Wind-induced vibration mitigation in tall buildings using the tuned mass-damper-inerter (TMDI)

TL;DR: In this article, a parametric numerical study is performed involving a top-floor-TMD-equipped planar frame capturing accurately the in-plane dynamic behavior of a 74-storey benchmark building exposed to a quasi-stationary spatially-correlated wind-force field accounting for vortex shedding effects in the across-wind direction.

Abstract: In this paper the classical linear tuned mass-damper (TMD) is coupled with an inerter, a two-terminal device resisting the relative acceleration of its terminals, in various tuned mass-damper-inerter (TMDI) topologies to suppress excessive wind-induced oscillations in tall buildings causing occupants’ discomfort. A parametric numerical study is undertaken involving a top-floor-TMD-equipped planar frame capturing accurately the in-plane dynamic behavior of a 74-storey benchmark building exposed to a quasi-stationary spatially-correlated wind-force field accounting for vortex shedding effects in the across-wind direction. It is found that the TMDI reduces the peak top floor acceleration more effectively than the TMD by considering smaller attached mass values, and TMDI topologies in which the inerter spans more stories in linking the attached mass to the host structure. Moreover, the inclusion of the inerter reduces dramatically the TMD stroke while it was verified that the magnitude of the developing inerter forces can be readily accommodated by the host structure. Pertinent illustrative examples are included showcasing that the TMDI meets code-prescribed serviceability design requirements for new tall buildings using significantly smaller attached mass compared to the TMD, and that inerter devices can be used to upgrade the performance of existing TMD-equipped tall buildings without changing the attached mass.

Summary

INTRODUCTION

• In fact, in many cases, vortex shedding induces higher peak floor accelerations in slender/tall buildings in the across-wind direction than those exhibited in the along-wind direction (Ciampoli and Petrini 2012; Bernardini et al. 2015).
• The effectiveness of the TMD relies on “tuning” its stiffness and damping properties for a given primary structure and attached mass, such that significant kinetic energy is transferred from the vibrating primary structure to the TMD mass and eventually dissipated through the dampers.
• In the meantime, in recent years, there is a World-wide trend towards the design and construction of ever-more lighter, slender, and, therefore, more susceptible to wind-induced vibrations tall buildings.

THE TUNED MASS-DAMPER-INERTER (TMDI) FOR MULTI-STOREY BUILDINGS

• Conceptually defined by Smith (2002), the ideal inerter is a linear massless two-terminal mechanical element resisting the relative acceleration at its terminals through the so-called inertance coefficient, b, measured in mass units.
• Treating the above system as the primary structure, the TMDI topology introduced by Marian and Giaralis (2013,2014) comprises a mass mTMDI attached to the top floor via a linear spring of stiffness kTMDI and a linear dashpot of damping coefficient cTMDI, and linked to the penultimate floor by an ideal inerter of inertance b.
• Note that the inclusion of the inerter device influences only the mass matrix M of the controlled structure (i.e., the matrices C and K are the same for the TMD and for the TMDI).
• These cross-terms alter the dynamics of the primary structure such that higher modes of vibration are damped besides the fundamental mode shape.

ADOPTED PRIMARY STRUCTURE AND WIND EXCITATION MODELLING

• Benchmark 74-storey building description and detailed FE model.
• To assess the potential of the TMDI in Fig. 1 for suppressing wind induced oscillations in tall buildings, a high-rise building previously considered for the development of a performance-based wind engineering framework (Spence and Gioffrè 2012; Petrini and Ciampoli 2012) is taken as a benchmark structure.
• The adopted structure is a 74-storey steel frame building of 305m total height with a 50m-by-50m footprint.
• For illustration, the first three normalized mode shapes obtained from the FE model, φ(FE)j (j=1,2,…,6) and from the reduced 74-DOF dynamical system φj (j=1,2,…,6) are superposed in Fig.2(b) shown to match very well.
• For natural frequencies above this range, increasing damping ratios with natural frequency are assumed converging asymptotically to an arbitrarily taken 18% damping ratio.

