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WEIGHT REDUCTION, VIBRATION SUPPRESSION
AND ENERGY HARVESTING FOR TUNED MASS-
DAMPER – INERTER (TMDI) EQUIPPED SUPPORT-
EXCITED STRUCTURES
Laurentiu Marian* PhD Candidate
School of Engineering and Mathematical Sciences
e-mail: [email protected]
Dr. Agathoklis Giaralis* Senior Lecturer in Structural Engineering
School of Engineering and Mathematical Sciences
e-mail: [email protected]
______________________________________________________________
______________________________________________________________
________________________________________
______________________________________________________________
*Structural Dynamics Research Group
Department of Civil Engineering
City University London
Introduction
• Passive vibration control of civil structures - Tuned Mass Damper (TMD).
• Tuned Mass Dampers Inerter (TMDI) passive control solution.
• Mass amplification devices – Inerter.
Proposed TMDI for single-degree-of freedom primary structures
• Equations of motion.
• Optimum design for harmonic base excitation and white noise base excitation.
• TMDI weight reduction effect
Proposed TMDI for multi-degree-of freedom primary structures
• Equations of motion.
• Optimum design for stochastic seismic excitation.
• TMDI performance assessment. TMDI as a lighter passive control solution.
Energy harvesting enabled TMDI
• Model description and characterization.
• Quantification of energy harvesting potential
Concluding remarks
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WEIGHT REDUCTION, VIBRATION SUPPRESSION AND ENERGY HARVESTING FOR TUNED MASS-DAMPER – INERTER (TMDI) EQUIPPED SUPPORT-EXCITED STRUCTURES 2/38
PRESENTATION OUTLINE
Seismic Design applications for buildings • Conventional design philosophy: allows controlled inelastic deformations (a)
• Passive Vibration Control of Civil Structures: the incorporation of various
devices to passively control the vibratory motion of structures.
______________________________________________________________________
• Passive response control systems: (b) seismic isolation, (c) energy
dissipation devices, (d) Tuned Mass Dampers (Simple design; Linearity)
(b) (c) (d) (a)
INTRODUCTION
WEIGHT REDUCTION, VIBRATION SUPPRESSION AND ENERGY HARVESTING FOR TUNED MASS-DAMPER – INERTER (TMDI) EQUIPPED SUPPORT-EXCITED STRUCTURES 3/38
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Tuned Mass Damper (TMD) for Passive Vibration Control
− The oldest device historically used for passive vibration control (e.g. Frahm, 1911)
− Comprises a mass (mTMD) attached to the primary structure via a (linear)
spring (kTMD) and a dashpot (cTMD).
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INTRODUCTION
SDOF
MDOF
WEIGHT REDUCTION, VIBRATION SUPPRESSION AND ENERGY HARVESTING FOR TUNED MASS-DAMPER – INERTER (TMDI) EQUIPPED SUPPORT-EXCITED STRUCTURES
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Tuned Mass Damper (TMD) for Passive Vibration Control
– The larger the attached mass considered, the more effective an optimally
designed TMD becomes to suppress excessive primary structure vibrations.
