Free and steady state vibration of non-linear structures using a finite element–non-linear eigenvalue technique

The problem of free vibration of non-linear structures is considered initially. It is shown that this problem can be represented as a non-linear eigenvalue problem. Variational principles for non-linear eigenvalue problems are defined. These variational principles are implemented with finite element models to define numerical approximations for the free vibration problem. The solution of these approximate equations provides a set of non-linear modal vectors and natural frequencies which vary with the amplitude of the solution. The non-linear eigenvalue parameters can be used in modal expansion approximations for the non-linear transient or steady state response of structural systems. To demonstrate the proposed techniques the free vibration and steady state vibration characteristics of a geometrically non-linear circular plate are determined.     

单跨简支梁竖向振动的磁悬浮半主动控制

由于传统的隔振器需要足够的竖向刚度来支撑上部结构,因而不能隔离竖向振动。为了解决这一问题,本文提出一种新的隔振策略,即磁浮式半主动控制方法,并将这一方法应用于弹性梁弯曲振动的半主动控制。将均质弹性梁简化为一带集中质量的简支梁,导出了控制系统的运动方程,讨论了系统在平衡点的稳定性,应用推广的Runge-Kutta方法,得到了系统在随机地面输入下的加速度响应。结果表明：杆件的初始悬浮位置是磁浮式半主动控制系统的平衡点,且平衡点是L稳定的;磁浮式半主动隔振系统具有类似于软弹簧的性质,与普通的弹性简支梁相比,磁浮式半主动振动控制系统的振动频率较低,加速度响应明显减小,系统具有良好的竖向隔振性能。     

大跨度斜拉桥钢塔施工阶段制振用TMD、TLD装置及其性能试验

本文以南京长江第三大桥为例,研制了用于钢塔施工阶段涡激振动响应制振的制振器TMD和TLD。对制振装置以及其所采用的一些关键技术进行了说明。通过振动台试验测试了制振器的动力特性。根据试验结果,对TMD的工作性能,即装置的频率特性、阻尼特性、起动时所需的外激励水平及装置的框架刚度等,进行了评价分析;对TLD实现了其阻尼方案的优化,并确定了其工作时的阻尼隔栅状态。确认了制作完成的制振器具有良好的工作性能。     

Ground motion spatial variability effects on seismic response control of cable-stayed bridges

The spatial variability of input ground motion at supporting foundations plays a key role in the structural response of cable-stayed bridges (CSBs); therefore, spatial variation effects should be included in the analysis and design of effective vibration control systems. The control of CSBs represents a challenging and unique problem, with many complexities in modeling, control design and implementation, since the control system should be designed not only to mitigate the dynamic component of the structural response but also to counteract the effects of the pseudo-static component of the response. The spatial variability effects on the feasibility and efficiency of seismic control systems for the vibration control of CSBs are investigated in this paper. The assumption of uniform earthquake motion along the entire bridge may result in quantitative and qualitative differences in seismic response as compared with those produced by uniform motion at all supports. A systematic comparison of passive and active system performance in reducing the structural responses is performed, focusing on the effect of the spatially varying earthquake ground motion on the seismic response of a benchmark CSB model with different control strategies, and demonstrates the importance of accounting for the spatial variability of excitations.     

Seismic response of steel structures with seesaw systems using viscoelastic dampers

Vibration control systems are being used increasingly worldwide to provide enhanced seismic protection for new and retrofitted buildings. This paper presents a new vibration control system on the basis of a seesaw mechanism with viscoelastic dampers. The proposed vibration control system comprises three parts: brace, seesaw member, and viscoelastic dampers. In this system, only tensile force appears in bracing members. Consequently, the brace buckling problem is negligible, which enables the use of steel rods for bracing members. By introducing pre‐tension in rods, long steel rods are applicable as bracing between the seesaw members and the moment frame connections over some stories. Seesaw mechanisms can magnify the damper deformation according to the damper system configuration. In this paper, first, the magnification factor, that is, the ratio of the damper deformation to the story drift, is delivered, which includes the rod deformation. Results of a case study demonstrate that the magnification factor of the proposed system is greater than unity for some cases. Seismic response analysis is conducted for steel moment frames with the proposed vibration control system. Energy dissipation characteristics are examined using the time‐history response results of energy. The maximum story drift angle distributions and time‐history response results of displacement show that the proposed system can reduce the seismic response of the frames effectively. Copyright © 2012 John Wiley & Sons, Ltd.     