ASSESSMENT OF TMDI VIBRATION SUPPRESSION CAPABILITIES VIS-À-VIS THE TMD

• A parametric investigation is undertaken to quantify the effectiveness of different TMDI topologies to mitigate vibrations in the across-wind direction of tall buildings accounting for vortex shedding effects.
• To this aim, the previously discussed 74-DOF structural system is taken as a paradigm of a primary structure exposed to wind loading modelled by the adopted 74FFS PSD matrix for top floor mean wind velocity Vref= 35m/s (Fig.3).
• These RFs are obtained by normalizing the peak response quantities in Eq. (11) by the corresponding values of the uncontrolled structure, while the inertance ratio is let to vary in the range of 0% to 100% of the primary structure mass, with the special case of β=0 being the TMD.
• Still, they do yield reasonable values for the stiffness and the damping properties of the TMDI, accounting for the mass amplification effect of the inerter, which suffice to draw valid and useful comparisons of the effectiveness of different TMDI topologies vis-à-vis the TMD (β=0) case.
• Overall, the herein reported numerical data suggests that the incorporation of the inerter to the TMD is rather beneficial in reducing floor accelerations and that the smaller the attached mass is the more significant this reduction becomes.

SOME PRACTICAL DESIGN CONSIDERATIONS FOR TMDI-EQUIPPED TALL BUILDINGS

• Having established the potential benefits of coupling TMDs with inerters to control wind-induced vibrations in tall buildings, it is herein deemed important to discuss certain practical design considerations for TMDI-equipped tall buildings related to the attached mass relative displacement (TMDI stroke), the inerter force, and the required size and weight of ideal inerter device realizations for the application at hand.
• Evidently, the inclusion of the inerter device reduces dramatically the TMDI stroke (note the logarithmic scale of the y-axis in the considered plots), though the reduction rate reduces as the inertance value increases for the same attached mass.
• This consideration can be further facilitated by using more than one inerter devices in parallel such the total force demand F is split into several inerter devices, each one transferring a significantly smaller than F force to the connection with the primary structure.
• The input energy to be accommodated by the flywheel is computed as the product of the peak inerter force in Fig.4 times the peak relative displacement at the inerter terminals, which yields a conservative value as these two quantities do not peak simultaneously.

MEETING SERVICEABILITY CRITERIA IN NEW AND EXISTING TALL BUILDINGS

• Existing wind-excited tall buildings prescribed by typical building regulations.
• Focusing first on new tall buildings, suppose that it is sought to design a TMD(I)-based passive vibration control system to meet the serviceability design criteria in Fig.6 for the benchmark building in Fig.2 assuming Vref=35m/s and apartment occupancy.
• 22 Turning the attention to the use of inerters to enhance the structural performance of existing TMD- equipped tall buildings, suppose that the site-specific design wind velocity, Vref, increases from 35m/s to 42m/s during the lifetime of the same benchmark building.
• The required RF in terms of peak top floor acceleration to meet the users’ comfort criteria in Fig.6 reduces from 0.803 to 0.595 as indicated in Fig.7 by the horizontal red broken lines.
• For “-3” TMDI topology the users’ comfort criteria for Vref=42m/s can be met even with the small attached mass of μ=0.1% by incorporating an inerter with sufficiently large inertance (β>0.69%).

CONCLUDING REMARKS

• The advantages and effectiveness of coupling inerter devices with linear passive TMDs to suppress excessive wind-induced oscillations in tall buildings in the across-wind direction have been numerically established and discussed.
• It was found that the TMDI reduces the peak top floor acceleration (i.e., the critical demand parameter in meeting serviceability criteria for occupants’ comfort) beyond a same-weight TMD more effectively by considering: (I) smaller attached mass values, and (II) TMDI topologies in which the inerter spans more stories in linking the attached mass to the host structure.
• To further support the feasibility of the above practical applications of the TMDI, numerical evidence were provided to argue that the developing inerter forces are of reasonable amplitude and can be locally accommodated by properly detailed inerter-structure connections.
• Moreover, it was illustrated through energy-based calculations that, even though inerter devices are not commercially available for control vibration applications in large-scale civil engineering structures, such inerters are physically and technologically feasible to manufacture by scaling-up current small-scale devices tailored for automotive applications.
• It is emphasized that the herein reported numerical data are based on sub-optimal TMDI properties.

Figures

Fig. 4. Peak top floor displacement (upper panels) and acceleration (bottom panels) of TMDI equipped primary structure for different inertance ratio, β, and attached mass ratio, μ, values normalised by the corresponding peak values of the uncontrolled structure for TMDI topologies (a)“-1”, (b)“-2”, and (c)“-3”.

Table 1: Illustrative inerter flywheel sizing for three different TMDI cases examined in Fig.3.