Wind and traffic-induced vibration : mTMD = 1% - 10% of the total
mass of the structure
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– Examples from TMD applications in civil engineering structures:
Earthquake-induced vibrations: mTMD = 25% - 100%
INTRODUCTION
WEIGHT REDUCTION, VIBRATION SUPPRESSION AND ENERGY HARVESTING FOR TUNED MASS-DAMPER – INERTER (TMDI) EQUIPPED SUPPORT-EXCITED STRUCTURES
______________________________________________________________________
(Ni/Zuo/Kareem 2011)
(Zuo/Tang 2013)
INTRODUCTION
Tuned Mass Damper (TMD) for Passive Vibration Control
6/38 WEIGHT REDUCTION, VIBRATION SUPPRESSION AND ENERGY HARVESTING FOR TUNED MASS-DAMPER – INERTER (TMDI) EQUIPPED SUPPORT-EXCITED STRUCTURES
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Tension leg platforms (TLPs)
(Taflanidis/Angelides/Scruggs 2009)
WEIGHT REDUCTION, VIBRATION SUPPRESSION, AND ENERGY HARVESTING FOR TUNED MASS-DAMPER –INERTER (TMDI) EQUIPPED SUPPORT-EXCITED STRUCTURES
INTRODUCTION
Tuned Mass Damper (TMD) for Passive Vibration Control
7/38
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Off-shore wind turbines Suspension and cable-stayed (foot-) bridges
WEIGHT REDUCTION, VIBRATION SUPPRESSION, AND ENERGY HARVESTING FOR TUNED MASS-DAMPER –INERTER (TMDI) EQUIPPED SUPPORT-EXCITED STRUCTURES
INTRODUCTION
Tuned Mass Damper (TMD) for Passive Vibration Control
8/38
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- Recently proposed passive vibration control configuration - considers the
classical tuned mass-damper (TMD) in conjunction with a two terminal flywheel
device – inerter for vibration suppression of SDOF and MDOF system.
- The TMDI – a generalization of classical TMD systems and thus, optimum
design (“tuning”) of the classical TMD are readily applicable to achieve
“optimal” performance for the new TMDI configuration.
- Taking advantage of the “mass amplification effect” of the inerter, the TMDI
improves the effectiveness of the classical TMD
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The Tuned Mass Damper Inerter (TMDI) (Marian & Giaralis, 2013, 2014)
INTRODUCTION
WEIGHT REDUCTION, VIBRATION SUPPRESSION AND ENERGY HARVESTING FOR TUNED MASS-DAMPER – INERTER (TMDI) EQUIPPED SUPPORT-EXCITED STRUCTURES
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- The Inerter has two terminals free to move independently and develops an
internal (resisting) force proportional to the relative acceleration of its
terminals. (M.C. Smith, 2002)
1 2( - )F b u u
1 1 1 1 11 1)( gc x k x mb axm
- Single-degree of freedom oscillator connected to the ground via an inerter:
- The inerter increases the m1 mass:
m1 m1+b
“mass amplification effect”
- Constant of proportionality b fully characterises its linear dynamical behaviour.
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The concept of the Inerter and its mass amplification effect
____________
Note:
1 2( - )F k u u
1 2( - )F c u u
INTRODUCTION
WEIGHT REDUCTION, VIBRATION SUPPRESSION AND ENERGY HARVESTING FOR TUNED MASS-DAMPER – INERTER (TMDI) EQUIPPED SUPPORT-EXCITED STRUCTURES
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1 2( - ),F b u u
2 2
2 21
( )n
f if
if i
rb m
p pr
- Assume a mechanical realisation of the inerter comprising a plunger that
drives a rotating flywheel through a rack, pinion and gearing system:
- The constant of proportionality b (inertance) - mass units (>> physical mass
of device)
- Inerter can have an inertance ("apparent" mass) much grater then its
physical mass .
11/38
Inerter – two terminal flywheel-based device (M.C. Smith, 2002)
INTRODUCTION
WEIGHT REDUCTION, VIBRATION SUPPRESSION AND ENERGY HARVESTING FOR TUNED MASS-DAMPER – INERTER (TMDI) EQUIPPED SUPPORT-EXCITED STRUCTURES
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Equations of motion
1 1 1 1 1 1 1
0
0
TMDI TMDI TMDI TMDI TMDI TMDI TMDI TMDI TMDI
g
TMDI TMD TMDI TMDI
m b x c c x k k x ma
m x c c c x k k k x m
Time domain:
Frequency domain:
2 2
21
1 1 22 2 2 2
2 2
1 1
1 2 1( )
1 2 2
TMDI TMDI TMDI
g
TMDI TMDI TMDI TMDI TMDI TMDI
ixG
ai i
1
TMDIm
m
TMDI
TMDI
TMDI
k
m b
2( )
TMDI
TMDI
TMDI TMDI
c
m b
1
TMDI
TMDI
1
b
m
12/38
TMDI FOR SDOF BASE EXCITATION
WEIGHT REDUCTION, VIBRATION SUPPRESSION AND ENERGY HARVESTING FOR TUNED MASS-DAMPER – INERTER (TMDI) EQUIPPED SUPPORT-EXCITED STRUCTURES
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Optimum design
- Design problem: given an undamped primary system with specific dynamic
characteristics (m1,k1,c1=0), determine the TMDI parameters (kTMDI, cTMDI)
which minimise the response of the primary system, given mTMDI and b.
