Experimental Modal Damping Identification of a Mechanical Structure Using Video Magnification Technique

Vibration can be introduced in all mechanical fields in our life.Engineers try to avoid its negative effect leading in some cases to deformation in the machines.Many researches are dedicated to study the identification of damping especially in multi degree of freedom systems with particular attention to the source of energy dissipation.They focus on developing new tools or methods which may be used in real problems to obtain accurate results about the amount(or value)and the location of energy dissipation in the structure.The aim of this paper is to present an original procedure aims to experimentally determine the modal damping ratio of a mechanical structure.The proposed procedure consists of extracting the Frequency Response Function of the vibrating system using the video magnification method and then calculate the modal damping ratio using the 3-dB method.These experimental measurements are carried out by giving an external force on a cantilever beam,then the modal damping ratios are extracted using motion magnification.The obtained results show a relative error less than 4.2% between the experimental measurements and the analytical calculation for the Frequency Response Function(FRF)curves.The novelty of the paper is to combine the video magnification technique and the 3dB method in a procedure that aims to experimentally measure the modal damping of a mechanical structure.The proposed procedure in this paper represents the damping identification as a simple and easy engineering application.

Modal parameter identification and damping ratio estimation from the full-scale measurements of a typical Tibetan wooden structure

Tibetan heritage buildings have a high historical and cultural value. They have endured adverse environmental loadings over hundreds of years without significant damage. However, there are few reports on their structural characteristics under normal environmental loadings and their behavior under dynamic loadings. In this research, a typical Tibetan wooden wall-frame building is selected to study its dynamic characteristics. Field measurements of the structure were conducted under environmental excitation to collect acceleration responses. The stochastic subspace identification （SSI） method was adopted to calculate the structural modal parameters and obtain the out-of-plane vibration characteristics of the slab and frames. The results indicated that the wall-frame structure had a lower out-of-plane stiffness and greater in-plane stiffness due to the presence of stone walls. Due to poor identified damping ratio estimates from the SSI method, a method based on the variance upper bound was proposed to complement the existing variance lower bound method for estimating the modal damping ratio to address the significant damping variability obtained from different points and measurements. The feasibility of the proposed method was illustrated with the measured data from the floor slab of the structure. The variance lower and upper bound methods both provided consistent results compared to those from the traditional SSI method.

Vibro-acoustic Radiation Characteristics Analysis of Railway Vehicle Wheel with Damping Ridges Based on Modal Strain Energy

The existing researches on the damping wheel mainly focus on investigating the influence of damping structure change on the vibro-acoustic control.The changes include the geometric size of the damping structure,the damping material parameters,and the placement,and so on.In order to further understand the mechanism in reducing the acoustic radiation of railway wheel with layer damping treatment,in this paper,the wheel is simply modified by a full-sized circular plate.The circle plate side has stuck circumference constrained damping ridges and radial constrained damping ridges on it.Based on a hybrid finite element method-boundary element method（FEM-BEM）,the paper develops a vibro-acoustic radiation model for such a distributed constrained damping structure.The vibration and acoustic radiation of the circular plate is analyzed.In the analysis,the dynamic response of the system is obtained by using the 3D finite model superposition method.The obtained vibration response is used as the initial boundary condition in solving Helmholtz boundary integral equation for the sound radiation analysis.In the procedure,firstly,the modal analysis of the circular plate is performed to get the distribution of the system modal strain energy.Secondly,the vibro-acoustic radiation characteristics of the plate with different kinds of circumference damping ridges and radial damping ridges are compared in order to try to find the best effective damping ridge structure.Thirdly,using the distribution of the plate modal strain energy investigates the effect of the ridge distribution locations on the circular plate on its vibro-acoustic radiation.The calculation and analysis research results show that,the sticking circumference and radial damping ridges on the plate can control the vibro-acoustic radiation of the plate effectively in different frequency range.The distribution of the constrained damping ridge has an effect on reduction in vibro-acoustic radiation of the circular plate.The present research is very useful in the design of railway wheel with low noise level.

