Analytical investigations of square Tuned Liquid Damper (TLD) for suppressing horizontal motion of SDOF system

A Tuned Liquid Damper (TLD) is a passive control device on the top of a structure so that dissipates the input excitation energy rely on the liquid sloshing in the container as well as through the liquid boundary layer friction, the free surface contamination and wave breaking. In order to design an efficient TLD, using Fujino’s model to illustrate the liquid behavior as well as knowing optimum TLD parameters are crucial importance. Numerical simulations of a single-degree-of-freedom (SDOF) structure, rigidly supporting a tuned liquid damper (TLD) and subjected to both wind and earthquake ground motions, show that a properly designed TLD can significantly reduce the structure''s response to these motions. The TLD is a rigid, square tank with shallow water in it. Its fundamental linear sloshing frequency is tuned to the structure''s natural frequency. The TLD is more effective in reducing structural response as the ground excitation level increases. This is because it then dissipates more energy due to sloshing and wave breaking. A larger water-depth to tank-length ratio than previous studies (0.1) suggested, which still falls within the constraint of shallow water theory, is shown to be more suitable for excitation levels expected in strong earthquake motions. A larger water-mass to structure-mass ratio is shown to be required for a TLD to remain effectiveness and ensure structural safety. Furthermore, the reduction in response is seen to be fairly insensitive to the bandwidth of the ground motion but is dependent on the structure''s natural frequency relative to the significant ground frequencies. By numerical method, therefore, observing that maximum response of system with TLD is in resonance condition.ACKNOWLEDGMENTS 1 ABSTRACT 2 TABLE OF CONTENTS 3 LIST OF TABLES 5 LIST OF FIGURES 6 CHAPTER 1 – INTRODUCTION 11 1.1 Tuned Liquid Damper-TLD 11 1.2 Scope of Study and Outline of Thesis 12 CHAPTER 2 – MATHEMATICAL FOMULATIONS 13 2.1 Linear Wave Theory 13 2.1.1 Fundamental natural frequency 13 2.2.2 Classification of wave sloshing in tank of TLD 13 2.2 Theory Modelling of Water Sloshing Inside TLD 14 2.2.1 Governing Equations 14 2.2.2 Derivation of Basic Equations 15 2.3 TLD-Structure Interaction Subjected to Horizontal Motion 18 2.4 Analysis Procedures 19 2.5 Selection of TLD Parameters 19 2.5.1 Turning ratio 20 2.5.2 Frequency ratio 20 2.5.3 Depth ratio 20 2.5.4 Mass ratio 21 CHAPTER 3 – NUMERICAL ANALYSIS 22 3.1 SDOF-TLD Interaction 22 3.1.1 Main structure 22 3.1.2 Tuned Liquid Damper 22 3.1.3 Excitation forces 23 3.2 Case Studies 23 3.2.1 Effect of TLD’s Turning ratio 23 3.2.2 Effect of TLD’s Frequency ratio 24 3.2.3 Effect of TLD’s Depth ratio 24 3.2.4 Effect of TLD’s Mass ratio 25 3.3 Results and Discussions 26 3.3.1 Excitation force 26 3.3.2 SDOF-TLD Interaction 26 a.Turning ratio 26 b.Frequency ratio 26 c.Depth ratio 27 d.Mass ratio 28 CHAPTER 4 – CONCLUSIONS AND FUTURE WORKS 29 4.1 Conclusions 29 4.2 Procedure to design Tuned Liquid Damper 30 4.3 Future works 30 REFERENCES 32 NOTATIONS 37 PRESENTED TABLES 39 PRESENTED FIGURES 44 APPENDIX A 132 A.1 Non-dimensionalization of Basic Equations 132 A.2 Discretization of Basic Equations 132 A.3 Runge – Kutta – Gill method 135 APPENDIX B 136 Matlab Code 136 RESUME 14