- Solution - ‘Equal points’ design method: there exist two fixed points where
the FRF curves intersect (noted P1 and P2), independent of cTMDI (ζTMDI).
- Optimum response is obtained if and only if there exists two local maxima and
both have the same amplitude (Den Hartog,1956)
-mass ratio μ=0.1,
-inertance ratio β=0.1,
-frequency ratio υTMDI=0.5.
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TMDI FOR SDOF HARMONIC
BASE EXCITATION
WEIGHT REDUCTION, VIBRATION SUPPRESSION AND ENERGY HARVESTING FOR TUNED MASS-DAMPER – INERTER (TMDI) EQUIPPED SUPPORT-EXCITED STRUCTURES
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− Minimum response <=> (if and only if) |G1(ω)| has two local maxima with
equal amplitudes at the stationary points P1 and P2.
− Enforce:
Optimum design
2 2
1 10
lim ( ) lim ( )TMDI TMDI
G G
1) |G1(ω)| is independent of ζTMDI :
2) Equal amplitude at points P1
and P2 for the limit ζTMDI → ∞:
1 1 1 2lim ( ) lim ( )TMDI TMDI
P PG G
1 (1 )(2 )
1 2(1 )TMDI
- Optimum frequency ratio υTMDI :
1 2
1 1( ) ( )0
P P
G G
3) |G1(ω)| is maximized locally
at points P1 and P2: 2 26 (1 ) (1 )(6 7 )
8(1 )(1 )[2 (1 )]TMDI
- Optimum TMDI damping ratio ζTMDI :
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TMDI FOR SDOF HARMONIC
BASE EXCITATION
WEIGHT REDUCTION, VIBRATION SUPPRESSION AND ENERGY HARVESTING FOR TUNED MASS-DAMPER – INERTER (TMDI) EQUIPPED SUPPORT-EXCITED STRUCTURES
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Optimum design parameters
- setting b=β=0, the optimal tuning formulae for the classical TMD reported in
the literature are retrieved (TMDI is a generalisation of classical TMD!)
- υTMDI decreases as β increases for all
values of μ considered.
- υTMDI decreases as mTMDI mass
increases
______________________________
- ζTMDI increases as β increases for all μ
values considered
- ζTMDI increases as mTMDI mass
increases
Optimum frequency ratio υTMDI Optimum TMDI damping ratio ζTMDI
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TMDI FOR SDOF HARMONIC
BASE EXCITATION
WEIGHT REDUCTION, VIBRATION SUPPRESSION AND ENERGY HARVESTING FOR TUNED MASS-DAMPER – INERTER (TMDI) EQUIPPED SUPPORT-EXCITED STRUCTURES
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Optimally designed TMDI equipped undamped SDOF primary
structure
For the same mTMDI mass, the inclusion of the inerter (TMDI vs. TMD):
- reduces the peak response of the primary structure (at ω1, ωP1 and ωP2),
- All FRF curves attain two local maxima of equal height at the frequencies
ωP1 and ωP2 whose location depend on the ratio β.
- increases robustness to “detuning effects” - Large β values - wider range of
frequencies peak response reduction compared to the classical TMD.
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- Practically, the inerter furnishes all the positive effects of increasing the
attached mass without the negative effect of the added weight.