Feasibility study of a large-scale tuned mass damper with eddy current damping mechanism

Tuned mass dampers （TMDs） have been widely used in recent years to mitigate structural vibration. However, the damping mechanisms employed in the TMDs are mostly based on viscous dampers, which have several well-known disadvantages, such as oil leakage and difficult adjustment of damping ratio for an operating TMD. Alternatively, eddy current damping （ECD） that does not require any contact with the main structure is a potential solution. This paper discusses the design, analysis, manufacture and testing of a large-scale horizontal TMD based on ECD. First, the theoretical model of ECD is formulated, then one large-scale horizontal TMD using ECD is constructed, and finally performance tests of the TMD are conducted. The test results show that the proposed TMD has a very low intrinsic damping ratio, while the damping ratio due to ECD is the dominant damping source, which can be as large as 15% in a proper configuration. In addition, the damping ratios estimated with the theoretical model are roughly consistent with those identified from the test results, and the source of this error is investigated. Moreover, it is demonstrated that the damping ratio in the proposed TMD can be easily adjusted by varying the air gap between permanent magnets and conductive plates. In view of practical applications, possible improvements and feasibility considerations for the proposed TMD are then discussed. It is confirmed that the proposed TMD with ECD is reliable and feasible for use in structural vibration control.

Influence of Girder Vibration on Cable Damper's Performance of A Cable-stayed Bridge

The model combined by cable,girder and damper is founded to study the influence of girder vibration on cable damper 's performance of a cable-stayed bridge. The complex mode method and nondimensionalization are used to analyze the relationship between the girder's parameters and the performance of cable-related damper. The results indicate that the performance of cable-related damper will decrease greatly when the girder frequencies are near the frequencies of cable. The smaller absolute displacement of damper's piston caused by the very small vibration phase shift of girder and cable is the physical cause of the negative impact mentioned above.

A method for stochastic seismic response analysis of non-classically damped structures

A method to calculate the stationary random response of a non-classically damped structure is proposed that features clearly-defined physical meaning and simple expression. The method is developed in the frequency domain. The expression of the proposed method consists of three terms, i.e., modal velocity response, modal displacement response, and coupled (between modal velocity and modal displacement response). Numerical results from the parametric study and three example structures reveal that the modal velocity response term and the coupled term are important to structural response estimates only for a dynamic system with a tuned mass damper. In typical cases, the modal displacement term can provide response estimates with satisfactory accuracy by itself, so that the modal velocity term and coupled term may be ignored without loss of accuracy. This is used to simplify the response computation of non-classically damped structures. For the white noise excitation, three modal correlation coefficients in closed form are derived. To consider the modal velocity response term and the coupled term, a simplified approximation based on white noise excitation is developed for the case when the modal velocity response is important to the structural responses. Numerical results show that the approximate expression based on white noise excitation can provide structural responses with satisfactory accuracy.

悬索桥竖弯涡振MTMD减振控制效果和参数优化研究

为研究多重调谐质量阻尼器(Multiple Tuned Mass Damper,MTMD)抑制桥梁单阶涡振的性能,建立桥梁结构-MTMD系统竖弯涡振广义单自由度动力方程,以某大跨度悬索桥为背景进行MTMD减振控制效果和参数优化分析。采用数值方法求解动力方程,获得系统在简谐涡激力下达到稳态谐振时结构的动力放大系数和MTMD对结构的附加模态阻尼比,并与单一频率调谐质量阻尼器(Single Tuned Mass Damper,STMD)的减振控制效果进行对比,然后以附加模态阻尼比为目标对MTMD进行参数优化。结果表明:MTMD比最优参数STMD拥有更宽的控制频带和更好的减振效果,经优化后的MTMD减振性能优于最优参数STMD。实际应用MTMD时,应选择较大广义质量、5~7种频率规格,并根据二者找到无量纲频率范围和各TMD阻尼比的惟一最优取值。

