分享-结构振动的阻尼模型-剑桥博士论文
本帖最后由 westrongmc 于 2013-2-1 11:12 编辑分享一篇不错的博士论文。
Damping Models for Structural Vibration
结构振动的阻尼模型
Cambridge University
Engineering Department
A dissertation submitted to the University of Cambridge
for the Degree of Doctor of Philosophy
by
Sondipon Adhikari
Trinity College, Cambridge
September, 2000
------------------------------------------------------------------------
Abstract
This dissertation reports a systematicstudy on analysis and identification of multiple parameter damped mechanicalsystems. The attention is focused on viscously and non-viscously dampedmultiple degree-of-freedom linear vibrating systems. The non-viscous dampingmodel is such that the damping forces depend on the past history of motion viaconvolution integrals over some kernel functions. The familiar viscous dampingmodel is a special case of this general linear damping model when the kernelfunctions have no memory.重点研究了粘性和非粘性阻尼多自由度线性振动系统。 Theconcept of proportional damping is critically examined and a generalized formof proportional damping is proposed. It is shown that the proportional dampingcan exist even when the damping mechanism is non-viscous.对比例阻尼概念做了深入研究，并进行了推广。 Classicalmodal analysis is extended to deal with general non-viscously damped multipledegree-of-freedom linear dynamic systems. The new method is similar to theexisting method with some modifications due to non-viscous effect of the dampingmechanism. The concept of (complex) elastic modes and non-viscous modes havebeen introduced and numerical methods are suggested to obtain them. It isfurther shown that the system response can be obtained exactly in terms ofthese modes. Mode orthogonality relationships, known for undamped or viscouslydamped systems, have been generalized to non-viscously damped systems. Severaluseful results which relate the modes with the system matrices are developed.将经典模态分析、模态正交性推广到一般非粘性阻尼系统，引入（复）弹性模态和非粘性模态概念。 Thesetheoretical developments on non-viscously damped systems, in line withclassical modal analysis, give impetus towards understanding damping mechanismsin general mechanical systems. Based on a first-order perturbation method, anapproach is suggested to the identify non-proportional viscous damping matrixfrom the measured complex modes and frequencies. This approach is then furtherextended to identify non-viscous damping models. Both the approaches aresimple, direct, and can be used with incomplete modal data.基于一阶摄动理论，提出由所测复模态和频率来识别非比例粘性阻尼矩阵的方法。 Itis observed that these methods yield non-physical results by breaking thesymmetry of the fitted damping matrix when the damping mechanism of the originalsystem is significantly different from what is fitted. To solve this problem,approaches are suggested to preserve the symmetry of the identified viscous andnon-viscous damping matrix.提出了保留粘性和非粘性阻尼矩阵对称性的方法 Thedamping identification methods are applied experimentally to a beam in bendingvibration with localized constrained layer damping. Since the identificationmethod requires complex modal data, a general method for identification ofcomplex modes and complex frequencies from a set of measured transfer functionshave been developed. It is shown that the proposed methods can give usefulinformation about the true damping mechanism of the beam considered for theexperiment. Further, it is demonstrated that the damping identification methodsare likely to perform quite well even for the case when noisy data is obtained. 用具有局部约束层阻尼的梁进行了试验验证。
下载链接：http://www-g.eng.cam.ac.uk/dv_library/Theses/sondiponthesis.pdf
补充内容 (2013-2-2 22:39):
粘贴时，没有很好的审查，上面文字中有些单词没有分开，抱歉，请参考日记中的文档。链接如下：
http://home.vibunion.com/home.php?mod=space&uid=190415&do=blog&quickforward=1&id=20719 {:{39}:}westrongmc 的贴子一向很给力。 本帖最后由 westrongmc 于 2013-2-2 23:33 编辑