TMDI FOR SDOF HARMONIC
BASE EXCITATION
WEIGHT REDUCTION, VIBRATION SUPPRESSION AND ENERGY HARVESTING FOR TUNED MASS-DAMPER – INERTER (TMDI) EQUIPPED SUPPORT-EXCITED STRUCTURES
P1 P2
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Optimally designed TMDI equipped undamped SDOF primary
structure
- TMDI reduction saturates as the ratio β increases
- Peak response amplitude for optimally designed TMDI normalized by the
peak response amplitude of the optimally designed classical TMD (β =b=0).
- Incorporation of the inerter to the classical TMD system is more effective for
vibration suppression for smaller attached masses mTMDI.
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TMDI FOR SDOF HARMONIC
BASE EXCITATION
WEIGHT REDUCTION, VIBRATION SUPPRESSION AND ENERGY HARVESTING FOR TUNED MASS-DAMPER – INERTER (TMDI) EQUIPPED SUPPORT-EXCITED STRUCTURES
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Optimally designed TMDI as a lighter passive control solution
- Required additional oscillating mTMDI mass values for achieving prescribed
levels of structural response in the H∞ sense:
- |G1(ω)| = 2.9 if:
- The TMDI configuration represents a much lighter passive control solution
compared to the case of classical TMD.
OR 2)TMDI solution - mass ratio μ=0.34
(for β=0.1)
1) TMD solution: mass ratio μ=0.63
Example:
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TMDI FOR SDOF HARMONIC
BASE EXCITATION
WEIGHT REDUCTION, VIBRATION SUPPRESSION AND ENERGY HARVESTING FOR TUNED MASS-DAMPER – INERTER (TMDI) EQUIPPED SUPPORT-EXCITED STRUCTURES
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Optimum design
22
1 1( ) ( )G S d
• Design problem: given an undamped primary system with specific
dynamic characteristics (m1,k1,c1=0), determine the TMDI parameters
(kTMDI, cTMDI) which minimise variance of the relative displacement x1 :
S(ω)=S0 (ideal white noise)
19/38
TMDI FOR SDOF WHITE NOISE
BASE EXCITATION
2 2
1 10 and 0TMD
[ ( 1) (2 )(1 )]1
1 2(1 )TMDI
( ) (3 ) (4 )(1 )
2 2(1 )[ (1 ) (2 )(1 )]TMDI
Impose:
- Optimum frequency ratio υTMDI :
- Optimum TMDI damping ratio ζTMDI :
WEIGHT REDUCTION, VIBRATION SUPPRESSION AND ENERGY HARVESTING FOR TUNED MASS-DAMPER – INERTER (TMDI) EQUIPPED SUPPORT-EXCITED STRUCTURES
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Optimum design parameters
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Optimum frequency ratio υTMDI Optimum TMDI damping ratio ζTMDI
- setting b=β=0, the optimal tuning formulae for the classical TMD reported in
the literature are retrieved (TMDI is a generalisation of classical TMD!)
- υTMDI decreases as β increases for all
values of μ considered.
- υTMDI decreases as mTMDI mass
increases
- ζTMDI increases as β increases for all μ
values considered
- ζTMDI increases as mTMDI mass
increases
______________________________
TMDI FOR SDOF WHITE NOISE
BASE EXCITATION
WEIGHT REDUCTION, VIBRATION SUPPRESSION AND ENERGY HARVESTING FOR TUNED MASS-DAMPER – INERTER (TMDI) EQUIPPED SUPPORT-EXCITED STRUCTURES
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• Displacement response variance for white noise base excitation for the
proposed TMDI configuration (β>0) and classical TMD (β=0)
21/38
Optimally designed TMDI equipped undamped SDOF primary
structure
- TMDI reduction saturates as the ratio β increases
- Incorporation of the inerter to the classical TMD system is more effective for
vibration suppression for smaller attached masses mTMDI.
TMDI FOR SDOF WHITE NOISE
BASE EXCITATION
WEIGHT REDUCTION, VIBRATION SUPPRESSION AND ENERGY HARVESTING FOR TUNED MASS-DAMPER – INERTER (TMDI) EQUIPPED SUPPORT-EXCITED STRUCTURES
______________________________________________________________________
Optimally designed TMDI as a lighter passive control solution
- Required additional oscillating mTMDI mass values for achieving prescribed
levels of structural response in the H2 sense:
- The TMDI configuration represents a much lighter passive control solution
compared to the case of classical TMD.