Fig. 7. Peak top floor acceleration of TMDI-equipped primary structure for different inertance ratio, β, and attached mass ratio, μ, values normalised by the corresponding peak values of the uncontrolled structure for two different design Vref values and for TMDI topologies (a)“-1”and (b)“-3”.

Fig. 5. Peak TMDI attached mass displacement over peak TMD attached mass displacement (upper panels), and peak inerter resisting force (lower panels) for different values of inertance ratio β and attached mass ratio μ for TMDI topologies (a)“-1”, (b)“-2”, and (c)“-3”.

Fig. 2. (a) FE model of the benchmark 74-story building, (b) First three lateral translational mode shapes of the FE model and of the primary structure, (c) Absolute frequency response function of the top floor acceleration of the primary structure, and of four TMD(I)-equipped primary structures.

Fig. 6. Code-prescribed serviceability design thresholds and performance of the adopted primary structure for different Vref values.

Fig. 3. Considered across-wind force spectra at three different floor heights.

Fig. 1. Lumped-mass linear model of a wind excited n-storey frame building equipped with a tuned massdamper-inerter (TMDI): (a)“-1” topology; (b)“-2” topology; and (c)“-3” topology.

Full text

City, University of London Institutional Repository
Citation: Giaralis, A. and Petrini, F. (2017). Wind-induced vibration mitigation in tall
buildings using the tuned mass-damper-inerter (TMDI). Journal of Structural Engineering,
143(9), 04017127. doi: 10.1061/(ASCE)ST.1943-541X.0001863
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Permanent repository link: https://openaccess.city.ac.uk/id/eprint/17190/
Link to published version: http://dx.doi.org/10.1061/(ASCE)ST.1943-
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Journal of Structural Engineering, ASCE (2017)
1
*
Corresponding author
Wind-induced vibration mitigation in tall buildings using the tuned mass-
damper-inerter (TMDI)
Agathoklis Giaralis
1*
, Francesco Petrini
2
1
Department of Civil Engineering, City, University of London, London, UK
2
Department of Structural and Geotechnical Engineering, Sapienza University of Rome, Rome, ITALY
ABSTRACT
In this paper the classical linear tuned mass-damper (TMD) is coupled with an inerter, a two-terminal device
resisting the relative acceleration of its terminals, in various tuned mass-damper-inerter (TMDI) topologies
to suppress excessive wind-induced oscillations in tall buildings causing occupants’ discomfort. A
parametric numerical study is undertaken involving a top-floor-TMD-equipped planar frame capturing
accurately the in-plane dynamic behavior of a 74-storey benchmark building exposed to a quasi-stationary
spatially-correlated wind-force field accounting for vortex shedding effects in the across-wind direction. It is
found that the TMDI reduces the peak top floor acceleration more effectively than the TMD by considering
smaller attached mass values, and TMDI topologies in which the inerter spans more stories in linking the
attached mass to the host structure. Moreover, the inclusion of the inerter reduces dramatically the TMD
stroke while it was verified that the magnitude of the developing inerter forces can be readily accommodated
by the host structure. Pertinent illustrative examples are included showcasing that the TMDI meets code-
prescribed serviceability design requirements for new tall buildings using significantly smaller attached mass
compared to the TMD, and that inerter devices can be used to upgrade the performance of existing TMD-
equipped tall buildings without changing the attached mass.
Keywords: wind-excited tall building, tuned mass damper, inerter, passive vibration control, occupants
comfort

