RWDI Inc.

Guelph, Canada

RWDI Inc.

Guelph, Canada
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Love J.S.,RWDI Inc. | Tait M.J.,McMaster University
Engineering Structures | Year: 2017

Multiple dynamic vibration absorbers (MDVAs) employ multiple auxiliary masses tuned to frequencies near the structural frequency to reduce building motions. Added effective damping is often used to quantify the structural motion reduction attributed to the structural control system. However, the level of added effective damping by a MDVA system is difficult to verify in the field. This study presents a simple method to predict the effective damping that a nonlinear MDVA system adds to a linear structure. The generalized mass of the structure and auxiliary masses must be known, and their responses measured. The characteristic that the mean total power output of a structural system under wind loading is invariant when an MDVA is coupled to the structure is utilized to predict the added effective damping. The added effective damping is proportional to the covariance of the structural acceleration and relative velocity of the auxiliary mass. Nonlinear simulations of several traditional structure-DVA systems and structure-MDVA systems are used to evaluate the performance of the proposed prediction method. Both optimal and non-optimal systems are considered. Structure-tuned liquid damper system tests are used to evaluate the method experimentally. For the simulations and tests considered, the method predicts the added effective damping with acceptable accuracy. The proposed technique can be used to verify the performance of an installed MDVA system using field measurements. © 2016 Elsevier Ltd


Love J.S.,RWDI Inc. | Tait M.J.,McMaster University
Engineering Structures | Year: 2015

Linearized equivalent mechanical models are often used to conduct preliminary tuned liquid damper (TLD) design; however, they cannot capture nonlinear behavior resulting from the coupling among sloshing modes. Therefore, these models underestimate the expected peak wave height, a quantity that is necessary to evaluate the required tank freeboard. In this study, a method is presented to estimate the nonlinear peak wave height using an equivalent mechanical model.A linearized equivalent mechanical model of the structure-TLD system is employed to determine the RMS responses of the structural displacement and the TLD fundamental sloshing mode wave height. Davenport's derivation is used to estimate the probability density function of the peak structural displacement. Subsequently, the probability density function of the peak wave heights is derived using a Rayleigh-Stokes model, which employs an extended second order Stokes wave theory to estimate the nonlinear peak wave heights. Expressions are derived to calculate the mean-peak wave height as a function of the RMS response of the fundamental sloshing mode, and the fluid depth ratio.Structure-TLD system tests and nonlinear simulations are used to evaluate the model. Findings reveal that the Rayleigh model is in agreement with the experimental and simulated peak structural response distributions. In addition, the Rayleigh-Stokes model is in agreement with the experimental and particular simulated peak wave height distributions. Discrepancies are expected to arise when the fluid depth ratio is small, the excitation amplitude is large, and the damping screens are positioned to provide significant damping to the second sloshing mode. © 2015 Elsevier Ltd.


Xie J.,Zhejiang University | Garber J.,RWDI Inc.
Wind and Structures, An International Journal | Year: 2014

The high-frequency force-balance (HFFB) technique and its subsequent improvements are reviewed in this paper, including a discussion about nonlinear mode shape corrections, multi-force balance measurements, and using HFFB model to identify aeroelastic parameters. To apply the HFFB technique in engineering practice, various validation studies have been conducted. This paper presents the results from an analytical validation study for a simple building with nonlinear mode shapes, three experimental validation studies for more complicated buildings, and a field measurement comparison for a super-tall building in Hong Kong. The results of these validations confirm that the improved HFFB technique is generally adequate for engineering applications. Some technical limitations of HFFB are also discussed in this paper, especially for higher-order mode response that could be considerable for super tall buildings. © 2014 Techno-Press, Ltd.