22/38
TMDI FOR SDOF WHITE NOISE
BASE EXCITATION
WEIGHT REDUCTION, VIBRATION SUPPRESSION AND ENERGY HARVESTING FOR TUNED MASS-DAMPER – INERTER (TMDI) EQUIPPED SUPPORT-EXCITED STRUCTURES
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The Tuned Mass Damper Inerter (TMDI) for MDOF
23/38
- Consider the TMDI as an inter-story connective device placed in a ‘diagonal’
configuration.
- The primary structure is assumed to behave linearly in alignment with
current trends in performance based requirements for minimally damaged
structures protected by passive control devices.
TMDI FOR MDOF PRIMARY STRUCTURES
WEIGHT REDUCTION, VIBRATION SUPPRESSION AND ENERGY HARVESTING FOR TUNED MASS-DAMPER – INERTER (TMDI) EQUIPPED SUPPORT-EXCITED STRUCTURES
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Equations of motion
( )gM X C X K X M a t
- Displacement vector
- Mass matrix - Damping matrix - Stiffness matrix
1 2( ) ( ) ( ) ( )T
TMD nX x t x t x t x t
1
2
3
0 0 0
0 0 0
0 0
0 0 0
0
0 0
TMDI
n
m b b
m
b m bM
m
m
1 1
1 1 2 2
2
1
1 1
0 0
0
0
0 0 0
0 0
TMDI TMDI
TMDI TMDI
n
n n n
c c
c c c c
c c c cC
c
c
c c c
1 1
1 1 2 2
2
1
1 1
0 0
0
0
0 0 0
0 0
TMDI TMDI
TMDI TMDI
n
n n n
k k
k k k k
k k k kK
k
k
k k k
24/38
Time domain:
Frequency domain:
1
2( 1)
( )( ) ( )
( )O n
Y sG s C sI A B
A s
1 1
1 1,
n nO IA
M K M C
1 1
1 1
n n
n n
O IB
I I
TMDI FOR MDOF PRIMARY STRUCTURES
WEIGHT REDUCTION, VIBRATION SUPPRESSION AND ENERGY HARVESTING FOR TUNED MASS-DAMPER – INERTER (TMDI) EQUIPPED SUPPORT-EXCITED STRUCTURES
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Optimum design for stochastic seismic excitation.
• Aim: Given a TMDI equipped primary system with specific dynamic
characteristics, determine the TMDI parameters (CTMDI , KTMDI) which
minimise the mean square displacements of the top floor.
|G1(ω)|2 - squared modulus of the frequency response function
S(ω,tmax) – evolutionary power spectral density function of the seismic
excitation modelled by a non stationary stochastic process .
• The following performance index is considered:
0/ ,TMDIPI J J Where: 2
1 max0
( ) ( , ) ,TMDIJ G S t d
J0 - the variance of the top floor displacement for the uncontrolled primary
(linear) structure
25/38
tmax - the instant in time at which the proposed non-stationary power spectrum
is maximized
TMDI FOR MDOF PRIMARY STRUCTURES
WEIGHT REDUCTION, VIBRATION SUPPRESSION AND ENERGY HARVESTING FOR TUNED MASS-DAMPER – INERTER (TMDI) EQUIPPED SUPPORT-EXCITED STRUCTURES
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Optimum design for stochastic seismic excitation.
Optimisation method:
• MATLAB® built-in “min-max” constraint optimization algorithm employing a
sequential programming method (Salvi & Rizzi , 2011).
Initial estimates:
• Optimum TMDI parameters for an undamped linear primary structure under
white noise base excitation (Marian & Giaralis, 2014).
Constraints:
• Appropriate constraints are imposed to the sought design parameters
relying on physical considerations.