A new damping ratio identification method based on pattern search

In order to improve the effectiveness of traditional time domain identification methods in identifying damping ratios, a new damping ratio identification method based on pattern search is proposed by fluctuating the reliable natural frequency obtained through traditional time domain identification methods by about 10% to build the boundary conditions, using all the initial identification results to establish the free decay response of the system, and using the pattern search method to correct the initial identification results with the residual sum of squares between the free decay response and the actually measured free-decay signal as the objective function. The proposed method deals with the actually measured free-decay signal with curve fitting and avoids enlarging the identified error caused by intermediate conversion, so it can effectively improve the identified accuracy of damping ratios. Simulations for a room-sized vibration isolation foundation show that the relative errors of analyzed three damping ratios are down to 1.05%, 1.51% and 3.7% by the proposed method from 8.42%, 5.85% and 8.5% by STD method when the noise level is 10%.

Effects of Fiber Volume Fraction on Damping Properties of Three-Dimensional and Five-Directional Braided Composites

The effects of fiber volume fraction on damping properties of carbon fiber three-dimensional and five-directional( 3D-5Dir)braided carbon fiber / epoxyres in composite cantilever beams were studied by experimental modal analysis method. Meanwhile,carbon fiber plain woven laminated / epoxy resin composites with different fiber volume fraction were concerned for comparison. The experimental result of braided specimens shows that the first three orders of natural frequency increase and the first three orders of the damping ratios of specimens decrease, when the fiber volume fraction increases. Furthermore,larger fiber volume fraction will be valuable for the better anti-exiting property of braided composites,and get an opposite effect on dissipation of vibration energy. The fiber volume fraction is an important factor for vibration performance design of braided composites. The comparison between the braided specimens and laminated specimens reveals that 3D braided composites have a wider range of damping properties than laminated composites with the same fiber volume fractions.

水中旋转圆盘振动阻尼测量与模拟

为了研究模态做功法在计算旋转式机械水力阻尼时的适用性和准确性,利用旋转圆盘阻尼测量系统的实验数据对该方法做了评估.研究表明,圆盘的水力阻尼值随转速的增加呈现下降的趋势;利用模态做功法计算水力阻尼值时必须考虑旋转效应带来的影响,如果直接使用静止条件下的模态结果,水力阻尼随转速的变化规律将完全和实验结果相反;在考虑旋转的条件下,计算精度有所提高,但整体呈现过预测的问题,该方法对旋转结构阻尼特性的预测精度还有待提高.

Output-only identification of the modal and physical properties of structures using free vibration response

The viability of a complete structural characterization of civil structures is explored and discussed. In particular, the identification of modal （i.e. natural frequencies, damping ratios and modal shapes） and physical properties （i.e. mass and stiffness） using only the structure＇s free decay response is studied. To accomplish this, modal analysis from flee vibration response only （MAFVRO） and mass modification （MM） methodologies are engaged along with Wavelet based techniques for optimal signal processing and modal reconstruction. The methodologies are evaluated using simulated and experimental data. The simulated data are extracted from a simple elastic model of a 5 story shear building and from a more realistic nonlinear model of a RC frame structure. The experimental data are gathered from shake table test of a 2-story scaled shear building. Guidelines for the reconstruction procedure from the data are proposed as the quality of the identified properties is shown to be governed by adequate selection of the frequency bands and optimal modal shape reconstruction. Moreover, in cases where the structure has undergone damage, the proposed identification scheme can also be applied for preliminary assessment of structural health.

Topology Optimization in Damping Structure Based on ESO

The damping material optimal placement for the structure with damping layer is studied based on evolutionary structural optimization (ESO) to maximize modal loss factors. A mathematical model is constructed with the objective function defined as the maximum of modal loss factors of the structure and design constraints function defined as volume fraction of damping material. The optimal placement is found. Several examples are presented for verification. The results demonstrate that the method based on ESO is effective in solving the topology optimization of the structure with unconstrained damping layer and constrained damping layer. This optimization method suits for free and constrained damping structures.