add its contents as follows:ContentsDeclaration vAbstract viiAcknowledgements ixNomenclature xxi1 Introduction 1 1.1 Dynamics of Undamped Systems . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . 2 1.1.1 Equation of Motion . . . . .. . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . 3 1.1.2 Modal Analysis .. . . . . . . . . . . . . . . . . . . . . . ….. . . . . . . . . 4 1.2 Models of Damping . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 1.2.1 SingleDegree-of-freedom Systems . . . . . . . . . . . . . . . . . . . . . 5 1.2.2 ContinuousSystems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 1.2.3 MultipleDegrees-of-freedom Systems . . . . . . . . . . . . . . . . . . . . 9 1.2.4 Other Studies .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 1.3 Modal Analysis of ViscouslyDamped Systems . . . . . . . . . . . . . . . . . . . 11 1.3.1 The State-SpaceMethod . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 1.3.2 Methods inConfiguration Space . . . . . . . . . . . . . . . . . . . . . . . 13 1.4 Analysis ofNon-viscously Damped Systems . . . . . . . . . . . . . . . . . . . . . 18 1.5 Identification ofViscous Damping . . . . . . . . . . . . . . . . . . . . . . . . . . 19 1.5.1 SingleDegree-of-freedom Systems Systems . . . . . . . . . . . . . . . . . 19 1.5.2 MultipleDegrees-of-freedom Systems . . . . . . . . . . . . . . . . . . . . 20 1.6 Identification ofNon-viscous Damping . . . . . . . . . . . . . . . . . . . . . . . . 21 1.7 Open Problems . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22 1.8 Outline of theDissertation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 232 The Nature of Proportional Damping 25 2.1 Introduction . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25 2.2 Viscously DampedSystems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26 2.2.1 Existence ofClassical Normal Modes . . . . . . . . . . . . . . . . . . . . 26 2.2.2 Generalizationof Proportional Damping . . . . . . . . . . . . . . . . . . . 28 2.3 Non-viscously Damped Systems. . . . . . . . . . . . . . . . . . . . . . . . . . . 32 2.3.1 Existence ofClassical Normal Modes . . . . . . . . . . . . . . . . . . . . 33 2.3.2 Generalizationof Proportional Damping . . . . . . . . . . . . . . . . . . . 34 2.4 Conclusions . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 353 Dynamics of Non-viscously Damped Systems 37 3.1 Introduction . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37 3.2 Eigenvalues andEigenvectors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38 3.2.1 Elastic Modes .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39 3.2.2 Non-viscousModes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43 3.2.3 Approximationsand Special Cases . . . . . . . . . . . . . . . . . . . . . . 43 3.3 Transfer Function . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45 3.3.1 Eigenvectors ofthe Dynamic Stiffness Matrix . . . . . . . . . . . . . . . . 46 3.3.2 Calculation ofthe Residues . . . . . . . . . . . . . . . . . . . . . . . . . 47 3.3.3 Special Cases .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49 3.4 Dynamic Response . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . 49 3.5 Summary of theMethod . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51 3.6 Numerical Examples. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52 3.7 The System . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52 3.7.1 Example 1:Exponential Damping . . . . . . . . . . . . . . . . . . . . . . 53 3.7.2 Example 2: GHMDamping . . . . . . . . . . . . . . . . . . . . . . . . . 56 3.8 Conclusions . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 584 Some General Properties of the Eigenvectors 61 4.1 Introduction . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61 4.2 Nature of theEigensolutions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61 4.3 Normalization ofthe Eigenvectors . . . . . . . . . . . . . . . . . . . . . . . . . . 62 4.4 Orthogonality ofthe Eigenvectors . . . . . . . . . . . . . . . . . . . . . . . . . . 63 4.5 RelationshipsBetween the Eigensolutions and Damping . . . . . . . . . . . . . . 66 4.5.1 Relationships inTerms of M−1. . . . . . . . . . . . . . . . . . . . . . . . 67 4.5.2 Relationships inTerms of K−1. . . . . . . . . . . . . . . . . . . . . . . . 68 4.6 System Matrices inTerms of the Eigensolutions . . . . . . . . . . . . . . . . . . . 68 4.7 Eigenrelations forViscously Damped Systems . . . . . . . . . . . . . . . . . . . . 69 4.8 Numerical Examples. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70 4.8.1 The System . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70 4.8.2 Eigenvalues andEigenvectors . . . . . . . . . . . . . . . . . . . . . . . . 71 4.8.3 Orthogonality Relationships. . . . . . . . . . . . . . . . . . . . . . . . . 72 4.8.4 RelationshipsWith the Damping Matrix . . . . . . . . . . . . . . . . . . . 72 4.9 Conclusions . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 725 Identification of Viscous Damping 75 5.1 Introduction . