Seismic Vibration Control

Nilesh Kala, Rajat Avasthi, Rajat Mangotra

CE629A Earthquake Design

Introduction

Seismic Performance of a structure is defined by its potential to withstand earthquake

damage and still be safely functional. To maintain seismic performance in areas highly prone

to earthquakes (e.g. Zone IV and Zone V in India), the structures must be equipped with

mechanisms that can reduce its response to seismic excitation up to a certain margin.

Seismic Vibration Control, first proposed by Kobori, involves the technologies employed to

mitigate earthquake damage in the structures. Lot of research is being carried out in this

area to achieve higher efficiency in the mechanisms employed.

Motivation

The conventional method of ductile design of structures to reduce earthquake damage is

widely practiced all over the globe. However there are few issues involved with this

approach, most obvious one is that the size of structural member increases as a result of

ductile design and consequently member stiffness also increases thereby attracting larger

earthquake forces. Also, there are some structures in which loss of functionality cannot be

permitted e.g. hospitals, monuments, bridges, defense buildings etc. In such cases it is

required to come up with a solution that altogether prevents the structure from going

excessive vibrations and thus restricting the earthquake damage to a minimum possible

limit.

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Methods of Vibration Control

Various methods adopted for seismic control can be distinguished primarily based on their

source of input energy and whether or not there is a feedback mechanism installed.

Following is a broad classification based on above mentioned criteria-

1. Passive Control Systems

2. Active Control Systems
3. Semi-active Control Systems
4. Hybrid Control Systems

All these methods work on one of the five basic principles of seismic control-

1. Cutting off the input energy from the earthquake ground motion; examples:

(a) Floating structures

(b) Frictional structures

2. Isolating the natural frequencies of the structures from the predominant seismic power

components; examples:

(a) Base-isolated structures

(b) Long period structures

3. Providing nonlinear structural characteristics and establishing a non-stationary state

non-resonant system; examples:

(a) Inelastic structures

(b) Varying stiffness and damping structures

4. Utilizing energy absorption mechanism; examples:

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 (a) Viscous damper

(b) Viscoelastic damper

(c) Inelastic behavior

5. Supplying control force to suppress the structural response; examples:

(a) Active mass damper

(b) Active tendon

(c) Joint damper

Passive Vibration Control

Passive control encompasses schemes involving energy dissipation by installing various

mechanisms which either increase the overall stiffness or damping of the structure. The

forces required to limit the amplitude of vibrations of the structure are generated as a

counter to earthquake and cannot be manually controlled at the time of event. However, an

operating frequency range can be specified under which their functioning is efficient.

Various methods falling under this category are

1. Seismic Base Isolation

2. Tuned Mass Dampers
3. Un-tuned Viscous Absorbers

Seismic Base Isolation

It is currently one of the most commonly employed control scheme in USA and Japan. The

basic mechanism involves connecting the substructure and super-structure (or pier cap and

deck in case of a bridge) by means of a spring-damper system such that upon ground

motion excitation the super-structure can only undergo side sway motion while behaving

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 essentially as a rigid body. The base for this system is kept flexible since it will be the part

undergoing high amplitude oscillations during excitation. Flexibility of the base depends on

how high can be the frequency of applied vibrations and also the fundamental frequency of

the structure. More the base flexibility, higher will be the filtering of high frequency

components from the input motion. To prevent the flexible base from deflecting too much

from its central position which can cause malfunctioning of the installed bearings, the use of

dampers is necessary. So the overall transmission of ground motion to the super structure is

reduced while also keeping the bearings in a functional state. The choice of bearing depends

on various factors such as-

Initial stiffness of the bearing material which is required to avoid frequent vibration

from wind and minor seismic events.

Self-Centering capability after deformation.
Vertical and horizontal stiffness of the bearing.
Damping ratio and Hysteretic behavior of bearing material.

Two commonly used bearings in flexible bases are-

1. Rubber bearings
2. Friction bearings

Rubber Bearings - Earlier rubber blocks were used which are unsuitable for earthquake

applications because they provide equal stiffness in all directions due to the weight coming

from the structure. Nowadays, laminated rubber bearings with steel plates are used which

provide flexibility in horizontal direction and high stiffness in vertical direction to prevent

rocking. Different types of rubber bearings are available nowadays with natural rubber

being the most suitable. The damping ratio of natural rubber is quite low in the range of

0.02-0.04 but it can be increased to 0.1-0.2 by the use of compound fillers (e.g. carbon

black). Kelly (2001) showed that for developing countries, steel plates can be replaced by

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 fiber mesh which is lighter and easy to manufacture. However, lead rubber bearing is the

most commonly used bearing since it has following several advantages-

It is not prone to fatigue.

