The tuned mass-damper-inerter (TMDI) for passive vibration control of multi-storey building structures subject to earthquake and wind excitations

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Academic excellence for business and the professions The tuned mass-damper-inerter (TMDI) for passive vibration control of multi-storey building structures subject to earthquake and wind excitations

1 Academic excellence for business and the professions The tuned mass-damper-inerter (TMDI) for passive vibration control of multi-storey building structures subject to earthquake and wind excitations Dr Agathoklis Giaralis Senior Lecturer in Structural Engineering Civil Engineering Structures Research Centre Department of Civil Engineering City University London Grant Ref: EP/M017621/1 City University London, March 9 th, 2016

2 ACKNOWLEDGEMENTS Prof. Nick Karcanias 2011: Do you know about what the inerter is? Can we use it for passive vibration control of buildings? Marian Laurentiu City University London studentship ( ) PhD thesis (viva 12/2016): The tuned mass damper inerter for vibration suppression and energy harvesting in dynamically excited structural systems EPSRC Big Pitch- Bright Ideas award (10/2014) Multi-objective performance-based design of tall buildings using energy harvesting enabled tuned mass-damper-inerter (TMDI) devices Grant Ref: EP/M017621/1 Dr Francesco Petrini (Performance-based wind engineering) Dr Jonathan Salvi (Smart structures and control) Assoc. Prof. Alexandros Taflanidis, University of Notre Dame, USA

3 Presentation Outline Introduction/Motivation The classical tuned mass-damper (TMD) Motivation for the tuned mass-damper-inerter (TMDI) TMDI for single-degree-of-freedom (SDOF) primary structures Optimum design formulae Vibration suppression performance and weight reduction TMDI for multi-storey seismically excited structures Eurocode 8 compatible seismic design and assessment of TMDI equipped building structures Reliability-based optimum design of TMDI equipped building structures accounting for higher modes of vibration TMDI for wind excited tall buildings Vortex shedding and occupants comfort Parametric analysis for a benchmark wind excited TMDI equipped 74- storey building Concluding remarks

4 The classical tuned mass damper (TMD) For primary structures modelled as single-degree-of-freedom (SDOF) systems Additional mass m TMD attached to the primary structure via a linear spring k TMD and dashpot c TMD in parallel. Given a primary structure and attached mass, find k TMD and c TMD such that the response of the primary structure is minimised. The larger the attached mass, the better level of vibration suppression is achieved in terms of peak response along a wider frequency band.

5 The classical tuned mass damper (TMD) For primary structures modelled as multi-degree-of-freedom (MDOF) systems The m TMD mass is attached to the lead mass via a linear spring k TMD and dashpot c TMD in parallel. Given a primary structure and attached mass, find k TMD and c TMD to control the first (fundamental) mode shape. Wind induced vibrations: m TMD 0.2% - 2% of the total building mass Earthquake-induced vibrations: m TMD >>2% of the total building mass

6 TMD applications in buildings Suppression of wind induced vibrations Ni/Zuo/Kareem (2011) Zuo/Tang, JIMSS (2013)

7 TMD applications in buildings Edificio Park Araucano, Santiago, Chile Suppression of earthquake induced vibrations

8 Motivation for the tuned mass-damper-inerter (TMDI) Protection of buildings for earthquakes Conventional design philosophy: allows for inelastic deformations (a) Passive vibration control: incorporates different devices to reduce the ground motion induced oscillations (b)-(d) (a) (b) (c) (d) Passive response control systems: (b) seismic isolation, (c) energy dissipation devices, (d) Passive TMDs (linear, easy to design) BUT: Require the attachment of very large attached masses

Motivation for the tuned mass-damper-inerter (TMDI) Multiple TMDs Large-mass and Non-linear TMDs Feng/Mita, JEM, (1996) Moutinho, EESD (2012) De Angelis/Perno/Reggio, EESD (2012) Need for a TMD-based