Output only modal identification and structural damage detection using time frequency ＆ wavelet techniques

The primary objective of this paper is to develop output only modal identifi cation and structural damage detection.Identif ication of multi-degree of freedom(MDOF) linear time invariant(LTI) and linear time variant(LTV—due to damage) systems based on Time-frequency(TF) techniques—such as short-time Fourier transform(STFT),empirical mode decomposition(EMD),and wavelets—is proposed.STFT,EMD,and wavelet methods developed to date are reviewed in detail.In addition a Hilbert transform(HT) approach to determine ...     

Vibration suppression of structures

A procedure for vibration suppression of elastic structures and systems is introduced in this paper. First, the equations of the response of the system to external forces, based on a discretized linear model, are developed. Next, the vibration suppression is formulated as a minimization problem with control (external) forces as unknowns. Then, the optimality condition is applied to this problem and a set of linear simultaneous equations is obtained for the unknown forces. The scheme is applied to a number of simple examples for illustration. The results show that the procedure is very effective and, at the same time, very flexible compared to methods that are based on continuous models (partial differential equations). The actual (hardware) implementation can be achieved by means of either passive absorbers or active forces (actuators).     

Vibration control of cable-stayed bridges—part 1: modeling issues

The objective of the research presented here is to increase the understanding of how the complexities associated with modeling cable-stayed bridges, such as non-linear behaviour and the participation of highly coupled, high-order vibration modes in the overall dynamic response, affect the overall effectiveness of active control schemes. The 316-degree-of-freedom analytical model studied here is based on the Jindo Bridge located in South Korea. Computational considerations associated with control analyses require the size of the model to be significantly reduced, without loss of the important vibration characteristics and complexities. Three separate reduced-order modelling techniques for creating effective control models are studied here: the IRS method, the internal balancing method, and a modal reduction method. These methods are studied and compared on their ability to capture the complex dynamic response of cable-stayed bridges subjected to multiple-support excitation and their ability to create viable and computationally sound state-space models for control analyses. Results show that the modal reduction technique, because of the ability to select only those modes causing the largest force and displacement response, is most effective for control applications. © 1998 John Wiley & Sons, Ltd.     

非平稳地震激励下隔震曲线梁桥振动控制研究

曲线梁桥由于其平面不规则性导致结构在地震激励下产生弯扭耦合效应,使得隔震曲线梁桥的地震响应更加复杂。目前常用的控制方法是将隔震技术与附加减震装置相结合对曲线梁桥进行控制。本文将地震动考虑为一均匀调制非平稳随机过程,针对隔震曲线梁桥长周期、低频率的特点,选取Clough-Pension平稳地震动功率谱模型作为随机地震动输入模型,对无控(NON-C)、经典线性最优控制(COC)以及序列最优控制算法(SOC)三种状态下的曲线桥梁进行随机响应分析。通过建立曲线梁桥在随机地震动作用下的运动方程,求出减震控制结构的位移谱密度、加速度谱密度响应及时变方差。分析结果表明:序列最优控制算法(SOC)在使隔震层位移得到减小的同时,可以更有效地控制上部结构的地震响应,具有更好的控制效果。     

Semiactive variable stiffness control for parametric vibration of cables

In this paper, a semiactive variable stiffness （SVS） device is used to decrease cable oscillations caused by parametric excitation, and the equation of motion of the parametric vibration of the cable with this SVS device is presented. The ON/OFF control algorithm is used to operate the SVS control device. The vibration response of the cable with the SVS device is numerically studied for a variety of additional stiffness combinations in both the frequency and time domains and for both parametric and classical resonance vibration conditions. The numerical studies further consider the cable sag effect. From the numerical results, it is shown that the SVS device effectively suppresses the cable resonance vibration response, and as the stiffness of the device increases, the device achieves greater suppression of vibration. Moreover, it was shown that the SVS device increases the critical axial displacement of the excitation under cable parametric vibration conditions.     

