Seismic Protection of Vibration‐Isolated Mechanical Equipment with Supplemental Hysteretic Damping
Andre Filiatrault
Professor, Department of Civil, Structural and Environmental Engineering, University at Buffalo, State University of New York, Buffalo, NY, USA
ROSE Faculty, Graduate School in Understanding and Managing Extremes, Pavia, Italy
Nikola Tatar
PhD Student, Department of Civil Engineering, Université de Liège, Liège, Belgium
Formerly Rose Master Student in Earthquake Engineering and Engineering Seismology Graduate School in Understanding and Managing Extremes, Pavia, Italy Timothy J. Sullivan
Assistant Professor, Department of Civil Engineering & Architecture, University of Pavia, Pavia, Italy.
Content
1. Introduction
2. Differences between Seismic Protection and Vibration Isolation
3. Performance of Vibration‐Isolated Equipment in Past Earthquakes
4. Seismic Protection of Vibration‐isolated Equipment by Supplemental Hysteretic Damping System
5. Incremental Dynamic Analyses
6. Conclusions
1. Introduction
• Mechanical equipment such as air‐handling units, chillers, boilers, and fans is an important category of nonstructural components in buildings. • Conventional buildings:
– Required to maintain habitability. – Short interruption in operation tolerated. • For critical facilities (e.g. hospitals): – Even a short interruption in operation endangers continued functionality expected during and after an earthquake. • Increased interest in energy conservation resulted in a growing trend of installing mechanical equipment on the roof and intermediate level of buildings just adjacent or above occupied areas. 2. Differences between Seismic Protection and Vibration Isolation
Mechanical equipment rigidly mounted to a building structure can be the source of mechanical vibration and noise. • Operation‐induced noise and vibration inside a building bring discomfort to occupants, damage sensitive equipment, and over a long period can be detrimental to the structural system. • Vibration and noise can be reduced by mounting equipment on flexible supports.
•
– e.g. coil springs (vibration isolators). •
Vibration isolators reduce the transmission of noise, shock, and vibration produced by the equipment into the building structure or into other equipment installed in the building.
2. Differences between Seismic Protection and Vibration Isolation
•
Vibration isolators must have: – Low natural frequencies.
– Very low damping.
•
Lightly damped dynamic systems attract large seismic displacements.
– Worst if natural frequencies of isolated equipment match the building natural frequencies.
•
Equipment may experience displacements much larger than the isolator capacity.
– Heavy equipment may be shaken off its supports and fail. – Massive equipment moving like a free projectile can damage other equipment installed in the building and can even damage the building structure. – Ducts, pipes, and electrical wirings connected to equipment may fail. 2. Differences between Seismic Protection and Vibration Isolation
• Elastomeric snubbers with air gaps provide seismic protection of vibration‐isolated equipment.
2. Differences between Seismic Protection and Vibration Isolation
Horizontal Restraint:
Vertical Restraint:
3. Performance of Vibration‐Isolated Equipment in Past Earthquakes
• Vibration‐isolated equipment protected by elastomeric snubbers fared far better than unrestrained vibration‐isolated equipment.
• Performance of elastomeric snubbers inconsistent at best. • Repeated failures of snubber mounts.
• Effects of snubber properties (gap size, thickness and hardness of elastomeric contact‐surface) on equipment seismic response not clearly understood.
4. Seismic Protection of Vibration‐isolated Equipment by Supplemental Hysteretic Damping System
• Concept (Fathali, 2008)
4. Seismic Protection of Vibration‐isolated Equipment by Supplemental Hysteretic Damping System
• Concept (Fathali, 2008)
4. Seismic Protection of Vibration‐isolated Equipment by Supplemental Hysteretic Damping System
• Numerical Modeling
m = equipment operational mass
mIR = mass of isolation/restraint system
x12 = x2 – x1
4. Seismic Protection of Vibration‐isolated Equipment by Supplemental Hysteretic Damping System
• Numerical Modeling
– Constitutive Relations for Isolation/Restraint System
• Tangent stiffness, Kt:

