Elimination of tall building vibration resulting from ground motions

In this paper, the vibration problems of tall buildings are considered. The focus is on vibration caused by earthquakes, semi–seismic phenomena and ground vibrations of other origins. The construction consists of the main system and a vibration eliminator (passive tuned mass damper – pendulum type) which is attuned to the first eigenfrequency of the main structure. The analysis focuses on elimination of structure vibration caused by horizontal components of ground motions, while the functioning of the eliminator is simultaneously influenced by the vertical component (parametric effect – the possibility of improper functioning of the device). The vertical periodic movement of the support point can cause changes of the vibration eliminator's stiffness. In such a case parametric excitation occurs in the system, which signifies that parametric resonance may appear. The numerical analysis of the problem was performed with the Newmark method in conjunction with FEM. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Parametric vibration of TMD installed in tall building during seismic excitation

In this paper shaking-table tests of a model-scale building with TMD (tuned mass damper) are conducted. The main aim of the research is to show the influence of kinematical excitation on the dynamic response of the model of tall building with pendulum TMD. The special attention is focused on the functioning of pendulum, which is simultaneously excited by the vertical component of ground motion. There are two kinds of analysis carried out — numerical and experimental. The numerical analysis of the problem is performed with using COSMOS/M system (a FEM numerical model is defined), while experimental analysis is carried out on a physical model-scale building with TMD. (© 2010 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Shaking table tests of a plate-column structure with semi-active tuned mass damper

This paper presents selected results of experimental tests carried out on the three-storey plate-column structure, which is a physical model of a building. On the top floor the semi-active tuned mass damper (STMD) is installed. That device is a kind of harmonic oscillator with a variable stiffness characteristic. The tuning of STMD is possible in the frequency range from 0 to 5 Hz, which allows to counteract the resonant vibration of plate-column structure for the three basic frequencies. The model's vibration are kinematically excited by using the earthquake simulator. It is assumed that during an experimental tests the plate-column structure's vibration are only excited by horizontal component of base motion (dominant influence on building's vibration). The aim of the experimental analysis presented in this paper is to verify the effectiveness of the semi-active tuned mass damper in vibration's amplitude reduction of the main structure. The tested device is prototype of STMD, which uses a competitive constructional solution of stiffness parameter control. By reason of above, special attention is focused on the testing of vibration eliminator in two aspects: change of stiffness characteristic (the rate of change), and the accuracy of tuning to the resonant frequencies. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

设置黏滞阻尼器的纵飘斜拉桥地震响应简化分析方法

针对纵飘体系斜拉桥现有黏滞阻尼器参数设计方法的不足,提出了更为快捷有效的分析方法.首先基于钟摆原理,采用双质点模型简化模拟纵飘斜拉桥的动力响应特征;然后基于能量耗散等效原理,提出了黏滞阻尼器的等效线性模型;最后基于结构动力学原理,建立了设置黏滞阻尼器的纵飘斜拉桥地震响应简化分析方法.在此基础上,针对某主跨392 m的纵飘斜拉桥建立了全桥分析模型,在正弦波作用下,对比分析了全桥模型、双质点简化模型数值解和解析解的计算误差.结果表明:双质点模型数值解计算结果精度较高,可以代替全桥模型的有限元计算结果;解析解与双质点数值解计算结果吻合良好,验证了双质点模型简化分析方法在理论上的可靠性;在不同地震动特性和体系周期下,三者计算误差均满足工程精度要求,表明该简化分析方法具有良好的适用性,可为阻尼器参数优化提供更简便的模型.     

Reduction of seismic vibration in multistorey structures retrofitted with nonlinear viscous dampers using mode summation method

Viscous dampers are the retrofitted devices used to reduce the vibration energy in mechanical systems. In the present paper an investigation is carried to see the effect of nonlinear viscous dampers (NVDs) in multistory buildings. A model of building consisting of NVDs in each floor is considered and is subjected to base shear excitation. The complete model is considered as an equivalent mechanical system and equation of motion is established for equilibrium condition. Using mode summation method analytical expressions are found for the displacement response of the building's floors due to shear waves. To see the role of NVDs different values of damping coefficients are considered and the result is compared with the response of building without NVDs. Analyzing the result it is found that NVDs present in the building's floors dissipate the vibration energy significantly.     

Mechanical model of a mistuned 2DOF-structure coupled by viscous damping

In this paper the vibration amplitude reduction of a mechanical system is investigated when applying a damper between different DOF of that structure. Thereby, an elementary mechanical model consisting of two mass-spring elements with slightly differing eigenfrequencies and which are connected via a viscous dashpot damper is regarded. To investigate the systems behavior, an analysis of the transfer function and its poles and zeros in the L APLACE domain is performed when varying the damping constant. This reveals that the achievable amplitude reduction depends on the mistuning of the system and that even ideal viscous damping leads to a coupling which results in a shift of eigenfrequencies. (© 2009 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

基于非线性能量阱的双频激励非线性系统减振

针对某型民用航空发动机双频带激励特点,建立了单自由度线性振子耦合非线性能量阱（nonlinear energy sink,NES）的动力学模型.根据典型双转子发动机在巡航状态下低、高特征频率比（1∶4.74）,为系统设定双频带简谐外激励.利用四阶Runge-Kutta算法,研究了耦合NES振子时系统的振动抑制特征,并从外激励频率对系统主振子动能、系统总体能量的影响等方面,与未耦合NES系统、耦合线性动力吸振器两种情况下的数值计算结果进行对比分析.研究结果表明NES对双频带外激励具有更好的振动抑制效果,用NES降低航空发动机振动有可行性.     

