Activecourses.washington.edu/cee517/EnergyDiss2012.pdf · 2012. 5. 13. · – Tuned mass dampers:!...
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Introduction to Energy Dissipation in Structural Engineering Dorothy Reed Civil & Environmental Engineering References • Kareem, A. T. Kijewski & Y. Tamura, “Mitigation of motions of Tall Buildings with Specific Examples of Recent Applications,” Wind & Structures, Vol. 2, No. 3, Sept. 1999. • Simiu and Scanlan, Chapter 9, Wind Effects on Structures, 3rd Ed. • Chopra, A., Dynamics of Structures, 2001. • Yu, J., Nonlinear Investigation of Tuned Liquid Dampers, PhD Thesis, UW, 1997. • Various advertising pamphlets from Japanese & US companies for damping products as noted Semi-active • “Fuzzy” category: sometimes lumped with active dampers • Includes – Tuned mass dampers: • Invented 1909 by Frahm • Extensive investigation by Den Hartog for ME applications (machinery, etc.) – Tuned liquid dampers – Variable stiffness and damping systems Active • Power added to system • Active tuned mass dampers • Active braced systems Focus on Semi-active • Observation • Mathematical models • Empirical analysis • Design methodology Observation • Simple model • Vibration • Effect of sloshing
Transcript of Activecourses.washington.edu/cee517/EnergyDiss2012.pdf · 2012. 5. 13. · – Tuned mass dampers:!...
Introduction to Energy Dissipation in Structural
Engineering!
Dorothy Reed!Civil & Environmental Engineering!
References!• Kareem, A. T. Kijewski & Y. Tamura, “Mitigation of
motions of Tall Buildings with Specific Examples of Recent Applications,” Wind & Structures, Vol. 2, No. 3, Sept. 1999.!
• Simiu and Scanlan, Chapter 9, Wind Effects on Structures, 3rd Ed.!
• Chopra, A., Dynamics of Structures, 2001.!• Yu, J., Nonlinear Investigation of Tuned Liquid Dampers,
PhD Thesis, UW, 1997.!• Various advertising pamphlets from Japanese & US
companies for damping products as noted!
Semi-active!
• “Fuzzy” category: sometimes lumped with active dampers!
• Includes!– Tuned mass dampers:!
• Invented 1909 by Frahm!• Extensive investigation by Den Hartog for ME
applications (machinery, etc.)!– Tuned liquid dampers!– Variable stiffness and damping systems!
Active!
• Power added to system!• Active tuned mass dampers!• Active braced systems!
Focus on Semi-active!
• Observation!• Mathematical models!• Empirical analysis!• Design methodology!
Observation!
• Simple model!• Vibration!• Effect of sloshing!
2DOF system!
m1 F1
displacement u1
k2
displacement u2
Stiffness of both columns = k1
m2
System Parameters: Ignore Damping!
let F1 = p0 sin!t so F =p0 sin!t0
" # $
% & '
M =m1
m2
(
) *
+
, -
K =k1 + k2 .k2.k2 k2
(
) *
+
, -
EOM!
m1˙ ̇ u 1 + k1 + k2( )u1 ! k2u2 = p0 sin"tm2˙ ̇ u 2 ! k2u1 + k2u2 = 0
Steady-State !
u1 = C1 sin!t, u2 = C2 sin!t˙ ̇ u 1 = "! 2C1 sin!t, ˙ ̇ u 2 = "! 2C2 sin!t
Substitute into EOM!
m1 !"2C1( )sin"t + k1 + k2( )C1 sin"t ! k2C2 sin"t = p0 sin"t
m2 !"2C2( )sin"t ! k1C1 sin"t + k2C2 sin"t = 0
Solve for constants!
!m1"2C1 + k1 + k2( )C1 ! k2C2 = p0
C1 = p0 ! k2C2
k1 + k2( ) !m1"2
This is zero (i.e., no displacement of m1) when C2 = p0
k2
.
What else? Tuning!
!m2"2 ! k2C1 + k2C2 = 0
C2(!m2"2 + k2) = k2C1
C1 =C2 !m2"
2 + k2( )k2
For C1 = 0 but C2 # 0, -m2"2 + k2 = 0
$" = k2
m2
for C1 = 0
Solution Comments!
u2 = p0k2sin k2
m2
t for ! = k2m2
Simiu & Scanlan!
DUOX: solid mass damper!
Kajima literature!
TRIGON!
Kajima literature!
TRIGON!
Simiu & Scanlan!
Two degree of freedom system !with damping added! Equivalent representation!