K v


K ss K es
K t  K v 
K ss  K es

K  K
ss
 v




if  x2  g  0 or  x2  g  x2 x 2  0 





if 0  x2  g  t  or  x2  g  x2 x 2  0 


if  x2  g  t 




if  x2  g  0 or  x2  g  x2 x 2  0 
0



K es  
h



 K  1 


if
0

x

g

t
or
x

g

x
x

2  0 
0
2
2
2
es






 1  c 

with:
εc 
x2  g
t
for 0  x2  g  t
g = gap size
t = rubber thickness
c = instantaneous compression strain
4. Seismic Protection of Vibration‐isolated Equipment by Supplemental Hysteretic Damping System
• Numerical Modeling
– Constitutive Relations for Isolation/Restraint System
• Tangent damping constant ,Ct:

Cv

C C

Ct  Cv  ss es
Css  Ces

C  C
ss
 v

with:



if  x2  g  0 or  x2  g  x2 x 2  0 





if 0  x2  g  t  or  x2  g  x2 x 2  0 


if  x2  g  t 
C  2 K m  m ; C  2
v
v
v
IR
ss
ss K ss m  mIR ; Ces  2 es K es m  mIR 
v , ss, and es are the equivalent viscous damping ratios of the vibration isolator, snubber support, and elastomeric snubber, respectively.
4. Seismic Protection of Vibration‐isolated Equipment by Supplemental Hysteretic Damping System
• Numerical Modeling
– Constitutive Relations for Hysteretic Damper (Sivaselvan and Reinhorn, 2004)
4. Seismic Protection of Vibration‐isolated Equipment by Supplemental Hysteretic Damping System
• Numerical Modeling
– Governing Dynamic Equilibrium Equations
4. Seismic Protection of Vibration‐isolated Equipment by Supplemental Hysteretic Damping System
• Numerical Modeling
– Numerical Solution Procedure
• Explicit approach using the Runge‐Kutta method with a variable step size (Cash and Karp, 1990).
• Differential equation solver of the MATLAB (2011) platform.
• Numerical solution procedure validated by comparing its predictions with the theoretical (closed‐form) solutions obtained recently by Bapat (2008) for a particular class of impact dynamic problems. 5. Incremental Dynamic Analyses
• Concept
IDA Curves
Fragility Curve
Performance Objective
^

β2/ 2 
(y)