Bi-harmonically excited pendulum: shifted resonances and quenching the low frequency excitation

The effect of the harmonic high-frequency vibration of the suspension point on a mathematical pendulum is well known [1]. It can be described as stiffening/softening or stabilization/destabilization of the up-pointing and down-pointing equilibriums for pure vertical or pure horizontal excitation. If the excitation is tilted the effect of biasing appears in addition [2]. The effects of bi-harmonic excitation are more complex. Two of them are discussed in the recent paper. The first one occurs if one of the excitation frequencies is high and another one is low. Then the so called shifted or conjugated resonances can be observed [3]. The second one takes place if the two excitation frequencies are high but their difference is small (slowly modulated high-frequency excitation according to [4]). It is shown that in that case it is possible to choose the bi-harmonic excitation in order to quench the resonance of the pendulum without changing its basic frequency. The analysis is fulfilled both for the external and parametric excitations. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

考虑屋盖整体空间工作时的单层偏心厂房的平扭耦联地震反应分析

本文研究了单层偏心厂房的平动-扭转耦联地震反应.建立了考虑屋盖整体空间工作时的地震反应运动方程,并进行了分析,讨论.指出在包含有地震动转动分量作用时,地震动各运动分量独立作用的迭加原理和动力反应分析的振型分解法已不再适用.本文在不计地震转动分量的前提下,对单层偏心厂房的平扭耦联地震反应进行了大量的计算及对比分析,结论是:考虑屋盖变形后的计算结果能更好地解释地震破坏现象,并指出了不考虑屋盖变形的适用范围.     

Investigation of Damping of Vibrations in a System With Two‐Disc Inseparable Clutch

This paper presents the results of tests on free and forced harmonic torsional vibrations in a system with a two‐disc inseparable clutch, with structural friction taken into account. Nonlinear histeresis loop describing the frictional‐elastic properties of the system was introduced into the model. The mathematical model of the vibrating system containing two disks inseparable clutch was built. During free vibrations of the system, its damping characteristics were tested by a digital simulation method. The vibration damping decrement as a function of amplitude torsional displacement was determined. When vibrations were harmonically forced, the amplitude ‐ frequency characteristics of the system were determined numerically. The system was used as a nonlinear torsional vibration damper in a linear system with a harmonic force. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

The motion characteristics of the double‐pendulum system with skew walls

Many components of machines and other technological devices (chains and bodies hanging on the ropes) can be modeled as multiple pendulums situated in tubes or holes of limited space. The investigation of motion of such systems represents the substance of many real technological problems; therefore, it stirred up motivation to perform research on vibration of a double pendulum situated between two skew rigid walls. The analyzed system was set into motion by the horizontal movement of its suspending. The results of the simulations show that the system can exhibit both the regular and chaotic movements depending on the excitation frequency. The development of the computational model, which is applicable for more complex investigations, and learning more on the motion character of a double pendulum, the movement of which is limited by skew walls, are the principal contributions of the presented article.     

覆冰输电导线舞动的Noether对称性和守恒量

为克服传统输电导线非线性振动响应数值模拟的非保结构缺点,研究了输电导线在覆冰和大风激励条件下双向舞动中的Noether对称性和守恒量.首先,考虑空气动力和导线几何的非线性,依据分析力学方法建立了垂向与扭振两自由度舞动模型;其次,引进群分析理论,根据不变性原则给出了系统存在Noether对称性的条件以及相应守恒量的形式;...     

Free vibration and buckling analysis of plates using B-spline wavelet on the interval Mindlin element

A finite element method (FEM) of B-spline wavelet on the interval (BSWI) is used in this paper to solve the free vibration and buckling problems of plates based on Reissner–Mindlin theory. By aid of the high accuracy of B-spline functions approximation for structural analysis, the proposed method could obtain a fast convergence and a satisfying numerical accuracy with fewer degrees of freedoms (DOF). The numerical examples demonstrate that the present BSWI method achieves the high accuracy compared to the exact solution and others existing approaches in the literatures. The BSWI finite element has potential to be used as a numerical method in analysis and design.     