Simiu & Scanlan!
Effect of TMD "is to change effective damping ratio of the main mass -- the
building!
Simiu and Scanlan!
! e = 12
"1 "2"3 #"1( ) #"0"32
"1 "2"3 #"1( ) + "3 $12 # 2"0( ) + "1
(Simiu & Scanlan)
"0 = f 2
"1 = 2 f !1 f + ! 2( )"2 = 1+ f 2 1+ µ( ) + 4 f!1! 2
"3 = 2!1 + 2! 2 f 1+ µ( )$1 = 2! 2 fµ = M2 M1 mass ratio
f = 2%n1
2%n2
ni = 12%
Ki
Mi
i = 1,2
! i = Ci 2Mi 2%ni( )( ) i = 1,2Simiu and Scanlan!
! eopt " µ
4+ 0.8!1 > !1
with
! 2opt " µ
2i.e., for µ = 0.01& !1 = 0.01,! eopt = 0.033 and ! 2
opt = 0.05
x2,norm2 !" x2 ,norm
2{ } = x22
x1,02
!" x2
2
" x1,0
2
# $ %
& %
' ( %
) % = 2*1+1
+1 +2+3 ,+1( ) ,+0+32
x1,0 ! displacement due to resonant amplification effects only of M1 in the original system, i.e., without the TMD
Simiu & Scanlan!
µ = 0.01, f = 0.98,!1 = 0.01,! 2 = 0.0515
x2,norm2 =13.7; x2,norm
2 = 3.7
Now consider liquid mass: TMD and TLD Model!
Yu (1995)! Yu (1998)!
TLD-experiment!
Yeh, et al. (1995)!
Deep water sloshing!
Chimewa (1998)!
Linear Wave Theory: Frequency of sloshing for rectangular tank!
fw = 12!
!gL
" # $
% & ' tanh
!h0L
" # $
% & '
Circular Tank!
fw = 12!
1.17!gD
" # $
% & ' tanh
1.17!h0D
" # $
% & '
Yu (1997)!Yu (1997)!
Yu (1997)!Yu (1997)!
Simulation !
Yu (1997)!
Simulation!
Yu (1997)!
Design Tuning Equation!
water depth per tank h0 = L!
tanh"1 4!Lfs2
g# 2
$
% &
'
( )
where # =1.038 umax
L$ % &
' ( )
0.0034
for umax
L* 0.03 weak wave breaking
# =1.59 umax
L$ % &
' ( )
0.125
for umax
L> 0.03 strong wave breaking
fs + structural frequency in Hz (usually fundamental)L + tank length; g + acceleration due to gravity
damping ratio of the tank with water ! d = 0.52"0.35
" = umax L; L # tank length; umax # structural displacement
Yu (1997)!
Design chart! Wakahara (1995)!
m=mass ratio of liquid to effective structural mass!
Shimizu Full-Scale Testing!
Yeh personal photo!
Yeh personal photo!
Post-Test Design: Shimizu TLD!
Reed personal photo!
Rooftop of Yokohama Hotel!
Reed personal photo!
Nanjing Tower [PRC]!
Chinese promotional brochure!
Sloped Bottom (Gardarsson, Olsen)!
Ways to increase damping!
Sloped Tank Notes!
• Angle of slope modifies water sloshing behavior!
• No simple water frequency equation exists so empirical investigation of sloshing required!
• Stiffness degrading system vs stiffness hardening!
Tank behavior: B=fexcitation/fwater!
Olsen & Reed (2001)!
Active Control Scheme!
T. Kobori, KRC EE 011 9407501!
Active Mass Damper"[AMD]!
Takenaka Advertising Literature!
AMD!
Takenaka Advertising Literature!
AVS!
Kajima Literature!
AVS!
Kajima Advertising Literature!
AVS!
Kajima Advertising Literature! Kareem, et al. (1999)!
Kareem, et al. (1999)!Tuned column-type damper:Kareem, et al. (1999)!
Conclusions!
!• Hybrid passive or semi-active coupled
active devices gaining in popularity!• TMD, TLD most popular outside of US,
especially for wind loadings!• AMD systems have promise but require
reliable power sources!!
Learning Objectives!• Be able to explain in your own words what “structural control” means.!
• Be able to identify the three main types of control, examples of each, and the associated the advantages and disadvantages. !
• Be able to identify the primary design considerations for the types we discussed in class: isolation, TMD and TLD.!
• Given the relevant equations, complete or evaluate a simple design for a TMD or TLD.!