Journal of Structural Engineering, ASCE (2017)
2
INTRODUCTION
Wind-excited slender high-rise buildings with rectangular floor plan are prone to excessive
oscillations in the across-wind direction (i.e., within the normal plane to the wind direction) due to vortex
shedding effects generated around their edges (Liang et al. 2002). In fact, in many cases, vortex shedding
induces higher peak floor accelerations in slender/tall buildings in the across-wind direction than those
exhibited in the along-wind direction (Ciampoli and Petrini 2012; Bernardini et al. 2015). In such cases,
ensuring that the across-wind floor accelerations remain below a certain threshold associated with users’
comfort becomes the critical serviceability design requirement for slender buildings (Kwok et al. 2009).
In this context, over the past three decades, tuned mass-dampers (TMDs) have been widely used in
practice, among other devices and configurations for supplemental damping, for vibration mitigation in
wind-excited tall buildings to meet occupants’ comfort performance criteria prescribed by building codes
and guidelines (Kareem et al. 1999; Tse et al 2012). In its simplest form, the linear passive TMD comprises a
mass attached towards the top of the building (primary structure), via linear stiffeners, or hangers in case of
pendulum-like TMD implementations, and supplemental damping devices (dampers). The effectiveness of
the TMD relies on “tuning” its stiffness and damping properties for a given primary structure and attached
mass, such that significant kinetic energy is transferred from the vibrating primary structure to the TMD
mass and eventually dissipated through the dampers. Focusing on the suppression of lateral wind-induced
vibrations in (tall) buildings, the TMD is tuned to the first natural frequency of the primary structure aiming
to control the fundamental (translational) lateral mode shape (e.g. Rana and Soong 1998; Li et al. 1999).
It is well-recognized that the vibration suppression capabilities of the TMD depends heavily on its
inertial property: the larger the attached TMD mass is, the more effective and robust to uncertainties in the
structural properties the TMD becomes (e.g. De Angelis et al. 2012). However, practical structural and
architectural constraints apply to the weight and to the volume of the TMD mass that can be accommodated
by the primary structure. These constraints are particularly critical for tall buildings for which the attached
mass rarely exceeds 0.5% to 1% of the total building mass. In the meantime, in recent years, there is a
World-wide trend towards the design and construction of ever-more lighter, slender, and, therefore, more
susceptible to wind-induced vibrations tall buildings. This is partly due to the increase cost of land in

Journal of Structural Engineering, ASCE (2017)
3
congested urban environments and partly due to requirements for more aesthetically pleasing and sustainable
structures. Furthermore, the existing TMD-equipped tall buildings risk increase downtime (and consequent
financial losses) in the foreseeable future due to an anticipated increase of the frequency of strong wind
fronts caused by climate change effects.
To address the above issues and concerns in an innovative manner, this paper explores the potential of
incorporating inerter devices to wind-excited TMD-equipped tall buildings in different tuned mass-damper-
inerter (TMDI) configurations (topologies) to achieve enhanced vibration suppression in the across-wind
direction without increasing the attached TMD mass. Specifically, the considered TMDI topologies, a
special case of which was originally introduced in Marian and Giaralis (2013) for seismic protection of
multi-storey shear framed structures, benefit from the mass-amplification and from the higher-modes-
damping effects of the inerter. The latter is a two-terminal device of negligible mass/weight resisting relative
acceleration in analogy to the linear spring and dashpot resisting relative displacement and velocity,
respectively (Smith 2002). Marian and Giaralis (2014) showed analytically and numerically that the TMDI
can be more effective than the TMD for the same attached mass in reducing the deformation variance of
stochastically base-excited linear primary structures due to the contribution of the inerter to the inertial
property of the attached mass (mass-amplification effect). Furthermore, Giaralis and Taflanidis (2015)
demonstrated that the inclusion of the inerter influences and can potentially suppress higher modes of
vibration in linear multi-storey primary structures (higher-modes-damping effect), as opposed to the TMD
which can only control a single vibration mode. The latter effect is rather important for wind-induced
vibration control in tall buildings since higher vibration modes have a significant contribution to floor
acceleration response (i.e., the critical design criterion for tall buildings at the serviceability limit state), as
opposed to floor displacements. It is noted in passing that a similar higher-modes-damping effect in linear
dynamically excited multi-storey buildings were also reported by Lazar et al. (2014) for the case of the tuned
inerter-damper (TID), which is a special case of a TMDI with no attached mass. In fact, this effect was
accounted for by Krenk and Høgsberg (2016) to achieve a simplified analytical approach for the optimal TID
design targeting a single vibration mode in multi-storey buildings.
Herein, a parametric numerical study is undertaken to assess the effectiveness of different TMDI
topologies vis-a-vis the TMD for fixed attached mass in reducing peak top floor displacements and

Frequently asked questions

Q1. What are the future works in this paper?

In this regard, accounting for the influence of non-linear inerter behavior to the effectiveness of TMDIs for tall building wind vibration mitigation warrants further research which need to be supported by prototyping and characterization of large-scale inerters. To this end, it is envisioned that this study will not only further familiarize the civil/structural engineering community to the potential benefits of considering inerter devices for vibration control in TMD-equipped structures, but also justify the pursue of experimental research to develop inerters suitable for large-scale civil engineering structures. 

Q2. What are the contributions in this paper?