9 Motivation for the tuned mass-damper-inerter (TMDI) Multiple TMDs Large-mass and Non-linear TMDs Feng/Mita, JEM, (1996) Moutinho, EESD (2012) De Angelis/Perno/Reggio, EESD (2012) Need for a TMD-based passive dynamic vibration absorber for earthquake engineering applications that: - does not involve excessively large attached mass -is linear -is amenable to the standard TMD optimum design approaches

Motivation for the tuned mass-damper-inerter (TMDI) The concept of the inerter and its mass amplification effect - The inerter is a linear device with two terminals free to

proportionality b ( inertance ) is in mass units (kg) - Single-degree of freedom oscillator connected to the ground via an inerter: ( m1 b) x c1x 1 k1x1 m1a g 1 - The inerter

10 Motivation for the tuned mass-damper-inerter (TMDI) The concept of the inerter and its mass amplification effect - The inerter is a linear device with two terminals free to move independently and develops an internal (resisting) force proportional to the relative acceleration of its terminals (Smith 2002) Note: F b( u1- u2) - The constant of proportionality b ( inertance ) is in mass units (kg) - Single-degree of freedom oscillator connected to the ground via an inerter: ( m1 b) x c1x 1 k1x1 m1a g 1 - The inerter increases the m 1 mass: m 1 m 1 +b F k( u1- u2) F c( u1- u2) mass amplification effect Smith, IEEE (2002); Takewaki/Murakami/Yoshitomi/Tsuji, SCHM (2012); Chen/Hu/Huang/Chen, JSV (2014)

Motivation for the tuned mass-damper-inerter (TMDI) Flywheel-based inerter with rack and pinion mechanism Smith, IEEE (2002) - Assume a mechanical realisation of the inerter comprising a plunger that

11 Motivation for the tuned mass-damper-inerter (TMDI) Flywheel-based inerter with rack and pinion mechanism Smith, IEEE (2002) - Assume a mechanical realisation of the inerter comprising a plunger that drives a rotating flywheel through a rack, pinion and gearing system: F b( u1- u2), b m f ( ) p pr 2 n 2 f ri 2 2 i1 f i - The constant of proportionality b (inertance) - mass units (>> physical mass of device) - Inerter can have an inertance ("apparent" mass) orders of magnitude higher than its physical mass.

The tuned mass-damper-inerter (TMDI) A linear potentially lighter

the TMD Marian/Giaralis, PBEE, (2013, 2014) SDOF primary structures

viscous damper + an inerter device which connects the attached mass

MDOF primary structures TMDI as an inter-story connective device

12 The tuned mass-damper-inerter (TMDI) A linear potentially lighter than the TMDI passive control solution with the deisgn simplicity of the TMD Marian/Giaralis, PBEE, (2013, 2014) SDOF primary structures Mass attached to the primary structure via a linear spring and a viscous damper + an inerter device which connects the attached mass to the ground. MDOF primary structures TMDI as an inter-story connective device placed in a diagonal configuration. For b=0: Tuned massdamper (TMD) For m TMDI =0: Tuned inerterdamper (TID) Lazar/Neild/Wagg, EESD (2013, 2014)

TMDI for SDOF primary structures Equations of motion Marian/Giaralis, PBEE, (2013, 2014) Time domain: mtmdi b 0 xtmdi ctmdi ctmdi xtmdi ktmdi ktmdi xtmdi mtmdi a 0 m x c c c x k k k x m TMDI 1 1 TMDI

13 TMDI for SDOF primary structures Equations of motion Marian/Giaralis, PBEE, (2013, 2014) Time domain: mtmdi b 0 xtmdi ctmdi ctmdi xtmdi ktmdi ktmdi xtmdi mtmdi a 0 m x c c c x k k k x m TMDI 1 1 TMDI 1 TMD 1 TMDI 1 TMDI 1 1 m k Frequency domain: i2 1 x G ( ) 1 2 TMDI TMDI TMDI ag TMDI i2 TMDITMDI 2 TMDI i2 TMDITMDI 1 1 TMDI TMDI TMDI b 2( m ) ctmdi m TMDI TMDI TMDI TMDI b TMDI m 1 1 g b m 1