Its hysteretic behavior is stable.
It is capable of dissipating significant energy in strong ground motions.

Figure 1 Lead Rubber Bearings

Following are some advantages of rubber bearings-

Lowest initial cost and easy to install.

May be combined with sliding steel surfaces to accommodate larger displacements.
Many different options are available according to site and building suitability.
Easy to examine and replace after seismic event (e.g. in bridges).

Following are the drawbacks of rubber bearings-

Not suitable on soft soils where low frequencies dominate.

Near fault sites are also not preferred as they have long period velocity pulses which

impart initial momentum causing large horizontal base displacement. In such cases,

provision of high damping or bilinear force-displacement behavior and a large ratio

of yield force to support weight is desirable.

Rubber bearings have very low resistance to chemical and biological attacks.
These bearings need self-centering after deformation.

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 Initial stiffness of the bearings should be high enough to avoid frequent vibrations

due to wind and minor seismic events.

Friction Bearings One of the main disadvantages of rubber bearings is that their

efficiency is affected by the frequency content of the ground motion. To overcome this

problem, friction based bearings were introduced. These systems have no inherent natural

period and hence are insensitive to variations in frequency content of the ground motion.

The damping force provided by these bearings depend on the vertical load coming from the

structure and therefore the center of mass and center of resistance coincide. As a

consequence, the torsional effects due to asymmetry of the building are diminished. One

example of friction bearing system is Resilient Friction Bearing (R-FBI). In this system,

concentric layers of Teflon coated friction plates are kept in contact with each other which

dissipate energy and a central core of rubber provides the resilient force there by absorbing

excess energy. Some drawbacks of friction bearings are as follows-

There is an absence of restoring force which ensues large residual displacements.

The sliding surfaces can deteriorate over large span of time and need frequent

inspection.
Material being used in friction bearings is prone to temperature and environmental

changes resulting in a change in friction coefficient and ultimately the amount of

energy dissipation.

Following is a brief list of buildings in USA which are rehabilitated with base isolators,

compiled by Ian G BUCKLE [WCEE, 2000]-

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 Tuned Mass Dampers

Tuned mass dampers are the application of anti-resonance phenomenon which occurs in

Multi-DoF systems. A secondary mass is attached to the structure and is then tuned to

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 absorb most of the vibrational energy. The basic principle is that when a mass having

natural frequency equal to that of the forcing frequency is added to an SDoF system, then at

a particular frequency ratio, the vibrations of the primary mass (in our case, structure) are

suppressed and all the energy is absorbed by the secondary mass, this phenomenon is

called anti-resonance. Usually, the mass of secondary system is kept equal to 1% of mass of

the structure. The secondary mass is generally fitted at the top or sometimes near top

stories depending on the feasibility. It is connected to the primary system using a flexible

link essentially involving a spring mechanism and it moves in out of phase motion with the

primary structure. Warburton and his collaborators showed that as long as the ratio w1/w2

0.5, parameters for TMD are optimal, where w1 and w2 denote the first and second

natural frequency of the system. The biggest drawback of this method is that earthquake

excitation occurs over a large range of frequencies, and the system cannot be tuned to

control all the frequencies but only a range of frequencies.

It is not possible to present a comprehensive list of all the buildings with tuned mass

dampers. Some famous structures are listed below-

Building/Project Information Damper Information

Name Location Height Mass (ton) Frequency
Jan Hancock Tower Boston, USA 344 m 2 x 370 0.14 Hz
Citicorp Building New York, USA 279 m 1 x 400 0.15 Hz
Burj al-Arab Dubai, UAE 321 m 11 x 5 0.8-2 Hz
Taipei 101 Taiwan, China 508 m 1 x 660 0.17/0.22Hz
Center-Point Tower Sydney, Australia 305 m 1 x 220 0.10/50 Hz
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 Crystal Tower Osaka, Japan 240 m 180 + 360 0.24-0.26 Hz

An extensive study of tuned mass damper installed in Taipei 101, Taiwan was carried out by

Alex Y. Tuan and G. Q. Shang [JASE, 2014]. They showed that the acceleration responses in

the along-wind and the across-wind directions were substantially reduced by 31.7% and

33.8%, respectively. For a remote earth quake event, the total acceleration was reduced by

13%.