0.5 1.10 0 1.00TMDI TMDIand
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TMDI FOR MDOF PRIMARY STRUCTURES
WEIGHT REDUCTION, VIBRATION SUPPRESSION AND ENERGY HARVESTING FOR TUNED MASS-DAMPER – INERTER (TMDI) EQUIPPED SUPPORT-EXCITED STRUCTURES
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Optimum design for stochastic seismic excitation.
Structure Story Mass (kg) Stiffness
(N/m)
3DOF
1 (top) 30 x 10^3 10 x 10^5
2 30 x 10^3 30 x 10^5
3 30 x 10^3 30 x 10^5
Structure Mode Period
(s) Frequency
(rad/s)
3DOF
1st 0.50 12.56
2nd 0.23 27.79
3rd 0.12 52.31
Modeling of the seismic excitation (C-P EPS compatible with EC8 spectrum)
Characteristics of primary
structures considered
2 4
2
2 22 2 2 2
2 2
1 4
( , ) exp( )2
1 4 1 4
g
g f
g g
g g f f
btS t C t
____
____
____
____
____
____
____
____
_
C
(cm/sec2.5)
b
(1/sec) ζg
ωg
(rad/sec) ζf
ωf
(rad/sec)
17.76 0.58 0.78 10.73 0.90 2.33
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Parameters for the definition of C-P evolutionary power
spectrum compatible with EC8 spectra
(Giaralis A, Spanos PD,2012)
TMDI FOR MDOF PRIMARY STRUCTURES
WEIGHT REDUCTION, VIBRATION SUPPRESSION AND ENERGY HARVESTING FOR TUNED MASS-DAMPER – INERTER (TMDI) EQUIPPED SUPPORT-EXCITED STRUCTURES
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Optimum TMDI parameters for stochastic seismic excitation.
- 3DOF primary structure
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TMDI FOR MDOF PRIMARY STRUCTURES
Optimum stiffness kTMDI Optimum TMDI damping cTMDI _
__
__
__
__
__
__
__
__
__
__
__
__
__
__
_
- kTMDI increases as β increases
- kTMDI decreases as mTMDI mass
increases
- cTMDI increases as β increases
- cTMDI increases as mTMDI mass
increases
WEIGHT REDUCTION, VIBRATION SUPPRESSION AND ENERGY HARVESTING FOR TUNED MASS-DAMPER – INERTER (TMDI) EQUIPPED SUPPORT-EXCITED STRUCTURES
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TMDI performance assessment for stochastic seismic excitation.
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TMDI FOR MDOF PRIMARY STRUCTURES
- The proposed TMDI configuration reduces the value of the Performance
Index as the value of b increases
- Incorporation of the inerter to the classical TMD system is more effective for
vibration suppression for smaller attached masses mTMDI.
WEIGHT REDUCTION, VIBRATION SUPPRESSION AND ENERGY HARVESTING FOR TUNED MASS-DAMPER – INERTER (TMDI) EQUIPPED SUPPORT-EXCITED STRUCTURES
TMDI as a lighter passive control solution
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TMDI FOR MDOF PRIMARY STRUCTURES
- Required additional oscillating mTMDI mass values for achieving prescribed
levels of structural response (Performance Index) for different b values.
Example:
- PI = 0.136 if:
1) TMD solution:
additional mTMDI =31000Kg
OR 2) TMDI solution
additional mTMDI =6000Kg (for b=48000Kg)
WEIGHT REDUCTION, VIBRATION SUPPRESSION AND ENERGY HARVESTING FOR TUNED MASS-DAMPER – INERTER (TMDI) EQUIPPED SUPPORT-EXCITED STRUCTURES
Performance assessment for field recorded EC8 compatible
accelerograms
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TMDI FOR MDOF PRIMARY STRUCTURES
WEIGHT REDUCTION, VIBRATION SUPPRESSION AND ENERGY HARVESTING FOR TUNED MASS-DAMPER – INERTER (TMDI) EQUIPPED SUPPORT-EXCITED STRUCTURES
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Ground acceleration no.
