Comments on “Vibration suppression for high-speed railway bridges using tuned mass dampers” [J.F. Wang,C.C. Lin,B.L. Chen, 2003. Int. J. Solids Struct. 40(2) 465–491]

In this comment, the discusser makes some remarks on the paper “Vibration suppression for high-speed railway bridges using tuned mass dampers” by Wang, J.F., Lin, C.C., Chen, B.L., published in the International Journal of Solids and Structures, 2003, Vol. 40, No. 2, pp. 465–491. First, the formulation of H(t, t_k) on p. 470 is questionable. Second, for a moving suspension mass model, the interaction force between moving mass and bridge is incorrectly given. Third, for a moving mass model for the train and without the installation of PTMD (passive tuned mass damper), the equation of motion of the bridge is incorrect. Lastly, for the train load model, which consists of one-half of a train car, one bogie, two wheel sets, spring and dashpot between bogie and half of a train car, and spring and dashpot between bogie and each wheel set, the authors did not put forward the formulation of interaction force between wheel set and bridge, but the discusser does.     

Analytical analysis for optimizing mass ratio of nonlinear tuned mass dampers

Nonlinear Dynamics - This paper investigates the forced vibration and dynamic stability of a simply supported axially moving beam coupled to a nonlinear energy sink with the aim of passive...     

Constrained reliability-based optimization of linear tuned mass dampers for seismic control

This paper deals with the optimum design of vibration absorbers utilized to reduce undesirable vibrational effects which are originated in linear structures by seismic excitations. The single linear tuned mass dampers problem is treated and it is assumed that earthquake can be represented by a stationary filtered stochastic process. In the present problem, the objective is to minimize the maximum of the dimensionless peak of displacement of the protected system with respect to the unprotected one. Moreover, the constrained optimization problem is also analysed, in which a limitation of tuned probability of failure is imposed, where failure is related to threshold crossing probability by the maximum displacement over an admissible value. Examples are given to illustrate the efficiency of the proposed method. The variation of the optimum solution versus structural and input characteristics is analysed for the unconstrained and constrained optimization problems. A sensitivity analysis is carried out, and results are presented useful for the first design of the vibrations control strategy.     

Seismic performance of multiple tuned mass dampers for soil–irregular building interaction systems

This paper deals with the applicability of multiple tuned mass dampers (MTMD) on the vibration control of irregular buildings modelled as torsionally coupled structures due to base motions considering the soil–structure interaction (SSI) effect. An efficient modal analysis methodology is used to systematically assess the combined soil–structure interaction and torsional coupling effects on asymmetric buildings. This method is implemented in the frequency domain to accurately incorporate the frequency-dependent foundation impedance functions. The performance index of MTMD is established based on the foundation-induced building floor motions with and without the installation of MTMDs. Unlike the traditional MTMD design criteria, the frequency ratio of each MTMD substructure to the controlled structural frequency is independent, in this paper, so that the MTMD with the optimal parameters can actually flatten the transfer functions of building responses. Numerical verifications show that the increase of height–base ratio of an irregular building and the decrease of relative stiffness of soil to structure generally amplify both SSI and MTMD detuning effect, especially for a building with highly torsionally coupled effect. With appropriately enlarging the frequency spacing of the optimal MTMDs, the detuning effect can be reduced. Moreover, the results of numerical investigations also show that the MTMD is more effective than single TMD as the SSI effect is significant.     

结构主动开闭环多重调谐质量阻尼器（AMTMD）新控制策略

提出了一种新控制策略——主动开闭环多重调谐质量阻尼器(AMTMD)。AMTMD控制系统频率呈线性分布。AMTMD中的MTMD保持相同的刚度和阻尼系数但质量变化。基于TMD的工作原理定义了AMTMD的主动控制力构成即保持相同的位移和速度反馈增益系数但变化结构和地震加速度反馈增益系数。基于结构的广义振型模型，导出了设置AMTMD时结构的动力放大系数(DMF)，于是优化准则可定义为：Min．Min．Max．DMF．通过最优搜寻，研究了反映AMTMD有效性和鲁棒性的参数。这些参数包括：频率间隔、平均阻尼比、调谐频率比、总数、质量比和标准化加速度反馈增益系数。为了比较，多重调谐质量阻尼器(MTMD)和主动开闭环调谐质量阻尼器(ATMD)也被考虑。     

Random vibration mitigation of beams via tuned mass dampers with spring inertia effects

Meccanica - The dynamics of beams equipped with tuned mass dampers is of considerable interest in engineering applications. Here, the purpose is to introduce a comprehensive framework to address...     