14 TMDI for SDOF primary structures Optimum design for harmonic excitation Marian/Giaralis, SCHM, (2014, 2016) - Design problem: given an undamped primary system with specific dynamic characteristics (m 1,k 1,c 1 =0), determine the TMDI parameters (k TMDI, c TMDI ) which minimise the response of the primary system, given m TMDI and b. -mass ratio 0.1, -inertance ratio β=0.1, -frequency ratio υ TMDI = Solution - Equal points design method: there exist two fixed points where the FRF curves intersect (noted P 1 and P 2 ), independent of c TMDI (ζ TMDI ). - Optimum response is obtained if and only if there exists two local maxima and both have the same amplitude

15 TMDI for SDOF primary structures Optimum design for harmonic excitation Den Hartog approach Minimum response <=> (if and only if) G 1 (ω) has two local maxima with equal amplitudes at the stationary points P 1 and P 2. Enforce: 1) G 1 (ω) is independent of ζ TMDI : - Optimum frequency ratio υ TMDI : 2 2 lim G ( ) lim G( ) TMDI TMDI 2) Equal amplitude at points P 1 and P 2 for the limit ζ TMDI : lim G( ) lim G( ) TMDI 1 P1 1 P2 TMDI 3) G 1 (ω) is maximized locally at points P 1 and P 2 : G1( ) G1( ) P1 P2 0 => For b=0 (β=0) optimum TMD design is retrieved TMDI TMDI 1 (1 )(2 ) 1 2(1 ) - Optimum TMDI damping ratio ζ TMDI : (1 ) (1 )(6 7 ) 8(1 )(1 )[2 (1 )] - Dynamic amplification factor: max G ( ) 1 (1+ )( 2 2) Marian/Giaralis, SCHM, (2014, 2016)

TMDI for SDOF primary structures Optimum design for harmonic excitation: vibration suppression Marian/Giaralis, SCHM, (2014, 2016) - All FRF curves attain two local maxima

TMD): - reduces the peak response of the primary structure (at ω 1, ω P1 and ω P2 ), - increases robustness to detuning effects - Large β values - wider range of frequencies

16 TMDI for SDOF primary structures Optimum design for harmonic excitation: vibration suppression Marian/Giaralis, SCHM, (2014, 2016) - All FRF curves attain two local maxima of equal height at the frequencies ω P1 and ω P2 whose location depend on the ratio β. For the same m TMDI mass, the inclusion of the inerter (TMDI vs. TMD): - reduces the peak response of the primary structure (at ω 1, ω P1 and ω P2 ), - increases robustness to detuning effects - Large β values - wider range of frequencies peak response reduction compared to the classical TMD. - Practically, the inerter furnishes all the positive effects of increasing the attached mass without the negative effect of the added weight.

TMDI for SDOF primary structures Optimum design for harmonic excitation: weight reduction - Peak response amplitude for optimally designed TMDI normalized by the peak response amplitude of the

17 TMDI for SDOF primary structures Optimum design for harmonic excitation: weight reduction - Peak response amplitude for optimally designed TMDI normalized by the peak response amplitude of the optimally designed classical TMD (β =b=0). - TMDI reduction saturates as the ratio β increases Marian/Giaralis, SCHM, (2014, 2016) - Incorporation of the inerter to the classical TMD system is more effective for vibration suppression for smaller attached masses m TMDI. Example: - G 1 (ω) = 2.9 if: 1) TMD solution: mass ratio )TMDI solution - mass ratio 0.34 (for β=0.1)