Optimal vibration abatement of mechanical systems

In this paper, a method is presented for forced vibration suppression of multi-degree-of-freedom systems with damping. The technique pursued in this investigation is based on applying control forces at a certain number of the system's degrees of freedom. The problem is organized as an unconstrained, non-linear optimization formulation so that the peak vibration amplitudes of a certain number of degrees of freedom would be minimized. An efficient mathematical programming algorithm is used to solve this optimization problem numerically. It will be shown that the scheme illustrated in this paper is remarkably effective in reducing the vibration of the system. In particular, the vibration amplitudes at selected degrees of freedom may be diminished substantially.     

地铁列车曲线运行引起学校建筑物振动响应分析

地铁以其快捷、准时、运量大等优点,已成为重要的轨道交通形式,但由此引起的环境振动问题日益突出.针对杭州市地铁3号线曲线地段的某中学建设工程,利用有限元软件ABAQUS,对车辆-普通整体道床轨道系统的竖向耦合模型进行振动响应分析,得到考虑轨道高低不平顺影响的轨道振动源强.应用有限元软件MIDAS GTS/NX,建立双孔平...     

圆球减振装置对风力发电高塔的振动控制研究

本文提出了圆球减振装置对风力发电高塔振动控制的工作原理和计算方法,并对其控制效果进行了理论研究。首先利用拉格朗日方程推导得到圆球减振装置的自振频率及其对单自由度系统的被动控制力,并推广至多自由度系统。进而将风力发电高塔等效为集中质点模型,建立了风塔-减振装置体系的运动微分方程。用谐波叠加法模拟得到脉动风速时程,分析比较了风力发电高塔在无控及有控状态下的动力响应及疲劳寿命。计算结果表明,圆球减振装置是一种简单、经济和实用的减振装置,能够有效减小风塔的动力响应,延长其疲劳寿命。     

Asynchronous driving principle and its application to vibration control

The vibration control of megaframes with suspension systems is developed in this paper. The interaction between the megaframe and the suspension systems is first analysed, then asynchronous driving principle is proposed for vibration control of such structures. A numerical example is presented to show the application of asynchronous driving principle in the design of vibration control. The response of the megaframe with suspension systems under evolutionary random excitation indicates the feasibility and effectiveness of the proposed method. The vibration control method, though studied in a special case of the megaframe with suspension systems, is also applicable to the vibration control of combined structures with large secondary‐to‐primary mass ratio. Copyright © 2000 John Wiley & Sons, Ltd.     

Efficient modal analysis for structures with soil-structure interaction

An efficient methodology is presented which uses modal analysis implemented in the frequency domain to obtain the structural response of a system with soil-structure interaction. The interaction effects are represented using a free-field ground motion modification factor, derived for each mode of vibration and used in the determination of structural response. Applying this algorithm, the advantages of the modal superposition method are fully exploited, and the interaction problem can be solved easily and effectively within the framework of the conventional frequency domain analysis for a fixed-base structure. In addition, this method produces accurate approximation with less computational effort due to consideration of only the first few vibration modes of the structure.     

Comparisons between ambient and forced vibration experiments

The ambient and forced vibration techniques for testing full-scale structures are critically compared. Both methods, based on small level excitation, may be used to determine many mode shapes and frequencies of vibration and the corresponding damping values, with adequate accuracy for most purposes. The two techniques give mutually consistent results. The mode amplitudes determined by ambient and forced vibration tests show systematic departure for high modes and near the top levels of buildings tested. This phenomenon is attributed to the participation of all mode shapes and is a consequence of excitation by a concentrated force near the top of a building and at a frequency differing by only a few per cent from a natural frequency of vibrations. A new way of showing the effect of unwanted modes on the response near resonance of the mode being sought is developed. It is particularly useful for the analysis of steady, forced vibration tests of structures using eccentric mass vibration generators.     