On the optimal strategy of stochastic-based reliability assessment of railway bridges for high-speed trains

Meccanica - The scope of this paper is to evaluate the performance and computational efficiency of various stochastic simulation methods for a stochastic based reliability assessment of railway...     

利用浅水水箱作为阻尼器的大连国贸大厦减振控制研究

针对一实际工程结构—大连国贸大厦,研究了风荷载作用下调液阻尼器的减振控制作用。首先建立了该结构的简化计算模型,利用Davenport谱给出了模拟风荷载;在大厦所处的位置进行多次测量,得到实际风速样本,选取其中风速较大、过程平稳的样本,对实测样本与模拟样本的频谱进行比较,验证了模拟风荷载的合理性。文中在大厦顶层设置浅水水箱,将其设计成可减少结构位移及加速度反应的控制装置TLD,以提高大厦在风荷载作用下的舒适度,并给出了高层建筑水箱减振方案实施的设计建议。数值计算结果表明,该大厦顶部设置TLD减振装置后,能有效地控制结构在风荷载作用下的反应。依据本文的TLD设计步骤,可供类似高层建筑进行TLD减小风振控制分析和设计时参考。     

环形调液阻尼器振动控制中拍的研究

对环形调液阻尼器减振控制中的拍现象进行研究,分析了环形调液阻尼器对结构纯扭转振动控制中的拍现象,分别考虑无阻尼结构体系、主体结构有阻尼而CTLCD无阻尼的体系及主体结构和CTLCD中均有阻尼的体系,从数学角度对拍现象发生的机理进行解释.研究结构表明,当拍现象发生时,主体结构的振动不仅不会受到抑制,有时反而会加强;当环形调液阻尼器的阻尼增大到一定程度时,拍现象会消失;对于受廹振动,发生拍现象时,由于结构反应的瞬态部分不能得到迅速衰减,结构的瞬态响应将会占结构响应的很大一部分,如果仅考虑结构的稳态响应会带来较大的误差.     

地震作用下高层钢结构MTMD控制参数取值及优化设计研究

本文对地震作用下结构－MTMD系统的动力特性及优化设计进行了探讨,通过数值分析研究了MTMD系统各设计参数间的关系,给出了MTMD系统最优参数取建设,提出了MTMD系统优化设计及结构－MTMD系统优化设计方法,最后,算例说明了本文方法的应用及MTMD对结构地震反应控制的有效性。     

Tuning methods for tuned inerter dampers coupled to nonlinear primary systems

This study develops displacement- and kinetic energy-based tuning methods for the design of the tuned inerter dampers (TIDs) coupled to both linear and nonlinear primary systems. For the linear primary system, the design of the TID is obtained analytically. The steady-state frequency–response relationship of the nonlinear primary system with a softening or hardening stiffness nonlinearity is obtained using the harmonic balance (HB) method. Analytical and numerical tuning approaches based on HB results are proposed for optimal designs of the TID to achieve equal peaks in the response curves of the displacement and the kinetic energy of the primary system. Via the developed approaches, the optimal stiffness of the TID can be obtained according to the stiffness nonlinearity of the primary system and the inertance of the absorber. Unlike the linear primary oscillator case, for a nonlinear primary oscillator the shape of its resonant peaks is mainly affected by the damping ratio of the TID, while the peak values depend more on the stiffness ratio. The proposed designs are shown to be effective in a wide range of stiffness nonlinearities and inertances. This study demonstrates the benefits of using inerters in vibration suppression devices, and the adopted methods are directly applicable for nonlinear systems with different types of nonlinearities.