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75 5.2 Background ofComplex Modes . . . . . . . . . . . . . . . . . . . . . . . . . . . 77 5.3 Identification ofViscous Damping Matrix . . . . . . . . . . . . . . . . . . . . . . 78 5.4 Numerical Examples. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80 5.4.1 Results forSmall γ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83 5.4.2 Results forLarger γ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86 5.5 Conclusions . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 926 Identification of Non-viscous Damping 95 6.1 Introduction . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95 6.2 Background ofComplex Modes . . . . . . . . . . . . . . . . . . . . . . . . . . . 97 6.3 Fitting of theRelaxation Parameter . . . . . . . . . . . . . . . . . . . . . . . . . . 98 6.3.1 Theory . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98 6.3.2 SimulationMethod . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100 6.3.3 NumericalResults . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102 6.4 Selecting the Value of ˆ μ .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105 6.4.1 Discussion . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109 6.5 Fitting of the CoefficientMatrix . . . . . . . . . . . . . . . . . . . . . . . . . . . 111 6.5.1 Theory . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111 6.5.2 Summary of theIdentification Method . . . . . . . . . . . . . . . . . . . . 113 6.5.3 NumericalResults . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114 6.6 Conclusions . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1207 Symmetry Preserving Methods 123 7.1 Introduction . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123 7.2 Identification ofViscous Damping Matrix . . . . . . . . . . . . . . . . . . . . . . 124 7.2.1 Theory . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124 7.2.2 NumericalExamples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 128 7.3 Identification of Non-viscousDamping . . . . . . . . . . . . . . . . . . . . . . . . 134 7.3.1 Theory . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134 7.3.2 NumericalExamples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137 7.4 Conclusions . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1408 Experimental Identification of Damping 143 8.1 Introduction . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143 8.2 Extraction ofModal Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . 144 8.2.1 LinearLeast-Square Method . . . . . . . . . . . . . . . . . . . . . . . . . 145 8.2.2 Determination ofthe Residues . . . . . . . . . . . . . . . . . . . . . . . . 146 8.2.3 Non-linearLeast-Square Method . . . . . . . . . . . . . . . . . . . . . . . 149 8.2.4 Summary of theMethod . . . . . . . . . . . . . . . . . . . . . . . . . . . 152 8.3 The BeamExperiment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153 8.3.1 ExperimentalSet-up . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153 8.3.2 ExperimentalProcedure . . . . . . . . . . . . . . . . . . . . . . . . . . . 155 8.4 Beam Theory . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 157 8.5 Results andDiscussions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 158 8.5.1 Measured andFitted Transfer Functions . . . . . . . . . . . . . . . . . . . 158 8.5.2 Modal Data . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 162 8.5.3 Identification ofthe Damping Properties . . . . . . . . . . . . . . . . . . . 166 8.6 Error Analysis . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 175 8.6.1 Error Analysisfor Viscous Damping Identification . . . . . . . . . . . . . 175 8.6.2 Error Analysisfor Non-viscous Damping Identification . . . . . . . . . . . 179 8.7 Conclusions . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1839 Summary and Conclusions 185 9.1 Summary of theContributions Made . . . . . . . . . . . . . . . . . . . . . . . . . 185 9.2 Suggestions forFurther Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 187A Calculation of the Gradient and Hessian of the Merit Function 191B Discretized Mass Matrix of the Beam 193References 195
多谢分享！ 好东西，下来看看 下载了，申请哲学博士学位做这方面的研究也可以啊？ 谢谢楼主分享。 {:{39}:}{:{39}:}{:{39}:}{:{39}:}
感谢董总，在Wilson的书里面也介绍了一些阻尼识别的方法，请参考：
Three dimensional static and dynamic analysis of structures: A physical approach with emphasis on earthquake engineering
Edward L Wilson
请在bookzz.org上下载。
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