Non-periodic and chaotic vibrations in a flow induced system

A flow induced system, consisting of an elastically mounted body with a pendulum attached, is considered here. The stability of the semi-trivial solution, representing the vibration of the body with the non-oscillating pendulum, is investigated. The analytical investigation shows that at a certain flow velocity, higher than the critical one, the pendulum begins to oscillate due to autoparametric resonance. For a convenient tuning, the vibration of the system can be substantially reduced. The analysis of both semi-trivial and non-trivial solutions is complemented by numerical integration of the differential equations of motion. A mapping technique based on Poincaré section, suitable for investigating the non-periodic vibrations occuring at higher flow velocities, is proposed.     

Stability study of the human body-seat system into an autovehicle

The paper presents the study of the human body, as a mechanical system, seated inside an autovehicle and exposed under the vertical harmonic vibration action during the auto vehicle motion time. The human body may be roughly approximated by a linear lumped parameter at low frequencies and low vibration levels. Therefore, the model has 5 DOFs in translation, where 4 DOFs represents the human body and 1 DOF is for the seat cushion The mechanical model of the human body, in sitting position on the seat cushion of a vehicle seat, consists of four parts: pelvis, upper torso, viscera and head.. The eigenvalues for the human body – seat system and the damping ratio for the system was been calculate. The system stability analysis is given by the existence of a Lyapunov function for the system. The stability of a system can also be characterized by the eigenvalues of the system. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Horizontal fast excitation in delayed van der Pol oscillator

This paper investigates the interaction effect of horizontal fast harmonic parametric excitation and time delay on self-excited vibration in van der Pol oscillator. We apply the method of direct partition of motion to derive the main autonomous equation governing the slow dynamic of the oscillator. The method of averaging is then performed on the slow dynamic to obtain a slow flow which is analyzed for equilibria and periodic motion. This analysis provides analytical approximations of regions in parameter space where periodic self-excited vibrations can be eliminated. A numerical study is performed on the original oscillator and compared to analytical approximations. It was shown that in the delayed case, horizontal fast harmonic excitation can eliminate undesirable self-excited vibrations for moderate values of the excitation frequency. In contrast, the case without delay requires large excitation frequency to eliminate such motions. This work has application to regenerative behavior in high-speed milling.     

A vertically acting tuned liquid column damper

The U-shaped tuned liquid column damper (TLCD) increases the effective structural damping of horizontal vibrations similar to the classical tuned mechanical pendulum type damper (TMD). The pipe-in-pipe TLCD applies to vertical vibrations, likewise to the spring-mass-dashpot TMD. When sealed, the gas-spring effect extends the frequency range of application to about five Hertz. The geometric analogy between the novel TLCD and the TMD still exists, making the first step in the tuning procedure “classical”. Subsequent fine tuning in state space when the TLCD is split into smaller ones in parallel action, renders an even more robust passive action. The experimentally observed averaged turbulent damping of the relative fluid flow and the weakly nonlinear gas-spring render the TLCD insensitive to overloads and parametric forcing. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Sensitivity and Hessian matrix analysis of power spectral density functions for uniformly modulated evolutionary random seismic responses

This paper describes a numerical method for calculation of the sensitivity and Hessian matrix of the response PSD functions of structures subjected to uniformly modulated evolutionary random seismic excitation. The method is formulated based on the pseudo excitation method and Newmark method. The evolutionary non-stationary random response analysis is converted into step-by-step integration computations using the pseudo excitation method. The formulas of the pseudo responses, their first and second derivatives with respect to the structural design variables are derived based on the Newmark method. The PSD functions, their sensitivity and Hessian matrix are calculated using the pseudo responses, their first and second derivatives, respectively. Then the computation procedure of sensitivity and Hessian matrix of PSD functions is given in detail. Finally, the PSD functions’ sensitivity and Hessian matrix analysis of a three-story, two-bay planar frame subjected to the uniformly modulated evolutionary random earthquake ground motion has been studied to elucidate the proposed method.     

Structural vibration control by means of nonlinear pendulum dampers

This paper discusses the application of a nonlinear Pendulum Tuned Mass Damper (PTMD) for the reduction of structural vibrations. Pendulum dynamic absorbers are used extensively to reduce the vibration level of slender elastic structures such as towers. A PTMD is a device consisting of a suspended mass, and a damper that is attached to the tower in order to reduce its dynamic response. The primary eigenfrequency of the nonlinear damper is tuned to a particular structural frequency. Energy is dissipated by the damping force acting on the structure. Here, the PTMD is applied to a tower as a continuous system consisting of distributed mass and elasticity. The optimum values of PTMD parameters are found based on minimization of the response of the tower tip–point. Time history and frequency domain responses for the tower with PTMD in linear and nonlinear condition are compared. In addition, the equations of motion of active pendulum control are intruduced. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

On modelling and analysis of gear drives with nonlinear couplings

The paper deals with modelling of vibration of shaft systems with gears and rolling-element bearings using the modal synthesis method with DOF number reduction. The influence of the nonlinear bearing and gearing contact forces with the possibility of the contact interruption is respected. The gear drive nonlinear vibrations caused by internal excitation generated in gear meshing, accompanied by impact and chaotic motions are studied. The theory is applied to a simple test-gearbox. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)