A currently popular type of tuned mass damper is tuned liquid column damper (TLCD).

These dampers dissipate energy by movement of an oscillatory column of liquid through

orifices provided in cross section of a U-shaped container. Extensive research is going on

regarding optimization of TLCDs for wide frequency range and a lot of ideas are proposed

every year. One such system is Tank Pipe Damper System proposed by A.D. Ghosh, P.C. Saha

and B. Basu (15 WCEE, 2012). It is discussed in detail below:

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 Tank Pipe Damper System- The damper utilizes the same principle as that of a liquid

column damper however it also includes some properties of a sloshing tank damper. It

Figure 2 Schematic of a Liquid Column Damper

consists of a 3 DoF system with two tanks connected by a cylindrical pipe. Different cross-

sections can be used for connecting pipe but Tait and Deng (2010) studied that horizontal

cylindrical type are most robust. In general a liquid undergoing vibrations has two

components (1) Impulsive component due to rigid motion of the liquid and (2) Convective

component caused by part of the liquid experiencing sloshing motion. Short broad tanks are

preferred because they have higher convective component and lesser impulsive component.

Both the motions can be assumed to be uncoupled since there is a large separation in

frequencies of both motions as shown by Veletsos and Tang (1990).

The studies carried out by Saha and Ghosh shows following distinctions between LCD and

TPD systems-

Responses dominated by a single mode are better controlled by Liquid column

dampers.
LCDs become ineffective when frequency of ground motion exceeds its tuned

frequency whereas Tank Pipe systems being multi-mode systems can be tuned to

multiple frequencies and thus can be used over a wide range of frequencies.
Optimal orifice damping coefficient of TP damper system shows a very little

variation over large range of operating frequencies so it need not be changed once

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 installed whereas if LCD is installed for a particular frequency its difficult to change

orifice diameter.
TP systems provide additional viscous damping ratio of about 1.1-1.7 % for white

noise base input response as compared to 2.8% provided by LCD.

For band limited white noise input restrained to 0.5-2.5 s period the damping ratio

provided by TP systems increased to 5.7%-6.5% whereas LCD was found to be

useless in such conditions.

Overall Tank-Pipe dampers were found to be a good substitute for liquid column

dampers.

Un-Tuned Viscous Absorber

These device uses the energy dissipation mechanism of dampers to dissipate most of the

vibrational energy of the structure. The added dampers result in an increase in the damping

coefficient of the building as a whole. Various types of dampers are used for this purpose

while a good amount of research is still going on. Some selective damping mechanisms are

discussed below-

1. Metallic Yield Damper These dampers are constructed using a series of steel

plates arranged in parallel forming an hourglass shape. The hourglass shape is

matched to the moment diagram of the damper to maximize uniformity of

plastification. Energy dissipation occurs through flexural yielding deformation of

mild steel plates. These dampers are shown to have stable hysteretic properties

and low fatigue value.

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Figure 3 Typical Metallic Yield Damper

 2. Friction Dampers - These devices make use of friction brakes to dissipate

energy. They mainly consist of braces attached to the four corners of the frame

with a damper attached at the crossing of the braces. When the frame sways

laterally the friction slider moves thereby dissipating kinetic energy. The use of

friction based dampers was popularized by Pall (1979). Pall friction dampers are

the most commonly used friction dampers. These consist of a series of steel

plates clamped together with high strength steel bolts and are allowed to slip

only at a predetermined load. These dampers offer a lot of advantages over other

damping mechanisms such that-

Retrofitting is easy and cost efficient
Large hysteresis loops with negligible fatigue
High dissipation capacity
No repair needed after earthquakes

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 Figure 4 Pall friction damper

Following is a list of buildings with Pall friction dampers installed (Pall Avtar,

