Damping Of Pedestrian‐Induced Bridge Vibrations By Tuned Liquid Column Dampers

Reiterer, Michael; Hochrainer, Markus J.

doi:10.1002/pamm.200410036

Cited by 5 publications

(6 citation statements)

References 2 publications

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“…A variant of this ALC formulation is to adopt a nested approach similar to Probs. (15) and (16). The outer loop of the ALC subproblem would solve for x p (j) and y (j) , whereas x c (j) would be obtained in an inner optimization loop.…”

Section: B Distributed Mdo Formulationsmentioning

confidence: 99%

“…The plant constraints, at least those that depend on state trajectories, should be included in both the inner and outer loops (Eqns. (15)(16)), but simplified plant design obscures this requirement. Fathy et al presented the nested co-design formulation sans g p (·) where the inner loop is solved using LQR (for linear systems).…”

Section: A Balanced Co-designmentioning

confidence: 99%

“…These vibrations required pedestrians to walk with a synchronized teetering motion to maintain stability, amplifying lateral vibrations and rendering the bridge unusable. [12][13][14][15][16][17] While designing the bridge, engineers accounted for the effect of pedestrians walking on the bridge, but did not account for the effect of bridge motion on pedestrians. Limited redesign [18][19][20][21] was performed to attenuate lateral vibrations using active control, but more comprehensive integrated modeling and design processes early on may have prevented the need for expensive redesign.…”

Section: Introductionmentioning

confidence: 99%

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Multidisciplinary Design Optimization of Dynamic Engineering Systems

Allison

Herber

2013

54th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference

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Dynamic engineering systems are playing an increasingly important role in society, especially as active and autonomous dynamic systems become more mature and prevalent across a variety of domains. Successful design of complex dynamic systems requires multidisciplinary analysis and design techniques. While multidisciplinary design optimization (MDO) has been used successfully for the development of many dynamic systems, the established MDO formulations were developed around fundamentally static system models. We still lack general MDO approaches that address the specific needs of dynamic system design. In this article we review the use of MDO for dynamic system design, identify associated challenges, discuss related efforts such as optimal control, and present a vision for fully integrated design approaches. Finally, we lay out a set of exciting new directions that provide an opportunity for fundamental work in MDO. Nomenclature a(·)= analysis function a, b = example problem parameters α, β = energy domain designations A = state matrix for a linear and time invariant system B = input matrix for a linear and time invariant system c = suspension damping coefficient ε = convergence tolerance f (·)= design objective function f (·)= derivative function f a (·) = algebraic constraint g(·)= design constraint functions g p (·) = physical system constraints γ(t) = algebraic variable vector h i = time step i = time step index j = Gauss-Seidel block index, multiple-shooting time segment index k = iteration counter k s = suspension spring stiffness K = gain matrix K * = optimal gain matrix L(·) = Lagrange or running cost term m = number of Gauss-Seidel coordinate blocks n s = number of states n t = number of time steps n T = number of time segments φ(·) = cost function φ * (·) = optimal-value function (inner loop solution) φ(·) = alternative plant design objective function ψ(·) = Mayer or terminal cost term π(·) = augmented Lagrangian penalty function t = time t F = length of the time horizon t i = time at step i T j = time at the end of time segment j u(t) = control input trajectories u * (t) = optimal control trajectories u i = control input at time step i U = matrix discretization of u(t) x = optimization variable vector x * = optimal solution x k = solution estimate at iteration k x c = control system design variable vector x p = physical system design variable vector x p * = optimal plant design X = Cartesian product of closed convex sets ξ(t) = state variable trajectories ξ * (t) = optimal state trajectories ξ i = state at time step î ξ(t) = subset of state trajectorieṡ ξ(·) = time derivative of ξ(t) Ξ = discretization of ξ(t) Ξ = subset of discretized state trajectories y = coupling variable Y = matrix of initial state values for multiple shooting time segments ζ(·) = defect constraint functions (residuals) ζ i (·) = defect constraint between time segments

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Section: B Distributed Mdo Formulationsmentioning

confidence: 99%

Section: A Balanced Co-designmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Multidisciplinary Design Optimization of Dynamic Engineering Systems

Allison

Herber

2013

54th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference

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“…The distance of C M with respect to C S is given by c and d, respectively. Further details of the mathematical model are given in the paper of Reiterer and Ziegler [4]. All numerical simulations are performed according to the laboratory model, where the attached TLCD is tuned to the fundamental frequency of the bridge whose corresponding mode has a dominant horizontal response, similar to Londons Millenium Bridge.…”

