BUFFETI NG RESPONSE PREDI CTI ON BUFFETI NG RESPONSE PREDI CTI ON - PowerPoint PPT Presentation

BUFFETI NG RESPONSE PREDI CTI ON BUFFETI NG RESPONSE PREDI CTI ON FOR CABLE FOR CABLE-STAYED BRI DGES STAYED BRI DGES LE THAI HOA LE THAI HOA Kyoto University Kyoto University

CONTENTS CONTENTS 1. I ntroduction 1. I ntroduction 2. Literature review on buffeting response 2. Literature review on buffeting response analysis for bridges analysis for bridges 3. Basic formations of buffeting response 3. Basic formations of buffeting response 4. Analytical method for buffeting response 4. Analytical method for buffeting response prediction in frequency domain prediction in frequency domain 5. Numerical example and discussions 5. Numerical example and discussions 6. Conclusion 6. Conclusion 1

I NTRODUCTI ON I NTRODUCTI ON Response prediction and evaluation of long-span bridges subjected to random fluctuating loads (or buffeting forces ) play very important role . Effects of buffeting vibration and response on bridges such as: (1) Large and unpredicted displacements affect psychologically to passengers and drivers (Effect of serviceable discomfort) (2) Fatique damage to structural components Characteristics of buffeting vibration (1) Buffeting random forces are as the nature of turbulence wind (2) Occurrence at any velocity range (From low to high velocity). Thus it is potential to affect to bridges (3) Coupling with flutter forces as high sense in high velocity range 2

WI ND WI ND-I NDUCED VI BRATI ONS I NDUCED VI BRATI ONS Serviceable Discomfort Dynamic Fatique Vortex-induced vibration Buffeting vibration Wind- Limited-amplitude induced Vibrations Wake-induced vibration Vibrations Rain/wind-induced And Bridge Galloping instability Aero- Divergent-amplitude Flutter instability dynamics Vibrations Wake instability Structural Catastrophe 3

RESPONSE AMPLI TUDE AND VELOCI TY RESPONSE AMPLI TUDE AND VELOCI TY Buffeting Response Vortex-induced Flutter and Galloping Response Amplitude Response Instabilities Karman-induced ‘Lock-in’ Response Response Random Forces Self-excited Forces in Turbulence Wind in Smooth or Forced Forces Self-excited Turbulence Wind Forces Resonance Peak Value U U re  Reduced Velocity nB Limited-amplitude Response Divergent-amplitude Response Low and medium velocity range High velocity range Note : Classification of low, medium and high velocity ranges is relative together 4

I NTERACTI ON OF WI ND I NTERACTI ON OF WI ND-I NDUCED VI BRATI ONS I NDUCED VI BRATI ONS Interaction of wind-induced vibrations and their responses is potentially happened in some certain aerodynamic phenomena. In some cases, the interaction of them suppresses their total responses, and in contrast , enhances total responses in the others. Vortex-shedding Physical Model + Mathematic Model Physical + Mathematic Individual Buffeting Random Vibration Phenomena Physical + Flutter Self-excited Vibration Case study Mathematic Vortex-shedding and Buffeting (Physical Model) Aerodynamic Vortex and Low-speed Flutter (Physical Model) Interaction Case study Buffeting and Flutter (Mathematic Model) Reduced Velocity Axis 5

MEAN WI ND VELOCI TY AND FLUCTUATI ONS MEAN WI ND VELOCI TY AND FLUCTUATI ONS Atmospheric boundary layer (ABL) Elevation (m) Amplitude of Velocity ADB’s Depth u(z,t): Fluctuation d= 300-500m U(z) z U(z) u(z,t) Mean Time Mean and fluctuating velocities of turbulent wind Horizontal component: U(z,t) = U(z) + u(z,t) Buffeting Forces Vertical component: w(z,t) Longitudinal component: v(z,t) Wind Fluctuations Wind fluctuations are considered as the Normal-distributed stationary random processes (Zero mean value) 6

WI ND FORCES AND RESPONSE WI ND FORCES AND RESPONSE Total wind forces acting on structures can be computed under superposition principle of aerodynamic forces as follows    ( ) ( ) ( ) F t F F t F n total QS B SE F : Quasi-steady aerodynamic forces (Static wind forces) QS ( n ) F SE : Self-controlled aerodynamic forces (Flutter) ( t ) F B : Unsteady (random) aerodynamic forces (Buffeting) Aerodynamic behaviors of structures can be estimated under static equilibrium equations and aerodynamic motion equations KX  : Static Equilibrium F QS        : Dynamic Equilibrium ( ) ( ) M X C X KX F n F t SE B Combination of self-controlled forces (Flutter) and unsteady fluctuating forces (Buffeting) is favorable under high-velocity range 7