TMD对结构地震响应控制效果的研究

TMD对简谐激励和风荷载引起振动的控制效果得到了一致的肯定,然而关于TMD地震控制的效果还没有一致的结论.文中比较了几种有代表性的TMD参数优化方法所确定的TMD参数;利用MAT-LAB编制了计算程序,分析了不同方法所确定的TMD参数用于地震控制时,控制效果的差别;从反应谱的概念出发,研究TMD对单自由度结构的地震控制效果.结果表明,TMD总体上对于单自由度结构的地震响应是有控制效果的,结构本身响应越大,控制效果越好;结构本身响应很小的时候,TMD有放大结构响应的现象,但由于结构本身响应很小,放大后的结构响应也不会导致结构有破坏的危险.     

场地条件对高速铁路地基土振动影响的研究

发展高速铁路是解决城市间交通问题的有效途径,但其所产生的振动和噪声引起的环境问题,对铁路沿线居民及周围建筑等造成不利影响。在对高速铁路引起的振动问题进行的研究中,关于高速列车引起的地基土振动随深度变化的相对较少。因此,本文针对Ⅱ、Ⅲ和Ⅳ类场地条件下的路堤式和高架桥式高速铁路,对0—5m不同深度处地基土的振动加速度响应进行了现场测试,并以测试数据为基础,分析了不同场地条件下高速列车引起的地基土振动加速度响应随深度的变化规律。结果表明,不同场地条件下,高速列车引起的振动加速度响应随深度的变化规律具有显著差异;Ⅱ类和Ⅲ类场地条件下,高速列车引起的地基土振动加速度响应总体随深度的增加而逐渐减小,并呈先快后慢的衰减趋势;而Ⅳ类场地条件下,高速列车引起的地基土振动加速度响应随深度的增加呈现先减小后放大的趋势,在深3m处加速度达到最大值。高速列车运行引起的振动频带随深度的变化特征与场地相关。     

Closure to “performance of a transparent Flexible Shear Beam container for geotechnical centrifuge modelling of dynamic problems” by Ghayoomi M., Dashti S., and McCartney J.S.

In response to the discussion, this closure presents a new set of analyses to confirm the satisfactory performance of the recently-developed transparent Flexible Shear Beam (FSB) container and its limitations. The lateral deformations of the box estimated using Finite Element analyses and measured during centrifuge experiments were compared. The maximum deformation to height ratio was sufficiently small to retain at-rest lateral earth pressures for loose to medium-dense cohesionless soils and all cohesive materials. In addition, higher frequency modes of vibration were estimated for the container, and were found to occur where the earthquake energy is less significant. Further, the box is expected to approximately replicate free field conditions under 1-D horizontal shaking for the range of soil properties under investigation. Overall, the deformation and vibration analyses indicate that the selection of appropriate rubber material properties and boundary conditions are critical when analyzing the performance of the container.     

Errors in response calculations for extensional vibrations of bars

The transient extensional vibrations of a slender and uniform bar, which is clamped at one end and is subjected to an axial force at the other free end, are investigated by applying three methods: the Laplace transform method, the normal mode and Newmark β methods in conjunction with the finite element method (FEM); the errors caused by the spatial discretization of the FEM and the direct integration of the Newmark β method are studied and compared with those of the previous paper where the flexural vibrations of a cantilever beam were considered. The reason why the extensional vibration problem is investigated here is that the condition seems to be severe due to the closeness of adjacent natural frequencies, the larger values of natural frequencies and the smaller number of nodal variables of the FEM in comparison with those of the flexural vibration problem. The numerical results show that the errors in response of the extensional vibration problem are large. However, if one follows the criterion proposed in this paper, accurate response is obtainable by the Newmark β method, which requires less computer time than either of the other methods mentioned above.