Use of Viscous Dampers

Transcription

1 Use of Viscos Dampers 粘性ダンパーを用いた免震設計 Kazhiko Kawashima Tokyo Institte of Technology 東京工業大学川島一彦 Response Modification Technologies Technologies which modifies the seismic response of strctres for aiming to enhance seismic performance of the strctres dring an earthqake Smart materials and smart (ato adaptable) strctres Damper technologies Sensor & actator systems Response Modification Technologies Classification in terms of energy dissipation Passive control Active control Semi-active control Classification of Passive Control Seismic isolation=period shift + Enhancement of energy dissipation Energy dissipation sing dampers Distribtion of seismic lateral force to sbstrctres.. Damper Technology Since Late 96s Damper Technologies = c& Damping force Velocity Damping coefficient kn/(m/s) Viscos Flid m k c Energy Dissipation by Dampers & m &&+ c& + k = F(t) = c& If F(t)=, an eqation of motion of free oscillation becomes && + hω& + ω = If can be written as a harmonic motion as = Asin( ωt & = Aω cos( ωt

2 = c& = Asin( ωt & = Aω cos( ωt Increase of ω & Energy dissipation of a device with restoring force F is W = Fd = c& d d c & d = c& dt = c& & dt dt Becase, Ths, energy dissipation of a damper per cycle is W π /ω d = c& & dt Sbstitting & W π /ω d = c& & dt = Aω cos( ωt = π / ω W d c ω A cos ( ωt d( ωt) = cωa π Increase of ω N Eqivalent damping coefficient (/3) F f = µn (t) Friction force Energy dissipation per cycle de to a constant friction force is W f = 4Ff If we consider a single degree-offreedom system with viscos damper, m k energy dissipation of a damper per c cycle is ω π W d = c A F Eqivalent damping coefficient (/3) By eqating (t) Friction force m k c W f = Wd F W W f ceq = πωa f = 4Ff W ωa d = c π Eqivalent damping coefficient (3/3) W f ceq = πωa Eqivalent damping ratio h eq for c eq is W f ceq A W f heq = = πω = c mk cr π ka W d We = Becase ka F W e W f W A heq = h d eq = 4π We 4π We Eqivalent damping ratio Effect of enhancing energy dissipation by viscos dampers? The seismic response of a strctre can be compted for any system sbjected to arbitrary grond motion by varying damping ratio based on compter analysis As damping ratio increases, response acceleration, velocity and displacement generally decrease Ths, installation of viscos dampers is beneficial for redcing the seismic response of a strctre

3 Response of strctres can be approximated sing response acceleration spectrm Response Acceleration a r max Peak Response Acceleration a r max a r max3 a r max a r max 4 T T T 3 * ξ = ξ T T T3 T4 Natral Period (s) T 4 Grond Acceleration Effect of enhancing energy dissipation by viscos dampers? S ( T, ) c ( T, ) A ξ D ξ = SA( T,.).8ξ. S ( T,.) 3ξ + 6 c ( T, ξ ) = +. A D 4ξ + amax Coefficient a(h) Damping Ratio h Coefficient b(h) Damping Ratio h. c D ( h) = +. 4h +. c D ( ) = +. =. c D (.) = +. = +. c D (.) = +. =.8 c D ( ) =. Coefficient a(h) Damping Ratio h Impact Force Gap Example of Analysis Relative Displacement Impact Spring Impact spring element Variable damper element Natral period of the first mode is.9 s. Natral period of the second mode is.94 s Acceleration (m/s ) - Grond Motion Used in the Analysis - 3 Time (s) Displacement Response Spectrm (m) Acceleration Response Spectrm (m/s ) Natral Period (s) JMA Kobe record (Measred at the JMA Kobe Observatory in the 99 Hyogo-ken Nanb EQ) Natral Period (s) Displacement (m) Response of the Bridge with Viscos Dampers Acceleration of Left Deck (m/s ) Displacement of Left Deck (m) Time (sec) Time (sec) Acceleration of Right Deck (m/s ) Displacement of Right Deck (m) No damper Viscos damping 3

4 Response of the Bridge with Viscos Dampers Response of the Bridge with Viscos Dampers 6 Moment vs. Crvatre at Plastic Hinge of Left Pier 6 Moment vs. Crvatre at Plastic Hinge of Right Pier Damping Force of Left Dampers (MN) 8 Damping Force of Right Dampers (MN) Damping Force (MN) 4-4 Damping Force (MN) Crvatre (m - ) No damper Crvatre (m - ) Viscos damping Stroke of Damper (m) Stroke of Damper (m) Design Reqirements of Viscos Dampers Amont of energy dissipation, or eqivalent damping ratio Stroke of dampers Maximm damping force of dampers Problems of Viscos Dampers Temperatre dependence of viscosity (Not necessarily now) Bild p of damping force at high velocity range (over design level velocity). This is dangeros for both devices and strctres. Generally viscos dampers are expensive compared to other types dampers sch as steel dampers. Increase of ω Viscos Damper Stoppers Distribtion of Lateral Force of Mlti-span Continos Bridges Using Viscos Damper Stoppers Lock-p dampers Increase viscosity of flid Viscos Flid M F M F M F M F M F Expansion Joints Viscos Force small for low rate movements reslting from thermal movements large for high rate movements reslting from seismic responses M F M M M Concentration of Lateral Force 4

5 Distribtion of Lateral Force of Mlti-span Continos Bridges Using Viscos Damper Stoppers (Contined) Implications of Damper Stoppers Ueno Viadct, Metropolitan Expressway Seismic Force Damper stoppers M F M M M Viscos Damper Stoppers Viscos Damper in an Italian Bridge Extensive implementation of viscos dampers Cortesy of Oiles Corporation Cortesy of Oiles Corporation

6 Damper sed to Rion AntiRion Bridge, Greece Cortesy of Oiles Corporation Nonlinear Viscos Dampers FD & & Avoid for bilding-p of damping force when the damper is sbjected to larger than anticipated grond motion 6