     

Experimental investigation of vibration attenuation using nonlinear tuned mass damper and pendulum tuned mass damper in parallel

The present paper experimentally and numerically explores the response attenuation of a hardening Düffing oscillator using a nonlinear tuned mass damper (NTMD) and an adaptive-length pendulum tuned mass damper (APTMD). The three degrees-of-freedom system is excited by harmonic ground motions. The cubic nonlinearity of the primary structure is obtained using an adaptive passive stiffness (APS) device. When an NTMD is used alone, a high amplitude detached resonance branch in the lower frequency range is identified in the experiment, which validates the results reported in earlier numerical research. In order to attenuate this high amplitude resonance branch, an APTMD with an adaptive frequency realized by means of a variable pendulum length is used in parallel with the NTMD. In the experiment, length of the APTMD is adjusted such that its natural frequency matches the dominant frequency of the harmonic ground motions. Results indicate that the high amplitude resonance branch in the case of an NTMD alone can be greatly attenuated using the APTMD, and significant attenuation of the structural responses over a large frequency range can be obtained. In addition, the APTMD can prevent the occurrence of the “jump phenomenon” existing in the forcing response curve of the nonlinear dynamic system, thereby protecting the primary nonlinear structure effectively when the forcing amplitude varies. Therefore, the present paper provides an effective and viable solution to control the hazardous bifurcations in a Düffing oscillator-NTMD dynamic system.     

Non-linear multimodal model for tuned liquid dampers of arbitrary tank geometry

Tuned liquid dampers (TLDs) utilize sloshing fluid to absorb and dissipate structural vibrational energy. Simple TLD tank geometries may not always be feasible due to space limitations. While the non-linear modelling of sloshing fluid is currently limited to tanks of simple geometries, this paper develops a non-linear multimodal model which describes the sloshing behaviour of a fluid in a flat-bottom tank of arbitrary geometry. The mode shapes of the sloshing fluid are found by solving the Helmholtz equation over the tank domain using the finite element method. The Bateman-Luke variational principle is used to develop a system of ordinary differential equations which account for the coupling of the sloshing modes through the non-linear free surface boundary conditions. Damping is incorporated into the model by considering the drag produced on a set of damping screens inserted in the fluid. The system of ordinary differential equations is solved using the Runge-Kutta-Gill Method to predict the wave heights and sloshing forces. In general, the mode shapes in an arbitrary tank will have components in two orthogonal (x- and y-) directions. This out-of-plane behaviour is an important consideration for TLD design. The model is validated with existing models for the special cases of rectangular and circular tanks. Lastly, new shake table tests are conducted on a tank of complex geometry.     

An interval framework for uncertain frequency response of multi-cracked beams with application to vibration reduction via tuned mass dampers

Meccanica - The paper addresses the frequency response of beams in presence of open cracks with interval parameters. On adopting the standard Euler–Bernoulli beam theory, every crack is...     

基于平稳过滤有色噪声地震动模型的MTMD性能评价

研究了由许多刚度和阻尼保持为常量且频率呈线性分布的TMDs形成的MTMD的地震特性。基于虚拟激励法和平稳过滤有色噪声地震动模型，建立了结构－MTMD系统的传递函数，进而导出了设置MTMD时结构的动力放大系数（DMF）明确表达式。于是MTMD的优化准则可定义为Min.Min.Max.DMF。通过最优搜寻可得MTMD的最优频率间隔、平均阻尼比、调谐频率比和相应的无量纲控制有效性指标。目前的论文通过考虑结构受控频率与地震加速度卓越频率比的不同取值和不同场地类型，研究地震卓越频率和场地类型对MTMD最优参数及有效性的影响。同时与基于Kanai-Tajimi平稳过滤白噪声地震动模型和不考虑地震加速度卓越频率(ωg=∝）两种情况的结果进行了比较。     