考虑高阶振型效应的大跨度钢桁拱桥瑞利阻尼参数取值研究

为了解高阶振型效应对大跨度钢桁拱桥地震反应的影响机制,以及在采用直接积分法时构建合适的瑞利阻尼矩阵,以某490 m跨径钢桁拱桥为背景,采用SAP 2000软件建立全桥弹性动力计算模型。针对主拱圈上(下)弦杆轴力、弯矩,研究振型参与质量最大的7阶(第1、4、8、11、13、23、49阶)振型反应与总反应的占比关系,并对构建瑞利阻尼矩阵的特征频率选取方法展开研究。结果表明:主拱圈上、下弦杆拱脚区域的轴力主要由1阶振型(第1阶)控制,由拱脚向拱顶过渡,逐渐转变为由2~4阶振型控制,高阶振型效应显著;同一阶振型对主拱圈上、下弦杆轴力贡献率及分布规律的影响不同;对于复杂钢桁拱桥,采用振动方向上振型参与质量较大的2阶振型特征频率构建瑞利阻尼矩阵可能因高估了高阶振型阻尼比,导致除拱脚区域以外的拱圈弦杆杆件轴力计算结果偏小,结构偏于不安全;采用直接积分法对复杂钢桁拱桥进行地震反应分析时,建议选取多阶控制振型构建相应的瑞利阻尼工况,并对其计算结果取包络用于抗震设计。

敷设约束阻尼层的工字梁振动特性研究

本文提出了一种计算带约束阻尼层梁振动响应的方法。以工字梁为研究对象,开展了室内振动试验,测得了不同位置的振动响应。并基于有限元法同步建立了数值仿真模型,利用模态应变能法准确计算了结构的自振频率和模态损耗因子。基于上述结果,利用模态叠加法进行谐响应分析,得到了约束阻尼层工字梁的振动响应结果。将振动响应的实测值与仿真值进行对比,验证了模型的准确性。分析了设计参数(阻尼层厚度、约束层厚度)对构件自振频率、模态损耗因子及加速度总振级的影响。研究结果表明:各板件的振动响应有着相似的变化规律,腹板加速度总振级最大,底板次之,顶板最小;总体上阻尼层厚度对工字梁前5阶自振频率影响不大,而随着约束层厚度的增大,构件前5阶自振频率先减小后增大;增大阻尼层厚度和约束层厚度都能持续增大构件的模态损耗因子,进而有效降低加速度总振级,且对腹板的减振效果好于顶板和底板。

The MDOF equivalent linear system and its applications in seismic analysis and design of framed structures

This paper reviews the applications of the multi degree-of-freedom(MDOF)equivalent linear system in seismic analysis and design of planar steel and reinforced concrete framed structures.An equivalent MDOF linear structure,analogous to the original MDOF nonlinear structure,is constructed,which has the same mass and elastic stiffness as the original structure and modal damping ratios that account for the effects of geometrical and material nonlinearities.The equivalence implies a balance between the viscous damping work of the equivalent linear structure and that of the nonlinearities in the original nonlinear structure.This work balance is established with the aid of a transfer function in the frequency domain.Thus,equivalent modal damping ratios can be explicitly determined in terms of the period and deformation levels of the structure as well as the soil types.Use of these equivalent modal damping ratios can help address a variety of seismic analysis and design problems associated with planar steel and reinforced concrete framed structures in a rational and accurate manner.These include force-based seismic design with the aid of acceleration response spectra characterized by high amounts of damping,improved direct displacement-based seismic design and the development of advanced seismic intensity measures.The equivalent modal damping ratios are also utilized in the context of linear modal analysis for the definition and construction of the MDOF response spectrum.Furthermore,the equivalent modal damping ratios are employed in a seismic retrofit method for steel-framed structures with viscous dampers.Finally,it is demonstrated that modal behavior(or strength reduction)factors can be easily constructed based on these modal damping ratios for a more rational and accurate force-based seismic design,including the determination of inelastic displacement profiles.

