻尼力的大小、阻尼参数等对结构扭转效应的影响规律,结合结构位移比的表达式提出阻尼墙的平面配置原则和最优阻尼参数的取值方法。以某L型高层建筑为工程背景,根据上述原则配置阻尼墙并选取阻尼参数,并对减震体系在最不利地震动输入方向上进行非线性时程分析,分析结果表明通过合理配置粘滞阻尼墙,L型结构的扭转响应得到了有效的控制,结构最大边界位移和位移比大大降低。该研究结果为采用阻尼墙控制不规则结构扭转效应提供了基本原则和方法,并为不规则结构的减震设计提供有益的借鉴和参考。     

Identification of stiffness,dissipation and input parameters of multi degree of freedom civil systems under unmeasured base excitations

A time domain dynamic identification technique based on a statistical moment approach has been formulated for civil systems under base random excitations in the linear state. This technique is based on the use of classically damped models characterized by a mass proportional damping. By applying the Itô stochastic calculus, special algebraic equations that depend on the statistical moments of the response can be obtained. These equations can be used for the dynamic identification of the mechanical parameters that define the structural model, in the case of unmeasured input as well, and the identification of the input itself. Furthermore, the above equations demonstrate the possibility of identifying the dissipation characteristics independently from the input characteristics. This paper discusses how the equations for solving the identification problem can be obtained and gives an application.     

车桥耦合系统的非线性动力分析

研究了车桥耦合系统的非线性动力特性。基于哈密尔顿能量原理和欧拉-贝努利梁假设,考虑梁的几何非线性影响,建立了移动振动车辆模型下桥梁的耦合非线性振动方程,应用伽辽金法和Runge-Kutta法对方程进行求解,算例中探讨了车辆质量、车速、桥梁阻尼和桥跨径等参数对车-桥耦合系统非线性振动性能的影响。     

Numerical model for dynamic analysis of masonry‐infilled steel and concrete frames

A numerical model for nonlinear dynamic analysis of planar masonry‐infilled concrete and steel frames strengthened with composites is briefly presented. The model is quite simple and it can simulate main nonlinear effects of these structures. Besides modelling of nonlinear behavior of concrete, steel, masonry, plaster and soil, it can simulate nonlinearities at contact surfaces, changes in structural geometry and construction of a structure over different time phases. The model is based on a relatively small number of material parameters and intended for practical application primarily. The model is verified by using the data of the performed shake‐table tests on masonry‐infilled steel and concrete frames. Numerical results show fairly good agreement with the experimental results. This shows the potential reliability of the developed numerical model for the analysis of planar masonry structures. However, further verifications of the model and corresponding computational software are most welcome.     

Timoshenko阻尼转轴的涡动不平衡响应

考虑系统的质量不平衡和材料的阻尼作用，应用Timoshenko梁理论和Hamilton原理，建立转轴的空间运动方程，它包含了剪切变形、旋转惯性、陀螺效应、动不平衡和内粘性阻尼与材料迟滞阻尼的影响。数值分析了系统的动力学响应和特性，由不平衡质量产生的强迫振动和材料阻尼引起的自激振动导致转轴产生复杂的涡动变形。     

A numerical algorithm for nonlinear dynamic problems based on BEM

A semi-analytical time-integration procedure for the integration of discretized dynamic mechanical systems is presented. This method utilizes the advantages of the boundary element method (BEM), well known from quasi-static field problems. Motivated by these spatial formulations, the present dynamic method is based on influence functions in time, and gives exact solutions in the linear time-invariant case. Similar to domain-type BEM’s for nonlinear field problems, the method is extended for different nonlinear dynamic systems having nonclassical damping and time-varying mass. The numerical stability and accuracy of the semi-analytical method is discussed in two steps for the nonclassical damping and for the nonlinear restoring forces, e.g. of the Duffing type. The damped Duffing oscillator and a linear oscillator with time-varying mass are used as representative model problems. For a nonlinear rotordynamic system, a comparison is given to other conventionally used time integration procedures, which shows the efficiency of the present method.     

Improved dynamic analysis of structures with mechanical uncertainties under deterministic input

This paper addresses the dynamic analysis of linear systems with uncertain parameters subjected to deterministic excitation. The conventional methods dealing with stochastic structures are based on series expansion of stochastic quantities with respect to uncertain parameters, by means of either Taylor expansion, perturbation technique or Neumann expansion and evaluate the first- and second-order moments of the response by solving deterministic equations. Unfortunately, these methods lead to significant error when the coefficients of variation of uncertainties are relatively large. Herein, an improved first-order perturbation approach is proposed, which considers the stochastic quantities as the sum of their mean and deviation. Comparisons with conventional second-order perturbation approach and Monte Carlo simulations illustrate the efficiency of the proposed method. Applications are discussed in order to investigate the influence of mass, damping and stiffness uncertainty on the dynamic response of the system.