18 TMDI for SDOF primary structures Optimum design for white noise excitation Closed form expressions for TMDI parameters to minimize the variance of the relative displacement of undamped primary structures 2 ( ) 2 ( ) 1 1 G S d S(ω)=S 0 (ideal white noise) TMDI TMDI TMDI Impose: 1 [ ( 1) (2 )(1 )] 1 2(1 ) ( ) (3 ) (4 )(1 ) 2 2(1 )[ (1 ) (2 )(1 )] and 0 TMD => For b=0 (β=0) TMD TMD TMD (1 / 2) 1 (1 / 4) 4(1 )(1 / 2) S (1 ) 2 1,min 0 1 (1 )[ (3 ) (4 )(1 )] ( )(1 ) S (1 ) 2 1,min 0 1 (1 )(4 ) Marian/Giaralis, PEM, (2014) Warburton, EESD, (1982)

performance in terms of displacement response variance for white noise base

19 TMDI for SDOF primary structures Optimum design for white noise excitation Additional m TMDI mass values (coefficient µ)required for achieving the same level of performance in terms of displacement response variance for white noise base excitationfor the proposed TMDI configuration (β>0) and classical TMD (β=0) Marian/Giaralis, PEM, (2014)

20 TMDI for MDOF primary structures Equations of motion: N-storey TMDI equipped shear frame building structure Marian/Giaralis, PEM (2013,2014) Mx Cx Kx Mδ x x t x t x t x t δ T a g TMD ( ) ( ) ( ) ( ) T 1 2 mtmdi b 0 b m1 0 0 b 0 m2 b 0 M m mn ctmdi ctmdi 0 0 ctmdi c1 ctmdi c1 0 0 c1 c1 c2 c 2 C 0 0 c2 0 c n1 0 0 cn 1 cn 1cn ktmdi ktmdi 0 0 ktmdi k1 ktmdi k1 0 0 k1 k1 k2 k 2 K 0 0 k2 0 k n1 0 0 kn 1 kn 1kn n - Mass matrix - Displacements vector - Damping matrix - Stiffness matrix

21 TMDI for MDOF primary structures Optimum design for evolutionary stochastic (seismic) excitation Given: A primary structure with specific dynamic characteristics, An inerter with pre-specified inertance b, A pre-specified TMD mass: Optimize for: TMD parameters : damping ratio (ζ TMDI ) and frequency ratio: ctmdi TMDI TMDI 2( m b) Considering the objective function m TMDI T M M TMDI S(ω,t) evolutionary power spectral density (EPSD) function modelling the support excitation modelled by a stationary stochastic process G 1 (ω) 2 - squared modulus of the frequency response function corresponding to peak floor displacement M 1 1 1n p 1n TMDI TMDI 1 TMDI 2 TMDI 0 /, 1( ) max (, ) 0 t PI J J Marian/Giaralis, PEM (2014) J G S t d

22 TMDI for MDOF primary structures Optimum design for evolutionary stochastic (seismic) excitation Equivalent mechanical model of the proposed frame structure. Mechanical admittance formulation. Mechanical admittances Marian/Giaralis, PEM (2014) Equations of motion in Laplace form: Admittance matrix [B]: Compute overall system transfer function:

Eurocode 8 compatible seismic design of TMDI equipped building structures Considered input evolutionary stochastic seismic excitation Modeling of the seismic excitation (EPSD compatible with the

23 Eurocode 8 compatible seismic design of TMDI equipped building structures Considered input evolutionary stochastic seismic excitation Modeling of the seismic excitation (EPSD compatible with the Eurocode 8 elastic response spectrum) Giaralis/Spanos, E&S (2012) g bt g f S(, t) C t exp( ) g 1 4 g g g f f C (cm/sec 2.5 ) b (1/sec) ζ g ωg (rad/sec) ζ f ω f (rad/sec)

24 Eurocode 8 compatible seismic design of TMDI equipped building structures Range of different 3-storey building frames

25 Eurocode 8 compatible seismic design of TMDI equipped building structures Performance in terms of top floor displacement variance Optimisation method: MATLAB built-in min-max constraint optimization algorithm employing a sequential programming method 0.5 TMDI 1.10 and 0 TMD 1.00

26 Eurocode 8 compatible seismic design of TMDI equipped building structures Weight reduction

27 Eurocode 8 compatible seismic assessment of TMDI equipped building structures TMDI assessment using Eurocode 8 compatible accelerograms Giaralis/Spanos, SDEE (2009)