大跨度桥梁多模态耦合颤振DTMD控制研究

DTMD是一种具有双频率的调谐质量阻尼器,与普通TMD相比,可以同时实现对主梁竖向和扭转运动的控制,具有较高的控制效率。本文基于多模态耦合颠振理论,导出带有DTMD的桥梁颠振系统运动微分方程,采用PK—F法求解系统颠振运动微分方程,并编制了多模态耦合颠振DTMD控制和参效分析程序,以崖门斜拉桥为算例,分析了DTMD对桥梁颤振控制的有效性并与普通TMD进行了对比,计算结果表明与传统TMD相比,DTMD对桥梁颠振具有更高的控制效率。     

Variable stiffness tuned particle dampers for vibration control of cantilever boring bars

This research proposes a novel type of variable stiffness tuned particle damper(TPD) for reducing vibrations in boring bars. The TPD integrates the developments of particle damping and dynamical vibration absorber, whose frequency tuning principle is established through an equivalent theoretical model. Based on the multiphase flow theory of gas-solid, it is effective to obtain the equivalent damping and stiffness of the particle damping. The dynamic equations of the coupled system, consisting of...     

Vibration suppression of FGM shells using embedded magnetostrictive layers

Analytical solutions of functionally graded material (FGM) shells with embedded magnetostrictive layers are presented in this study. These magnetostrictive layers are used for the vibration suppression of the functionally graded shells. The first-order shear deformation shell theory (FSDT) is employed to study the vibration suppression characteristics. The exact solution for the FGM shell with simply supported boundary conditions is based on the Navier solution procedure. Negative velocity feedback control is used. The parametric effect of the location of the magnetostrictive layers, material properties, and control parameters on the suppression effect are investigated in detail. It is found that (i) the shortest vibration suppression time is achieved by placing the actuating layers farthest from the neutral axis, (ii) the use of thinner smart material layers leads to better vibration attenuation characteristics, and, (iii) the vibration suppression time is longer for a smaller value of the feedback control coefficient.     

Fluid formulae for damping changeability conceptual design of railway semi-active hydraulic dampers

Damping changeability design and evaluation is the most fundamental issue at the beginning of any new railway semi-active hydraulic damper development. Therefore, physical fluid mechanics for the calculation of basic structure and resistance parameters of the damper should be carefully studied in the conceptual phase. Fluid formulae for changeable damping performance evaluation of two commercial railway semi-active hydraulic dampers are established. Simulation results show that the damper switched by high-speed solenoid valves obtains a wide range of changeable damping coefficients, which guarantees the absorption of a wide spectrum of vibrations; however, a different low cost damper regulated with an inversely proportional relief valve, whose Force-velocity characteristics share the same rising curve, is relatively limited in damping ability. In order to overcome the drawback of the latter one with no obvious cost increase, a new semi-active hydraulic damper which is regulated by a simple proportional throttle valve is proposed. Continued fluid formulation and simulation suggests that the damper can change its damping force rising curves or “effective” damping coefficients continuously, within a considerably wide range. Thus, fluid formulae explicitly established in this study are of significance in the damping changeability conceptual design, further refinement and control design for the three semi-active hydraulic dampers. The proposed new damper, which has both a simple configuration and an easy-to-control ability, might be feasible for industry applications.     

Optimization of high-speed railway pantographs for improving pantograph-catenary contact

A crucial system for the operation of high-speed trains is the pantograph catenary interface as it is the sole responsible to deliver electrical power to the train. Being the catenary a stationary system with a long lifespan it is also less likely to be redesigned and upgraded than the pantographs that fit the train vehicles. This letter proposes an optimization procedure for the improvement of the contact quality between the pantograph and the catenary solely based on the redesign of the pantograph head suspension characteristics. A pantograph model is defined and validated against experimental dynamic characteristics of existing pantographs. An optimization strategy based on the use of a global optimization method, to find the vicinity of the optimal solution, followed by the use of a deterministic optimization algorithm, to fine tune the optimal solution, is applied here. The spring stiffness, damping characteristics and bow mass are the design variables used for the pantograph optimization. The objective of the optimal problem is the minimization of the standard deviation of the contact force history, which is the most important quantity to define the contact quality. The pantograph head suspension characteristics are allowed to vary within technological realistic limits. It is found that current high-speed railway pantographs have a limited potential for mechanical improvements, not exceeding 10%–15% on the decrease of the standard deviation of the contact force.