Section: Mathematical Modelmentioning

confidence: 99%

Damping Of Pedestrian‐Induced Bridge Vibrations By Tuned Liquid Column Dampers

Reiterer

Hochrainer²

2004

Proc Appl Math and Mech

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The excessive lateral vibrations of Londons Millenium Bridge and the Toda Park Bridge in Japan due to a large number of crossing pedestrians have raised an unexpected problem in footbridge constructions. Secondary tuned structures, like the conventional tuned mass damper (TMD) or the tuned liquid damper (TLD) were installed to the bridge in order to suppress these vibrations. In the present investigation it is proposed to apply the more efficient and more economic tuned liquid column damper (TLCD), which relies on the motion of a liquid mass in a sealed tube to counteract the external motion, while a built-in orifice plate induces turbulent damping forces that dissipate kinetic energy. For optimal tuning of TLCDs the natural frequency and equivalent linear damping coefficient have to be chosen suitable, likewise to the conventional TMDs, as given in Den Hartog [1]. The advantages of TLCDs are: simple tuning of natural frequency and damping, low cost of design and maintenance and a simple construction. A mathematical model of a three degree-of-freedom (DOF) bridge coupled with an optimal tuned TLCD is derived and analyzed numerically. Furthermore, a small scale experimental model set-up has been constructed in the laboratory of the TU-Insitute. The experimental results are in good agreement with the theoretical predictions and indicate that TLCDs are effective damping devices for the undesired pedestrian induced footbridge vibrations. Mathematical ModelThe equations of motion for the complex hybrid bridge/TLCD system are derived by a substructure synthesis method, which splits the problem into two parts. Thus, the TLCD is separated from the bridge and considered under combined horizontal v t , vertical w t and rotational ϕ t excitations. Applying the modified Bernoulli equation along the relative non-stationary streamline in the moving frame and in an instant configuration, which is given in Ziegler [2, p. 497], yields the nonlinear, parametric excited equation of motion of the TLCD,where a A,x =ẅ t cos ϕ t −v t sin ϕ t and a A,z =ẅ t sin ϕ t +v t cos ϕ t denote the horizontal and vertical acceleration of the reference point A projected to the moving reference frame. Ω =φ t andΩ =φ t define the angular velocity and angular acceleration. The undamped circular frequency of the TLCD in case of an open pipe system is given by ω A = 2 g sin β/L ef f , where g is the gravity constant, β is the opening angle of the inclined pipe section and L ef f = 2H + B in case of constant cross sections. Furthermore, in Eq.(1) the geometry dependent factors are given by, κ = (B + 2H cos β)/L ef f , κ 1 = 2H sin β/L ef f and κ 2 = (B cos β + 2H)/L ef f , where B and H are the horizontal length of the liquid column and the length of the liquid column in the inclined pipe section at rest. The head loss coefficient δ L due to turbulent losses along the relative non-stationary streamline can be controlled by the opening angle of the built in orifice plate. Eq.(1) is nonlinear due to turbulent damping of the fluid motion, which is consider...

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“…One of the earlier applications to enhance footbridges behavior and mitigate vibrations induced by pedestrians is the tuned liquid column damper. The efficiency tunned liquid column damper has been proved numerically and experimentally [4]. The other damper used in such cases is the tuned mass damper which is a passive damper.…”

Section: Introductionmentioning

confidence: 99%

Viscoelastic damper for vibration mitigation of footbridges

Alhasa,

Vafaei,

Ali

et al. 2023

IOP Conf. Ser.: Earth Environ. Sci.

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Footbridges are among long-span light-weight structures that because of their low damping ratio are susceptible to vibration. Excessive vibration in footbridges usually occurs when they are subjected to rhythmic dynamic loads caused by human activities like walking and running. In order to mitigate the human induced vibrations in footbridges, an increase in the damping ratio is often suggested as the most economical approach. Tuned mass dampers have been widely used for this purpose, however, their installation and maintenance costs are high. This has encouraged researchers to examine the efficiency of the other types of dampers. Viscoelastic dampers have been successfully employed for vibration mitigation of structures against wind and earthquake loads. However, their efficiency for reducing human induced vibration in footbridges has not been addressed. In this study, a real footbridge with a free span of 22.5 m and a width of 2.3 m was selected for numerical investigations. SAP2000 program was used to establish the finite element (FE) model of the footbridge. The established FE model was validated by comparing its natural frequencies with those measured on the field. FE model results indicated that the acceleration response of the footbridge exceeded the code specified limit. Therefore, a viscoelastic damper was designed and installed under the footbridge in order to reduce the acceleration response below the allowable level. Installation of the viscoelastic damper significantly decreased the vibrations. It was concluded that viscoelastic dampers were an economical and efficient solution for vibration problems in footbridges.

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Damping Of Pedestrian‐Induced Bridge Vibrations By Tuned Liquid Column Dampers

Cited by 5 publications

References 2 publications

Multidisciplinary Design Optimization of Dynamic Engineering Systems

Multidisciplinary Design Optimization of Dynamic Engineering Systems

Damping Of Pedestrian‐Induced Bridge Vibrations By Tuned Liquid Column Dampers

Viscoelastic damper for vibration mitigation of footbridges

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