28 Eurocode 8 compatible seismic assessment of TMDI equipped building structures

29 Eurocode 8 compatible seismic assessment of TMDI equipped building structures The TMDI suppresses the higher modes of vibration, not just the fundamental mode as the TMD does

30 TMDI for MDOF primary structures Equations of motion: N-storey TMDI equipped shear frame building structure Marian/Giaralis, PEM (2013,2014) Mx Cx Kx Mδ x x t x t x t x t δ T a g TMD ( ) ( ) ( ) ( ) T 1 2 mtmdi b 0 b m1 0 0 b 0 m2 b 0 M m mn ctmdi ctmdi 0 0 ctmdi c1 ctmdi c1 0 0 c1 c1 c2 c 2 C 0 0 c2 0 c n1 0 0 cn 1 cn 1cn ktmdi ktmdi 0 0 ktmdi k1 ktmdi k1 0 0 k1 k1 k2 k 2 K 0 0 k2 0 k n1 0 0 kn 1 kn 1kn n - Mass matrix - Displacements vector - Damping matrix - Stiffness matrix

31 Reliability-based optimum design framework for TMDI equipped seismically excited building structures i d floor i b floor k d c d m n m d m 1 b x n x id x ib x 1 Alternative connectivity arrangements T T Ms Rd drd Rc Rc xs drd Rc T C x Ksxs M R m R R m b m b y s s s d d d s g and T T T ( m b) y m R br x c y k y m R R x d d d c s d d d d s g R d R b : TMD location vector : inerter location vector R R R : connectivity vector c d b x x g Reliability-based design accounting for higher modes contribution: Minimize the probability that any interstorey drift, or total floor acceleration, or the attached mass displacement (stroke) outcrosses a predefined threshold within the duration of stationary seismic excitation Inertance b is treated as a free/design parameter Giaralis/Taflanidis, (2015) Seismic input and structural uncertainty can be accounted for

32 z 3 P ( φ) P D for some t ] F B 2 z 3 z( t) s [ 0,T z 2 z 2 First-passage probability for vector output D : z( t) n z : z i ( t), i 1,..., n z 1 Performance variables -interstorey drifts -total floor accelerations -attached mass stroke z 1 s i z Reliability-based optimum design framework for TMDI equipped seismically excited building structures B : z ( t ) i i i Vector-output z() t C( φ) x( t) output z i (t) white noise (input) x( t) A( φ) x( t) E( φ) w() t φ b Augmented state-space matrix z i (t)=β i z i (t)=-β i t Design variables d 32 d First-passage probability for scalar output Hyper-rectangular in the performance variables space Giaralis/Taflanidis, (2015)

33 Reliability-based optimum design framework for TMDI equipped seismically excited building structures z ( t ) s [ 0,T xp ( φ) T P F ( φ ) P D for some t [ 0,T ] 1 e z z 2 First-passage probability for vector output z 1 Assumption: Stationary excitation and response φ Reliabilitybased design * arg min P ( φ ) φ Φ F + arg min v ( φ) φφ z Unconditional outcrossing rate for vector output v + z E [number of out-crossings in [ t,t + t ] no out-crossings in [ 0,t ]] ( φ )= lim t 0 t n z i1 P + ( φ) ( φ) r ( φ) Rice s conditional outcrossing rate for scalar output z z z i i i Correction factor for vector output, considering correlation of outcrossing s at different parts of boudnary Temporal correlation factor correction for unconditional outcrossing rate Giaralis/Taflanidis, (2015)

34 Reliability-based optimum design framework for TMDI equipped seismically excited building structures Properties of the 10-storey TMDI equipped frame structure Stories Storey Mass (ton) Storey Stiffness (MN/m) k i Mode Period (s) Participation factor st % 2 nd % 3 rd % Nominal modal damping: 3.5% Seismic Excitation: Clough-Penzien spectrum Adopted thresholds S g ( ) s o g g g g 4 g g f 4 f f 2 Interstorey drifts: 3.3cm Floor acceleration: 0.5g Stroke: 1m with mean values ω g =3π, ω f =π/2, ζ g =0.4, ζ f =0.8, a RMS =0.09g Giaralis/Taflanidis, (2015)