Pall Rashmi, 1996)-

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 3. Viscoelastic Dampers These dampers consist of a viscoelastic material

bonded to steel plates. The viscoelastic materials usually used are copolymers or

glassy substances. This material dissipates energy in shear deformation while

the heat generated due to dissipation is released through steel members of the

damper. Behavior of these dampers depends on frequency of vibrations, strain

induced and ambient temperature. Mathematical relationship between shear

and strain can be shown as-

G(w)/w)*(t) __________________________ (1
( t ) =G' ( w ) ( t )+
Where,
w = frequency of vibration
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 G ' ( w ) = Shear storage modulus of viscoelastic material
(t) = time dependent strain
G"(w) = Shear loss modulus
The ratio of shear loss modulus to shear storage modulus is defined as loss

factor. Loss factor decreases with increase in temperature. Furthermore it can be

shown that-
'
AG ( w )
K (w)=

G (w)/w
And
C ( w )=(A / )
Where,
A = shear area of viscoelastic material
= thickness of viscoelastic material
K(w) = Overall stiffness of damper
C(w) = overall damping of system
It can be clearly seen that both stiffness and damping are a function of shear

modulus, area of cross section and thickness. Nonlinearities are induced in the

material when a large amount of heat is generated after which these linear

relationships fail and the damper becomes inefficient.

4. Viscous Fluid Dampers These dampers are often installed as part of bracing

Figure 5 Typical Configuration of a Visco-Elastic Damper

systems. They dissipate energy through to and fro motion of the viscous liquid

inside a piston. In our mathematical relationships, while defining viscous

damping we often assume the viscous force to be proportional to the velocity of

fluid but in reality even moderate pressure hydraulic flow through a simple

orifice follows a relationship in which differential pressure is proportional to

velocity2. Output force of basic hydraulic dampers can be written as-

a
F ( t )=sgn ( x ( t ) )c|x ( t )|
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 Most of the fluid dampers used in the buildings today are of low exponent type

where the value of a ranges from 0.3 to 1, with 0.4 - 0.5 being the most popular

choice for seismic inputs.

Active Vibration Control

In this method, a feedback system is used along with an actuator to provide greater control

and effectiveness over a wider range of frequencies. The feedback system consists of

sensors (e.g. accelerometer, displacement, velocity, strain) and a control system (e.g. optimal

control, fuzzy control). Following is a schematic diagram of active control systems-

External Excitation Structure Structural Response

Control Forces

Sensors Sensors
Actuators

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Computation of
control forces
 Choice of outputs which are to be controlled is decided by the designer based on comfort

(e.g. acceleration) or safety (e.g. stresses). Mathematically active systems can be described

as-

Equation of motion in the absence of external force for an SDoF system-

m x +c x+ kx=0

Where k, m and c are stiffness, mass and damping respectively. Now, in design of passive

controls, we want to increase stiffness and damping as k+k and c+c. Here k and c are

fixed and chosen by the designer. In case of active systems, this k is used as a

proportionality constant which is to be determined. As a result the actuator force becomes

equal to (k)x . First use of active control system was done in Kyobashi Seiwa Building in

Japan. Various advantages of active control systems are-

Wide frequency range

Superior frequency control

Following are some drawbacks of active systems-

Requires external power source to drive actuators which may not be available

during earthquakes
Can destabilize structures
Advanced device control is required which makes them expensive.

Following various types of actuators can be used in an active control system-

1. Electromagnetic Actuator
2. Hydraulic Actuator
3. Pneumatic actuator

The control systems used in the feedback mechanism are governed by control theory. A

method developed in 1980s known as Robust Control is mostly used. This theory employs a
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Figure 6 Schematic of a hydraulic actuator

 static control scheme assuming that the control parameter is unknown but bounded.

Different types of control systems used to provide feedback to the actuator are-

1. Optimal Control Systems

2. Fuzzy Control Systems

Apart from these

Following are various types of active control systems-

1. Active Control with Tendons

2. Active Mass Dampers

Active Control with Tendons

In this method, active braces controlled with the help of sensors and actuators are

used to provide counterforces to the earthquake.

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Figure 7 Model of MDoF system with active tendons

 The tendons are installed as braces which are connected to the actuator. Equation of

motion for this system can be written as-

m x +c x+ kx=m x g4 k c u cos

Few tests on these systems were performed by Nigdeli and Boduroglu [IJCESCA,

2010] on a three storey building model with various tendon angles and

configuration. They concluded that for a multiple degree of freedom system,

installing tendons only at first storey is not sufficient. Also if tendons are installed at

the all the stories and connected to a common actuator installed in first storey, the

system causes some side effects because the length of tendons become too much and

the increase in vertical angle of tendons causes forces in columns to increase making

the system impractical. So, the best way is to put both tendons and actuators on all

the floors.