m
ln
y e


Lognormal CDF(y)  Θ


β


Response Parameter
5. Incremental Dynamic Analyses
• Vibration‐isolation Equipment Characteristics
Physical Properties
Operational mass
Symbol
m
Isolation/restraint system mass
Vibration isolator stiffness
Vibration isolator viscous damping
ratio
Snubber support stiffness
Snubber support viscous damping ratio
mIR
Kv
Numerical Values
0.00325 kN-s2/mm
0.0001 kN-s2/mm
0.134 kN/mm
v
0.02
Kss
350,000 kN/mm
 ss
0.02
Elastomeric snubber initial stiffness at
zero compression strain
Elastomeric snubber viscous damping
ratio
Kes0
1.34 kN/mm
 es
0.05
Gap size
Rubber thickness
g
t
Varied from 3.2 mm to 25.4 mm
Varied from 3.2 mm to 12.7 mm
Elastic horizontal fundamental period of the vibration‐isolated equipment = 1 sec
5. Incremental Dynamic Analyses
• Supplemental Hysteretic Damping Characteristics
Physical Properties
Initial stiffness
Symbol (see Fig. 3)
K1ED
Numerical Values
4.55 kN/mm
Yield force
Fy
27.9 kN
Strength hardening ratio
r
0.037
Can be achieved by a lead‐rubber bearing of 135 mm diameter, a total rubber height of 65 mm and a led plug diameter of 50 mm.
Increase of less than 1% of the elastic horizontal fundamental period of the vibration‐
isolated equipment (before yielding of the led plug).
5. Incremental Dynamic Analyses
• Performance Damage States
– Two performance objectives for the mechanical equipment (American Society for Heating, Refrigerating and Air Conditioning Engineers (ASHRAE) Handbook – Chapter 54) :
• DS1: Peak acceleration limit of 2.0g acceleration at the center of gravity of the equipment associated with a functional damage, which would cause a temporary interruption of the equipment's operation (e.g. dislodging of electronic components in a control panel).
• DS2: Peak acceleration limit of 4.0g acceleration at the center of gravity of the equipment associated with physical damage, which will cause permanent interruption of the equipment's operation (e.g. bolted flange failure inducing loss of refrigerant in a centrifugal liquid chiller).
– One performance objective for the supplemental hysteretic damping system:
• DS3: Maximum displacement of 62 mm associated with failure of the damping system (allowable seismic‐induced rubber shear strain of approximately 100% for a lead‐rubber bearing of 135 mm diameter with a total rubber height of 65 mm).
• From dynamic equilibrium, acceleration of 1.17 g at the center of gravity of the equipment achieves the performance objective DS3.
5. Incremental Dynamic Analyses
• Earthquake Ground Motions
– Suite of 22 pairs of scaled bi‐
directional historical ground motion records (44 records total) provided as part of the far‐field ground motion set considered by the FEMA P695 methodology.
– Seismic intensity measure: median 5% damped spectral acceleration at 1 s period.
– Design Earthquake (DE): • Sa = 0.6 g at 1 sec
– Maximum Considered Earthquake (MCE): • Sa = 0.9 g at 1 sec
5. Incremental Dynamic Analyses
• Analysis Results
DS3
6
DS1
DS2
1
IDAs
5
4
3
2
1
0
g = 12.7 mm
t = 3.2 mm
0
Fragility
Curves
0.9
Probability of Exceedence
Median Spectral Acceleration at 1 sec (g)
– Vibration isolated equipment with supplemental hysteretic damping; gap size g = 12.7 mm; rubber thickness t = 3.2 mm.
1
2
3
4
5
Maximum Acceleration at the Center of Mass of Equipment (g)
^
0.8
m y  1.36g
0.7
DS1
^
m y  2.93g
0.6
DS2
^
m y  4.90g
0.5
0.4
0.3
0.2
g = 12.7 mm
t = 3.2 mm
0.1
6
DS3
0
0
1
2
3
4
5
6
Median Spectral Acceleration at 1 sec (g)
7
5. Incremental Dynamic Analyses
• Analysis Results
– Median Sa(T=1sec) capacities for vibration isolated equipment with and without supplemental hysteretic damping.
Without supplemental hysteretic damping
Gap Size,
g
3.2 mm
6.4 mm
12.7 mm
25.4 mm
3.2 mm
DS1
DS2
0.13g
0.16g
0.12g
0.14g
0.10g
0.10g
0.13g
0.13g
Rubber Thickness, t
6.4 mm
DS1
DS2
0.25g
0.35g
0.20g
0.27g
0.16g
0.20g
0.18g
0.19g
12.7 mm
DS1
DS2
0.45g
0.76g
0.32g
0.54g
0.28g
0.39g
0.23g
0.31g
With supplemental hysteretic damping
Gap Size,
g
3.2 mm
6.4 mm
12.7 mm
25.4 mm
DS1
2.97g
2.90g
2.93g
2.91g
3.2 mm
DS2
4.97g
4.90g
4.90g
4.93g
DS3
1.58g
1.40g
1.36g
1.13g
Rubber Thickness, t
6.4 mm
DS1
DS2
DS3
2.98g
4.95g
1.57g
2.90g
4.87g
1.38g
2.93g
4.90g
1.20g
2.92g
4.90g
1.12g
DS1
2.97g
2.80g
2.90g
2.90g
12.7 mm
DS2
4.97g
4.90g
4.95g
4.90g
DS3
1.50g
1.38g
1.20g
1.09g
5. Incremental Dynamic Analyses
•
Analysis Results
– Probabilities of exceedence of damage states DS1 and DS2 for vibration equipment without supplemental damping and probabilities of exceedence of damage state DS3 for vibration isolated equipment incorporating supplemental hysteretic damping. 5. Incremental Dynamic Analyses
•
Analysis Results
– Fragility curves for rubber thickness t = 3.2 mm.
5. Incremental Dynamic Analyses
•
Analysis Results
– Fragility curves for rubber thickness t = 6.4 mm.
5. Incremental Dynamic Analyses
•
Analysis Results
– Fragility curves for rubber thickness t = 12.7 mm. 6. Conclusions
• Vibration‐isolation systems with snubbers alone are not appropriate for use in regions of high seismicity.
• Incorporation of properly designed supplemental hysteretic damping positioned between the vibration isolation devices and the equipment can provide significant seismic protection without impeding the operation of the vibration‐isolated equipment.
• With further numerical and experimental validations, the proposed concept could lead to harmonized seismic performances between vibration isolated equipment and building seismic force‐resisting systems, which is essential for truly performance‐based earthquake engineering. To find out more…
Questions/Discussions