35 Topology mass ratio μ d i d i b 0.1% 0.3% 0.5% 0.75% 1% 1.5% 2% 3% 4% 5% (217.7) (122.2) (224.7) (234.7) (139.6) (240.63) (126.5) (315.85) (180.27) (326.6) (143.7) (418.5) (210.9) (120.1) (230.8) (228.9) (136.8) (251.0) (133.2) (309.7) (176.6) (341.9) (151.3) (413.9) + * Optimal out-crossing rate z ( φ ) 100 and optimal inerter ratio β % (in parenthesis) for different TMDI topologies. TMD denotes the cases for which β=0 is optimal (204.7) (119.7) (238.34) (223.3) (134.7) (260.3) (151.2) (303.5) (173.2) (413.9) (171.8) (410.4) (TMD) (114.2) (TMD) (216.4) (133.2) (341.9) (152.4) (296.4) (169.9) (416.7) (172.5) (404.3) (TMD) (110.1) (TMD) (209.8) (129.5) (345.8) (153.3) (296.5) (167.1) (420.1) (174.6) (403.6) (TMD) (104.6) (TMD) (125.9) (TMD) (156.3) (277.7) (161.9) (424.9) (176.8) (394.0) (TMD) (TMD) (120.8) (TMD) (TMD) (266.5) (157.4) (429.7) (179.4) (387.2) (TMD) (TMD) (TMD) (TMD) (111.5) (TMD) (148.5) (TMD) (184.1) (376.6) (TMD) (139.6) (TMD) (188.7) (TMD) (TMD) (TMD) (TMD) (129.6) (TMD)

36 Feasibility of inerters spanning multiple floors Taipei 101 tower

37 Effectiveness of the TMDI to suppress higher modes Normalized Transfer function for top floor acceleration uncontrolled TMD (i d =9) TMDI (i d =9 i b =8) TMDI (i d =9 i b =7) TMDI (i d =8 i b =10) ω 1 : fundamental structural frequency ω/ω 1

38 Scalar threshold a [cm/s 2 ] Loss of integrity of non-structural elements Displacements Motion perception by building occupants Accelerations Serviceability in wind-excited high-rise (tall) buildings V m (z 3 ) Loss of serviceability V(t;z 2 ) V m (z 2 ) w(t;z 2 ) u(t;z 2 ) v(t;z 2 ) V m (z 1 ) Z H Y 100 X Office Apartment θ B 1 B Discomfort level in terms of perception thresholds Usually cross-wind vibration is critical for occupants comfort 1 f 1 0,1 1 Italian Guidelines f [Hz] 3 The reference period for comfort evaluation is 1 year 4 1 st natural frequency is dominant

Vortex shedding 140 effect 120 100 80 60 40 20 0-20 Across-wind θ=0

39 Cross-wind forces due to vortex shedding Vortex shedding phenomenon Experimental results (wind tunnel testing) Vortex shedding effect n Vortex shedding 140 effect Across-wind θ=0 Across-wind -40 θ=15 Across-wind -60 Along Across t [s] 3800 n F [KN] n

40 Case study of a typical tall building subject to vortex shedding Perimetric frame system Central core Complete FE model Ciampoli/Petrini, PEM (2011) Bracing system (outriggers) Case study- Structure 74 floors Height H=305m Footprint B 1 =B 2 =50m Total mass= tons

41 a p p L,D L,D [cm/s [cm/s 2 ] 2 ] Case study of a typical tall building subject to vortex shedding For buildings having H/B>3 the across-wind direction is dominant in terms of accelerations Peak response accelerations a L p [cm/s 2 ] Z V m (z3) V m (z2) V m (z1) Y X V(t;z2) w(t;z 2 ) u(t;z v(t;z 2 ) 2 ) θ B 1 B 2 Across H a L p Along a D p Structural response accelerations Along Across t [s] a L, a D [cm/s 2 ] Comfort evaluation Office Apartment a L p a D p Due to vortex shedding effect 10 Across Along 5 q [deg] f n [Hz] n [Hz]