Active Mass Dampers

This system consists of a frame like structure in which an active mass is installed at

the top in the form of a controllable cart. The cart is driven by a motor through a

suitable arrangement and is free to move along the direction of the structure. The

position and acceleration of the mass is located using a sensor. More mass can be
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 added to the system as per the requirements. The optimization of controller logic

can be done in both frequency as well as time domain. By the optimization method,

the feedback gain as well as the parameters of TMD can be simultaneously adjusted

to increase robustness of the system. Isao Nishimura along with his team carried out

a research indicating various advantages of an active tuned mass damper over a

passive tuned mass damper.

Passive TMD Active TMD

Figure 8 Active vs. Passive TMD schematic diagram

Mass ratio is defined as the ratio of secondary mass to primary mass. The optimum

tuning frequency in the passive systems vary as the inverse of the mass ratio.

Nishimura concluded that using an optimum algorithm along with active mass

dampers results in decrease in control forces and robustness of the structure.

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 Semi-Active Vibration Control

In this system, the focus is to change the structural properties of the system according to

dynamic response of the structure by using variable stiffness or variable damping. These

systems provide high energy efficiency and sometimes can be even battery powered.

Various types of semi-active control systems are-

1. Electro/Magneto-Rheological Fluid Damper aka Smart Materials These

systems make use of ER or MR materials to generate counter forces. When an

electric current/magnetic field is passed through these materials, their viscosity

changes in turn changing the damping of the system.

Figure 9 Schematic of MR damper

2. Variable Orifice Damper This system incorporates use of a controllable

electro-mechanical variable orifice valve to alter the resistance of flow of a

conventional hydraulic fluid damper.

3. Controllable Friction Damper In these systems force at frictional interface is

Figure 10 Schematic of a variable orifice damper

adjusted by allowing slippage in controllable amount. One example of this type

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 of control method is Semi-active Electro-Magnetic Friction Damper. The normal

reaction to generate frictional force is provided by attractive electromagnetic

force generated between two outer (insulated) solenoids.

Figure 11 Schematic of an EM friction Damper

Conclusion

While the research in the field of seismic control is enormous, there are still some

limitations in each of the methods as described in this report. Without getting a fully

functional method, we cannot replace ductile design. As a candid remark, we would like to

conclude that, if employed, semi-active control methods are best followed by active control

methods and then passive control methods.

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References

1. [A. Makino, J. Imamiya, N. Sahashi], Seismic vibration control of a high-rise R.C.

building by a large tuned mass damper utilizing whole weight of the top floor,

The 14th World Conference on Earthquake Engineering, October 12-17, 2008,

Beijing, China
2. [Xiang Ping, Nishitani Akira], Seismic vibration control of building structures

with multiple tuned mass damper floors integrated, The Journal of the

International Association for Earthquake Engineering, Volume 43, Issue 6,

May 2014, Pages 909925.

3. [Takayoshi Kamada, Takafumi Fujita, Takayoshi Hatayama, Takeo Arikabe,

Nobuyoshi Murai, Satoru Aizawa, and Kohtaro Tohyamax], Active vibration

control of frame structures with smart structures using piezoelectric actuators,

April 1997
4. [Ghosh A.D., Saha P.C., Basu B.], Study of a Tank-Pipe Damper System for Seismic

Vibration Control of Structures, 15 WCEE, 2012, LISBOA

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 5. [Aguilar Mike, edited by: Lamar Stonecypher], Basics of Seismic Vibration

Control, http://www.brighthubengineering.com/building-construction-

design/44657-basics-of-seismic-vibration-control/, March 2009

6. [G. Song, V. Sethi], Vibration control of civil structures using piezoceramic smart

materials: A review, Engineering Structures 28, 2006.

7. [Heysami Alireza], Types of Dampers and their Seismic Performance During an

Earthquake, CWE 10, April 2015

8. [Necdet TORUNBALCI], Seismic isolation and energy dissipating systems in

earthquake resistant design, 13th WCEE, 2004

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