Bridge Aeroelasticity

Transcription

1 Bridge Aeroelasticity I, Sensitivity Analysis and Optimal Design J.A. Jurado, S. Hemandez. F. Nieto & A. Mosquera University of La Coruiie, Spain WITpRESS Southampton, Boston

2 Contents Preface Chapter Chapter Aeroelastic analysis and design optimization of cable-supported bridges... 1 Introduction 1 Aeroelastic phenomena... 3 Methodologies of tlutter analysis 5 Sensitivity analysis: a design tool... 9 Optimum design in engineering: application to bridge aeroelasticity 12 References 14 Cable-supported bridges since 1940: The Tacoma effecl Collapse ofthe Tacoma Narrows Bridge The "Tacoma effect" 22 Recent history ( ) \ Decks with aerodynamic sections Cable-stayed bridges Recent history ( ) Bridges ofthe Honshu-Shikoku route in Japan European bridges Bridges in China: networks in Hong Kong 47 The 21st century: achievements and projects Stonecutters Bridge in Hong Kong Bridge over the GulfofCorinth, linking Rion and Antirion Sutong Bridge in China Xihoumen Bridge in China Bridge project over the Strait ofmessina Fehmam Strait link project Projects to link Japanese islands Bridge planned for the entrance oftokyo Bay Ise Bay Bridge project Link over the Kitan Strait Project for Ho-Yo Strait link Project for the Tsugaru Strait link xv

3 2.6 Chapter Chapter Chapter Bridge project over the Chacao Channel The Rias Altas Link in Spain Suspension bridges Arch bridge References 75 Methodologies of flutter analysis for cable-supported bridges Introduction 77 Experimental aeroelasticity in long-span bridges Applications ofwind-tunnel testing on bridge engineering Types ofwind tunnel Sectional tests of bridge decks Aerodynamic tests Aeroelastic testing 86 Basic principles ofanalytical aeroelasticity Theodorsen's theory applied to flutter in flat plates Linearization ofaeroelastic loads through flutter derivatives Bridge flutter considering three aeroelastic forces 92 Movement equations for bridge decks 94 Modal analysis Aeroelastic response of a bridge 100 Wind speed and frequency at the outset of flutter 103 Existence of sirnultaneous flutter frequencies 105 References 107 Flutter analysis ofsuspension bridges during construction Introduction 109 Höga Kusten Bridge in its construction phase I Construction phases ofthe Höga Kusten Bridge... I1I Phase I: 18% ofthe main span I Phase 2: 51% ofthe central span Phase 3: 68% of the central span Phase 4: 97% ofthe rnain span Flutter parameter evolution in the construction phase of the Höga Kusten Bridge... I 19 The Great Belt Bridge in its construction phase Construction phases ofthe Great Belt Bridge Flutter parameter evolution in the construction phase of the Great Belt Bridge 127 References 129 Flutter analysis of completed cable-supported bridges 131 lntroduction 131 Great Belt Bridge Frequencies and natural modes for the Great Belt Bridge

4 Chapter Chapter Aeroelastic analysis ofthe Great Belt Bridge 138 Bridge over the Akashi Strait Natural frequencies and modes for the Akashi Strait Bridge Aeroelastic analysis ofthe Akashi Strait Bridge Original Tacoma Bridge Frequencies and natural modes for the Tacoma Bridge Aeroelastic analysis ofthe Tacoma Bridge 163 The Vasco da Gama Bridge Frequencies and natural modes for the Vasco da Gama Bridge Aeroelastic analysis ofthe Vasco da Gama Bridge 173 References 181 Sensitivity analysis ofeigenvalue problems lntroduction 183 Approximation by finite difference 184 Analytical sensitivity for eigenvalue problems Sensitivity derivatives in case ofvibration and buckling Sensitivity derivatives for non-hamiltonian eigenvalue problems 189 References 191 Analytical sensitivity analysis offree vibration problems Introduction Matrix calculation for bar structures in linear. second-order theory Frequencies and natural vibration modes in linear and second-order theories 198 Sensitivity analysis of frequencies and vibration eigen modes in 1inear and second-order theories Sensitivity analysis in linear theory Sensitivity analysis in second-order theory 202 Description ofthe "ADfSNOL3D" code 204 Practical examples with ADfSNOUD Example 1: main cable ofthe Golden Gate Bridge Example 2: suspension bridge over the Great Belt Caracteristics ofthe Great Belt suspension bridge Free vibration analysis ofthe Great Belt Bridge Free vibration sensitivity analysis ofthe suspension bridge over the Great Belt References 231

5 Chapter 8 Chapter 9 Sensitivity analysis offlutter response for cable-supported bridges Introduction Obtaining flutter speed Sensitivity analysis of the tlutter parameters in a bridge Design variables x Calculating 8A 18x Calculating 8AI8Uj Calculating 8A18Kf Solving the eigenvalue problem FLAS Code References 250 Sensitivity of flutter response for suspension bridges under construction Introduction Example I: Höga Kusten Bridge at the construction phase Example 2. Great Belt suspension bridge under construction References 265 Chapter 10 Flutter response sensitivity ofcompleted cable-supported bridges Example I. Great Belt Bridge Sensitivity of the aeroelastic analysis with 2 modes for the Great Belt Sensitivity ofthe aeroelastic analysis ofthe Great Belt using 18 modes Comparison of the sensitivity analyses for the Great Belt Flutter speed in modified designs for the Great Belt Bridge Example 2. Akashi Strait Bridge Sensitivity ofaeroelastic analysis using two modes for the Akashi Strait Bridge Sensitivities from the 17-mode aeroelastic analysis ofthe Akashi Strait Bridge Comparing the sensitivity analyses for the Akashi Strait Bridge Flutter speed in modified designs ofthe Akashi Strait Bridge Example 3. Original Tacoma Bridge Sensitivity from bimodal aeroelastic analysis ofthe Tacoma Bridge Sensitivity from the aeroelastic analysis using 10modes for the Tacoma Bridge Comparing sensitivity analyses for the Tacoma Bridge Flutter speed within modified designs of the Tacoma Bridge 290

6 10.4 Example 4. Vaseo Da Gama Bridge Sensitivity from the bimodal aeroelastie analysis ofthe Vaseo da Gama Bridge, l l-rnode sensitivity aeroelastie analysis for the Vaseo da Gama Bridge Comparing the sensitivity analyses for the Vaseo da Gama Bridge Flutter speed in the modified design ofthe Vaseo da Gama Bridge 297 t0.5 Referenees 298 Chapter 11 A formulation of optimization in bridge aeroelasticity lntroduction Conventional design method Sensitivity analysis Optimum design Suspension bridges optimum design Formulation ofthe optimum design problem Extensions ofthe sensitivity analysis formulation due to the assumption of variable mass Solving the optimum design problem: deseription ofthe DIOPTlCA code Symmetrie box cross seetion: geometrie properties and analytieal derivatives with regard to thieknesses Referenees Chapter 12 Optimization ofsuspension bridges with aeroelastic and kinematic constraints lntroduction Messina Strait Bridge general deseription Messina Strait Bridge optimum design formulation Messina Strait Bridge sensitivities results 326 [2.5 Messina Strait Bridge optimum design results. Problem C Messina Strait Bridge optimum design results. Problem L Messina Strait Bridge optimum design results. Problem CL Conelusions Referenees 337