风电机组纯钢塔架和组合式塔架动力特性对比研究

对某风电场2.0 MW风电机组120 m高单管式风力发电钢塔和钢-混凝土组合式风力发电塔的振动进行长期监测,分别采用峰值拾取法(PP)和随机子空间法(SSI)对塔架的模态参数进行识别和分析,并与数值分析结果进行对比。结果表明:两座塔架的振动主要以前三阶模态为主,高阶模态的影响不可忽略。相较于钢-混凝土组合塔架,纯钢塔架受塔顶叶轮转动的影响更大,更易发生共振。模态阻尼中气动阻尼占比较大,其与环境风速和桨距角关系密切,与风速呈非线性关系,并且在桨叶变桨时变化明显。对比实测识别和数值分析结果发现,两座塔架的模态频率以及混塔的振型数值分析结果与实测结果比较吻合,钢塔的振型数值分析结果与实测结果存在差异,在运维养护时应重点关注。

大跨度单层柔性光伏支架结构气动阻尼的试验研究

大跨光伏支架结构轻柔,在风荷载作用下易产生显著气动效应。为研究该类结构的气动阻尼特征,对不同风速和张力工况下两种典型倾角(0°和10°)的大跨度柔性光伏支架结构开展气弹风洞试验。基于气弹模型风洞试验结果,分别利用经验小波变换(empirical wavelet transform,EWT)和变分模态分解(variational modal decomposition,VMD)结合改进的随机减量方法(random decrement technique,RDT)识别得到了柔性光伏支架结构在不同风速风向、组件倾角和拉索预张力下的气动阻尼比。研究结果表明,气动阻尼对风向角的变化较为敏感。当组件倾斜铺设时(10°倾角),大跨光伏结构气动阻尼在180°迎风向时会出现负值。张力增加可能导致高风速下平铺组件的气动阻尼比显著降低。气动阻尼比随风速的增加整体呈减小趋势,低风速下基本为正值,而高风速下可能出现负气动阻尼。不同方法识别出的气动阻尼比结果存在一定的差异,但反映出的气动阻尼的变化特征具有一致性。

基于模态阻尼指标的空间杆系结构作动器位置优化

针对空间杆系结构作动器的位置优化问题,本文基于线性二次型最优控制理论(LQR),建立了空间杆系结构振动的主动控制系统,提出了目标控制模态的模态阻尼最大化的作动器位置优化准则.采用四角锥网架结构和Levy型索穹顶结构来验证本文方法的有效性,并在控制效果和控制能量输入两方面与常用的模态控制力方法进行了对比分析.结果表明:随着作动器数量的增加,本文方法的控制效果和控制能量输入比模态控制力方法提升更快;在作动器数量相同或控制能量输入相同时,本文方法对外界激励的控制效果优于模态控制力方法.

基于改进SSI法的加工机器人工作模态在线辨识

为提高串联式机器人的加工能力,提出一种基于改进SSI法的加工机器人工作模态在线辨识方法,该方法首先在传统SSI法的基础上进行改进,利用NExT法、模态置信因子及模态保证准则3种手段来提高加工机器人工作模态参数辨识精度。其次,利用加工机器人铣削加工振动数据对其走刀路径上关键点位出的模态频率和阻尼比进行在线辨识。最终,通过机器人切削加工实验验证该方法,实验结果表明,相比于锤击实验结果,改进SSI法模态参数辨识误差在7%以内,且相比于传统SSI法,改进SSI法模态参数辨识精度更高。因此,若仅关心模态频率及阻尼比,该方法可实现加工机器人走刀过程中模态参数的在线辨识,可为后续机器人进行工艺规划和优化提供输入条件。

柔性直流引发火电机组次同步振荡的电气负阻尼关键因素分析

电力电子装置大量接入电力系统,会产生电气负阻尼,而电气负阻尼是导致机组产生次同步振荡的直接原因。确定引起电气负阻尼的关键环节和参数,对于理解电气负阻尼产生机理、制定抑制措施十分重要。针对这个问题,首先采用改进复转矩系数的电气阻尼分析方法,基于模式解耦展开复转矩系数传递函数,定义电气阻尼极值,确定引起负阻尼的关键振荡模式及分式。其次,引入电气阻尼相关因子和灵敏度,确定电气负阻尼的关键影响环节和参数,根据灵敏度分析结果给出参数调整方案以抑制次同步振荡。最后,通过PSCAD模型进行时域仿真验证。