42 Case study of a typical tall building subject to vortex shedding Considered vortex shedding input spectra Petrini/Giaralis (2016)

43 Case study of a typical tall building subject to vortex shedding Structural analysis in the frequency domain Input/output relationship from random vibrations theory Petrini/Giaralis (2016) Response variances Peak responses

44 Model reduction from detailed finite element model (FEM) 1) A diagonal mass matrix is assumed corresponding to a lumped mass 74 DOF system populated by the floor masses 2) Natural frequencies (eigenvalues) and mode shapes (eigenvectors) corresponding to the 74 lateral dominantly translational are obtained from the detailed FEM model 3) Derivation of a full stiffness matrix Case study of a typical tall building subject to vortex shedding Petrini/Giaralis (2016) 3) Derivation of a full damping matrix Mode j Assumed damping ratio 1-3 2% 4-6 4% % % % % >60 18%

45 Independent parameters TMDI damping ratio β= 0:1 0.3%; 0.5%; 0.8%; 1%; 1.5% frequency ratio: TMDI Connectivities F n F n-1 m n Case study of a typical tall building subject to vortex shedding k TMDI m n c TMDI m TMDI b k TMDI m n c TMDI m TMDI b k TMDI m n c TMDI m TMDI b m n-1 m n-1 m n-1 m n-1 F n-2 m n-2 m n-2 m n-2 m n-2 F n-3 m n-3 m n-3 m n-3 m n-3 F 2 m 2 m 2 m 2 m 2 F 1 m 1 m 1 m 1 m 1

46 Case study of a typical tall building subject to vortex shedding Petrini/Giaralis (2016) Top floor peak displacement Top floor peak acceleration TMDI connectivity

47 Case study of a typical tall building subject to vortex shedding Petrini/Giaralis (2016) Peak TMDI Stroke Peak inerter forces TMDI connectivity

48 Case study of a typical tall building subject to vortex shedding Sub-optimal inertance values and mass amplification factor Conn type Response Parameter Sub-optimal values of β type µ=0.3% µ=0.5% µ=0.8% µ=1.0% µ=1.2% µ=1.5% -1 Displ β Displ β Displ β Conn type Response amplification factors at sub-optimal values of β Response type Parameter µ=0.3% µ=0.5% µ=0.8% µ=1.0% µ=1.2% µ=1.5% -1 Displ ampl factor Displ ampl factor Displ ampl factor The same response can be equivalently obtained by a classical TMD with µ=3.12%, and the same η, ξ values Mass/weight reduction by about 10 times Petrini/Giaralis (2016)

49 Major concluding remarks The TMDI 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 This is an important consideration, especially for earthquake engineering applications and for tall buildings under wind excitations The TMDI controls more than one modes of vibration which may or may not be accounted for in the design This is an important consideration in suppressing floor accelerations in earthquake and wind excited buildings

50 THANK YOU FOR YOUR ATTENTION Marian Laurentiu City University London studentship ( ) PhD thesis (viva 12/2016): The tuned mass damper inerter for vibration suppression and energy harvesting in dynamically excited structural systems EPSRC Big Pitch- Bright Ideas award (10/2014) Multi-objective performance-based design of tall buildings using energy harvesting enabled tuned mass-damper-inerter (TMDI) devices Grant Ref: EP/M017621/1 Dr Francesco Petrini- EPSRC funded post-doctoral fellow Dr Jonathan Salvi- EPSRC funded post-doctoral fellow Assoc. Prof. Alexandros Taflanidis, University of Notre Dame, USA

City, University of London Institutional Repository

City Research Online City, University of London Institutional Repository Citation: Marian, L. & Giaralis, A. (04). Optimal design of a novel tuned mass-damperinerter (I) passive vibration control configuration