BUFFETI NG BUFFETI NG The buffeting is defined as the wind-induced vibration in wind turbulence that generated by unsteady fluctuating forces as origin of the random ones due to wind fluctuations. The purpose of buffeting analysis is that prediction or estimation of total buffeting response of structures (Displacements, Sectional forces: Shear force, bending and torsional moments) Buffeting response prediction is major concern (Besides aeroelastic instability known as flutter) in the wind resistance design and evaluation of wind-induced vibrations for long-span bridges Fluctuating Forces Buffeting Response Wind Fluctuations Prediction of Response Nature as Random (Forces+ Displacement) Stationary Process 8

LI TERATURE REVI EW I N BUFFETI NG ANALYSI S (1) LI TERATURE REVI EW I N BUFFETI NG ANALYSI S (1) The buffeting response analysis can be treated by either: 1) Frequency-domain approach (Linear behavior) or 2) Time-domain approach (Both linear and nonlinear behaviors Quasi-steady buffeting Linear analysis forces Frequency Domain Methods Turbulence modeling (Power spectral density) Spectral analysis method (Correction functions) Buffeting response prediction methods Quasi-steady buffeting model Time Domain Methods Time-history turbulence simulation Time-history analysis Linear and Non-linear 9

LI TERATURE REVI EW I N BUFFETI NG ANALYSI S (2) LI TERATURE REVI EW I N BUFFETI NG ANALYSI S (2) H.W.Liepmann (1952) : Early works on computational buffeting prediction carried out for airplane wings . The spectral analysis applied and statistical computation method introduced . Alan Davenport (1962) : Aerodynamic response of suspension bridge subjected to random buffeting loads in turbulent wind proposed by Davenport. Also cored in spectral analysis and statistical computation, but associated with modal analysis . Numerical example applied for the First Severn Crossing suspension bridge (UK). H.P.A.H I win (1977) : Numerical example for the Lions’ Gate suspension bridge (Canada) and comparision with 3Dphysical model inWT. Recent developments on analytical models based on time-domain approach [Chen&Matsumoto(2000), Aas-Jakobsen et al.(2001)]; aerodynamic coupled flutter and buffeting forces [Jain et al.(1995), Chen&Matsumoto(1998), Katsuchi et al.(1999)]. 10

EXI STI NG ASSUMPTI ONS I N BUFFETI NG ANALYSI S EXI STI NG ASSUMPTI ONS I N BUFFETI NG ANALYSI S (1) Gaussian stationary processes of wind fluctuations Wind fluctuations treated as Gaussian stationary random processes (2) Quasi-steady assumption Unsteady buffeting loads modeled as quasi-steady forces by some simple approximations: i) Relative velocity and ii) Unsteady force coefficients (3) Strip assumption Unsteady buffeting forces on any strip are produced by only the wind fluctuation acting on this strip that can be representative for whole structure (4) Correction functions and transfer function Some correction functions ( Aerodynamic Admittance, Coherence, Joint Acceptance Function ) and transfer function ( Mechanical Admittance ) added for transform of statistical computation and SISO (5) Modal uncoupling: M ultimodal superposition from generalized response is validated 10

TI ME TI ME-FREQUENCY DOMAI N TRANFORMATI ON FREQUENCY DOMAI N TRANFORMATI ON AND POWER SPECTRUM AND POWER SPECTRUM Transformation processes Time Domain Frequency Domain Fourier Transform Correlation Power Spectrum Transform between time domain and frequency domain using Fourier Transform’s Weiner-Kintchine Pair   1           ( ) ( ) exp( ) X X t j t dt ( ) ( ) exp( ) X t X j d  0 0 Power spectrum (PSD) of physical quantities known as Fourier Transform of correlation of such quantities             ( ) [ ( ) ( )] ( ) ( ) exp( ) R X E X t X t S R j d X X 11 0

BASI C FORMATI ONS OF BUFFETI NG BASI C FORMATI ONS OF BUFFETI NG RESPONSE ANALYSI S RESPONSE ANALYSI S NDOF system motion equations subjected to sole fluctuating buffeting forces are expressed by means of Finite Element Method (FEM)       ( t ) M X C X KX F F B (t): Buffeting forces B         2 [ ] ( ) ( ) Fourier Transform M j C K X F B     ( ) ( ) ( ) X H F H(  ): Complex frequency response matrix B         X(  ), F B (  ): F 2 1 .Ts of response and ( ) [ ] H M j C K buffeting forces Fourier Transform of mean square of displacements and that of buffeting forces   ( 0 ) [ ( ) ( )] R E F t F t ( 0 ) [ ( ) ( )] R X E X t X t F B B S X (  ), S B (  ): Spectrum of response     2 ( ) | ( ) | ( ) S H S X b and buffeting forces  Mean square of response      2 ( ) S X d 12 0