#1 #2 #3 #4 #5 #6 #7 Average
3 DOF structure
(T1=0.5s)
Primary structure
alone
14.2
9
10.3
6
11.2
8
10.0
2
11.5
4
12.4
3 14.45 12.05
TMD
(m=9000 Kg,
b=0 Kg)
5.58 5.90 6.79 6.93 5.30 6.46 5.54 6.07
(50.4%)
TMDI
(m=9000 Kg,
b=68000 Kg)
3.98 3.73 4.86 4.09 4.15 4.28 5.05 4.31
(35.7%)
Maximum top floor displacements (cm)
______________________________________________________________________
- The potential of energy harvesting from structures equipped with TMDs has
been recently recognized in the literature and attracted the interest of various
researchers (eg. Buelga et al, 2014).
A typical energy harvesting enabled TMD configuration
- Objective: channel part of the kinetic energy of the attached mass to a
device which can transform part of the kinetic into electric energy
- Functionality: the harvester device “resists” the relative motion (x1-xTMD) by
developing an additional electromechanical “damping” force FEM.
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ENERGY HARVESTING ENABLED TMDI
WEIGHT REDUCTION, VIBRATION SUPPRESSION AND ENERGY HARVESTING FOR TUNED MASS-DAMPER – INERTER (TMDI) EQUIPPED SUPPORT-EXCITED STRUCTURES
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Model description and characterization
- Electromagnetic device connected in parallel to the TMDI spring and damper
2
( )EM
C L
Jc
R R
- Energy harvesting enabled TMDI total damping : ,TMDI EM Mc c c
1( )TMDIV J x x - Moving magnet travels within a magnetic
field of constant flux density J generating voltage:
- Force “transmitted” to the “mechanical domain”: 1( )EM EM TMDIF c x x
RL - resistive load
RC - internal “parasitic” resistance
J - magnetic field flux density
33/38
- cEM - electromechanical damping coefficient:
ENERGY HARVESTING ENABLED TMDI
WEIGHT REDUCTION, VIBRATION SUPPRESSION AND ENERGY HARVESTING FOR TUNED MASS-DAMPER – INERTER (TMDI) EQUIPPED SUPPORT-EXCITED STRUCTURES
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Quantification of energy harvesting potential
- Energy harvesting enabled TMDI - optimally designed for vibration suppression!
The power P that can be harvested
2
2
2( )
( )RV L
C L
JP G R
R R
|GRV(ω)| - relative velocity between m1 and
mTMDI mass
______________________
______________________________________________________________________
- |GRV(ω)| decreases as β increases (for a fixed μ) - enhanced vibration suppression
- |GRV(ω)| reduction is not beneficial in terms of energy harvesting!
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ENERGY HARVESTING ENABLED TMDI
WEIGHT REDUCTION, VIBRATION SUPPRESSION AND ENERGY HARVESTING FOR TUNED MASS-DAMPER – INERTER (TMDI) EQUIPPED SUPPORT-EXCITED STRUCTURES
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Energy harvesting capabilities Vibration suppression capabilities
__________________
______________________________________________________________________
- The increase of the ratio β has a negative effect in terms of the available
energy for harvesting at resonant frequency.
- The peak values of the magnitude of FRFs saturates for β>0.5, but the
range of frequencies that the FRFs take on non-negligible values increases
- It confirms that: “an optimal absorber is not an optimal harvester”.
- However, the TMDI is not confined by apriori fixed inertial properties of the
TMD.
