Experimental Identification of a Structural Damping Matrix Using Natural and Zero Frequencies

The main objective of this dissertation is to develop a new experimental damping matrix identification method. Newly developed damping matrix identification method consists of finite element (FE) model updating and experimental modal analysis. In order to accomplish the goal of this study, first, the experimental modal analysis which is available for non-proportional viscous damping system is examined. Second, the sensitivity-based FE model updating method using natural frequencies and zero frequencies as target parameters is proposed. Proposed FE model updating method is validated via two examples using numerical and experimental models. Next, an efficient technique, that can identify the structural damping matrix of the damped structure through combination of the experimental modal analysis and the FE model updating method, is developed. The developed method is verified by estimating the damping matrix of a real cantilever beam attached damping material on one side.CONTENTS ABSTRACT i CONTENSTS ii LIST OF TABLES iv LIST OF FIGURES v 1. INTRODUCTION 1 1.1 Motivation 1 1.2 Review of damping matrix estimation method 2 1.3 The need 5 1.4 Objective of the dissertation 6 1.5 Outline of the dissertation 7 2. EXPERIMENTAL MODAL ANALYSIS 9 2.1 Non-proportional damping system 9 2.2 General classification of modal parameter identification methods 16 2.3 Modal parameter identification methods 19 2.3.1 Selection of modal parameter identification methods 19 2.3.2 Non-Linear Least Squares method 20 2.3.3 Peak Amplitude method 23 3. MODIFICATION OF FE MODEL 27 3.1 Recent researches on FE model updating 27 3.2 Zero frequencies 31 3.2.1 Necessity of zero frequencies as additional information 31 3.2.2 Explanation of zero frequencies 31 3.2.3 Computation of zero frequencies 33 3.3 Sensitivity analysis method using natural and zero frequencies 36 3.4 Verification of the FE model updating method 40 3.4.1 Numerical verification 40 3.4.2 Experimental verification 49 3.5 Degree of freedom reduction method 61 3.6 Modal transformation 65 4. DEVELOPMENT OF A DAMPING MATRIX ESTIMATION METHOD 67 4.1 New damping matrix estimation method based on EMA and FE model updating 67 4.2 Features of the developed damping matrix estimation method 70 5. EXPERIMENTAL VERIFICATION OF THE DEVELOPED DAMPING MATRIX ESTIMATION METHOD 71 5.1 Demonstration of the developed method for a damped cantilever beam 71 5.1.1 Modal analysis of a damped beam 71 5.1.2 Finite element model updating of a damped beam 81 5.1.3 Damping matrix estimation 87 5.2 Comparison of experimental mode shapes and identified mode shapes 96 5.2.1 Experimental and identified mode shapes 96 5.2.2 Modal Assurance Criteria 102 6. DISCUSSION OF RESULTS 104 6.1 NLLS method 104 6.2 Proposed sensitivity-based FE model updating method 104 6.3 Developed damping estimation method 105 6.4 Errors 106 7. CONCLUSION 108 REFERENCES 11