In this paper the classical linear tuned mass-damper ( TMD ) is coupled with an inerter, a two-terminal device resisting the relative acceleration of its terminals, in various tuned mass-damper-inerter ( TMDI ) topologies to suppress excessive wind-induced oscillations in tall buildings causing occupants ’ discomfort. A parametric numerical study is undertaken involving a top-floor-TMD-equipped planar frame capturing accurately the in-plane dynamic behavior of a 74-storey benchmark building exposed to a quasi-stationary spatially-correlated wind-force field accounting for vortex shedding effects in the across-wind direction. 

Q3. What is the energy approach used to determine the required flywheel radius?

an energy approach is used assuming no losses and linear device behaviour in which it is sought to determine the required flywheel radius given a pre-specified flywheel thickness and flywheel tangential velocity. 

Q4. What is the effect of the TMDI on the response acceleration of the structure?

the TMDI suppresses not only the portion of the structural vibration response corresponding to the fundamental mode shape, as the TMD strictly does, but all higher modes as well, which contribute significantly more to response acceleration than to response displacement. 

Q5. What is the effect of the cross-terms on the primary structure?

These cross-terms alter the dynamics of the primary structure such that higher modes of vibration are damped besides the fundamental mode shape. 

Q6. Why did the authors choose to consider such a large number of translational horizontal DOFs?

Note that the choice to consider such a large number of translational horizontal DOFs equally spacedalong the height of the building model was made to capture accurately the influence of the stiff outriggers to the local dynamics of the structure (see Fig.2b), and to facilitate a fine spatial discretization of the wind loading. 

Q7. What is the effect of the inerter on the amplitude of the stroke?

the TMDI topology does affect the amplitude of the stroke (but not the trends for increasing inertance): the more stories the inerter spans the higher the peak stroke is for the same TMDI properties. 

Q8. Why is the TMD important for tall buildings?

The latter effect is rather important for wind-induced vibration control in tall buildings since higher vibration modes have a significant contribution to floor acceleration response (i.e., the critical design criterion for tall buildings at the serviceability limit state), as opposed to floor displacements. 

Q9. What is the effect of vortex shedding on the building?

In fact, in many cases, vortex shedding induces higher peak floor accelerations in slender/tall buildings in the across-wind direction than those exhibited in the along-wind direction (Ciampoli and Petrini 2012; Bernardini et al. 2015). 

Q10. What is the significance of the higher-mode damping effect of the TMDI?

The significance of this higher-mode-damping effect of the TMDI is related to the position of the cross-terms in the matrix M: the further away they lie from the main diagonal, the more effective theTMDI becomes in damping the higher modes (see e.g. Fig.2(c)). 

Q11. What is the effect of the TMDI on the design of tall buildings?

More importantly from a practical viewpoint, it was numerically shown that: (i) the TMDI can meetcode-prescribed serviceability design requirements by considering significantly smaller attached mass24(depending on the TMDI topology and inertance coefficient) compared to the TMD, enabling more lightweight construction and efficient material usage in the design of new tall buildings, and (ii) inerter devices can be used to upgrade existing TMD-equipped tall buildings, without changing the attached mass, to meet more stringent serviceability design requirements than those considered in the initial design due to site-specific climate change effects or changes to the surrounding built environment (i.e., increased wind exposure). 

Q12. What is the value of the input energy to be accommodated by the flywheel?

The input energy to be accommodated (stored) by the flywheel is computed as the product of the peak inerter force in Fig.4 times the peak relative displacement at the inerter terminals, which yields a conservative value as these two quantities do not peak simultaneously. 

Q13. What is the reason why the TMDI is better suited to suppress floor accelerations than?

The fact that the herein considered non-optimal TMDIs are better suited to suppress flooraccelerations rather than floor displacements, compared to the TMD, is readily attributed to the highermode-damping effect of the TMDI. 

Q14. What is the effect of the inerter on the peak top floor displacement?

From the first row of plots in Fig. 4, it is seen that the inclusion of the inerter is beneficial in terms ofreducing the peak top floor displacement compared to the TMD, only for relatively small attached mass values. 

Q15. Why can't the TMD be used to control the vibration of a single building?

Giaralis and Taflanidis (2015) demonstrated that the inclusion of the inerter influences and can potentially suppress higher modes of vibration in linear multi-storey primary structures (higher-modes-damping effect), as opposed to the TMD which can only control a single vibration mode.