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Quantification of energy harvesting potential
ENERGY HARVESTING ENABLED TMDI
WEIGHT REDUCTION, VIBRATION SUPPRESSION AND ENERGY HARVESTING FOR TUNED MASS-DAMPER – INERTER (TMDI) EQUIPPED SUPPORT-EXCITED STRUCTURES
SIMULTANEOUS ENERGY HARVESTING
AND VIBRATION SUPPRESSION
36/38
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- optimally designed TMDI for vibration suppression with mass ratio μ= 0.1 and
inertance ratio 𝛽=0.6
Quantification of energy harvesting potential
- by keeping constant the weight of the TMDI, changes in the inertance b allows for
controlling the trade-off between energy harvesting and vibration suppression
WEIGHT REDUCTION, VIBRATION SUPPRESSION AND ENERGY HARVESTING FOR TUNED MASS-DAMPER – INERTER (TMDI) EQUIPPED SUPPORT-EXCITED STRUCTURES
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SIMULTANEOUS ENERGY HARVESTING
AND VIBRATION SUPPRESSION
WEIGHT REDUCTION, VIBRATION SUPPRESSION AND ENERGY HARVESTING FOR TUNED MASS-DAMPER – INERTER (TMDI) EQUIPPED SUPPORT-EXCITED STRUCTURES
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• The TMDI system, exploits the mass amplification effect of the inerter to:
- improve the classical TMD performance for a fixed oscillating
additional mass, or to
- “replace” part of the TMD vibrating mass by achieving an overall
lighter passive control solution
• The energy harvesting capabilities of TMDI depends on the inerter constant
b in a optimally designed TMDI for vibration suppression, which can vary by
means of a gearbox for the case of a flywheel based inerter
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CONCLUDING REMARKS
WEIGHT REDUCTION, VIBRATION SUPPRESSION AND ENERGY HARVESTING FOR TUNED MASS-DAMPER – INERTER (TMDI) EQUIPPED SUPPORT-EXCITED STRUCTURES
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• H. Frahm, “Device for Damping Vibrations of Bodies,” U.S. Patent 989958, 1911.
• J. Ormondroyd, J.P. Den Hartog, “The theory of the dynamic vibration absorber,” J. Appl. Mech., vol.
50, pp. 9–22, 1928.
• J.P. Den Hartog, Mechanical Vibrations, 4th ed., New York: McGraw-Hill, 1956.
• S. Krenk, “Frequency analysis of the tuned mass damper,” J. Appl. Mech. ASME pp. 936–942, 2005.
• A. Gonzalez-Buelga, L. R. Clare, A. Cammarano, S. A. Neild, S. G. Burrow and D. J. Inman, “An
optimised tuned mass damper/harvester device, Struct. Control Health Monit.,2014, DOI:
10.1002/stc.1639.
• X. Tang and L. Zuo, “Simultaneous energy harvesting and vibration control of structures with tuned
mass dampers,” J. Intelligent Material Sys. and Struct., vol. 23(18), pp. 2117–2127, 2012.
• S. Adhikari, F. Ali., “Energy Harvesting Dynamic Vibration Absorbers,” J. App.Mech., vol. 80, pp. 1-9,
2013.
• L. Marian, A. Giaralis, “Optimal design of inerter devices combined with TMDs for vibration control of
buildings exposed to stochastic seismic excitations,” In: Proceedings of the 11th ICOSSAR
International Conference on Structural Safety and Reliability for Integrating Structural Analysis, Risk
and Reliability 2013; New York, US) (eds: Deodatis G, Ellingwood BR and Frangopol DM), CRC Press.
• L. Marian, A. Giaralis, “Optimal design of a novel tuned mass-damper-inerter (TMDI) passive vibration
control configuration for stochastically support-excited structural systems,” Probab. Eng. Mech.
DOI:/10.1016/j.probengmech.2014.03.007.
• M.C. Smith, “Synthesis of mechanical networks: The Inerter,” IEEE Trans. Autom. Contr., vol. 47-10,
pp. 1648-1662, 2002.
SELECTED REFERENCES
WEIGHT REDUCTION, VIBRATION SUPPRESSION AND ENERGY HARVESTING FOR TUNED MASS-DAMPER – INERTER (TMDI) EQUIPPED SUPPORT-EXCITED STRUCTURES
THANK YOU!
______________________________________________________________________
Laurentiu Marian PhD Candidate School of Engineering and Mathematical Sciences
e-mail: [email protected]
Dr. Agathoklis Giaralis Senior Lecturer in Structural Engineering
School of Engineering and Mathematical Sciences
e-mail: [email protected]