Love J.S.,RWDI Inc. | Tait M.J.,McMaster University
Computers and Fluids | Year: 2013

Tuned liquid dampers (TLDs) utilize sloshing fluid to absorb and dissipate structural vibrational energy. A prerequisite to TLD design is establishing a suitable model to describe the fluid response. Numerous fluid models have been presented in literature; each utilizes simplifying assumptions which make the model valid under certain flow conditions. TLDs are often designed with fluid depth to tank length ratios less than 25%. At these depths, response characteristics change relatively rapidly with decreasing fluid depth, making it unlikely that one model is suitable over the entire range. The goal of this study is to determine when certain fluid models can be used.Three fluid models are considered: shallow water wave theory, a small depth multimodal model, and an intermediate depth multimodal model. The models are briefly presented and their basic assumptions are identified. A parametric shake table testing program is conducted which varies the fluid depth of a rectangular tank equipped with damping screens. Experimental time history and frequency response plots are created for comparison with each fluid model at several fluid depth ratios and excitation amplitudes. The range of validity for each model is described in terms of the fluid depth ratio, and the Ursell parameter. The results of this study will help TLD designers determine a suitable fluid model for dynamic analysis of a structure-TLD system. © 2013 Elsevier Ltd.


Love J.S.,RWDI Inc. | Tait M.J.,McMaster University
JVC/Journal of Vibration and Control | Year: 2015

Tuned liquid dampers (TLDs) employ sloshing fluid to reduce the resonant response of structures. Existing structure-TLD models are limited to rectangular or circular tanks, shapes that may not always be feasible in practice due to geometric restrictions of the building floor plan. This paper utilizes an equivalent linearized mechanical model and a nonlinear multimodal model to predict the response of the structure-TLD systems where the TLD tank geometry is irregular.Experimental structure-TLD system tests are conducted that consider two irregular tank shapes. Response history plots and frequency response plots of the structural displacement and TLD wave heights are created to evaluate the models using the experimental results. The parent distributions and 10-minute peak distributions of the structural displacements and TLD wave heights are created for the simulated and experimental results. These distributions indicate that both the linearized and nonlinear models can accurately predict the structural response; however, the linearized model substantially underestimates the peak wave heights. Since wave heights are required to establish the required tank free board, or roof impact pressures, it is concluded that nonlinear analysis of the structure-TLD system model is required before a TLD design is finalized. © The Author(s) 2013.


Love J.S.,RWDI Inc. | Tait M.J.,McMaster University
Journal of Sound and Vibration | Year: 2015

Dynamic vibration absorbers (DVAs) with nonlinear damping are often modelled using a power-law equivalent viscous damping relationship. There is currently not a method available to predict the peak response of this type of nonlinear DVA without resorting to computationally expensive nonlinear simulations. Since the peak response of the DVA is required during the design process, it is advantageous to have a simplified method to estimate the peak response. In this study, statistical linearization is employed to represent the nonlinear damping as amplitude-dependent viscous damping and predict the rms response of the structure-DVA system. Subsequently, statistical nonlinearization is used to describe the probability density function of the DVA response amplitude. A probability density function is developed, which enables the peak response expected during an interval of time (e.g. 1-h) to be estimated from the rms response of the structure-DVA system. Higher power-law damping exponents are shown to result in smaller peak factors. Results of nonlinear simulations reveal that the model can estimate the peak structural and DVA responses with acceptable accuracy. A plot is developed to show the peak factors for nonlinear DVAs as a function of the number of system cycles for several power-law damping exponents. This plot can be used to estimate the peak response of a nonlinear DVA as a function of its rms response. © 2015 Elsevier Ltd All rights reserved.


Love J.S.,RWDI Inc. | Tait M.J.,McMaster University
Journal of Fluids and Structures | Year: 2013

Tuned liquid dampers (TLDs) utilize sloshing fluid to absorb and dissipate structural vibrational energy. TLDs of irregular or complex tank geometry may be required in practice to avoid tank interference with fixed structural or mechanical components. The literature offers few analytical models to predict the response of this type of TLD, particularly when the fluid depth is small. In this paper, a multimodal model is developed utilizing a Boussinesq-type modal theory which is valid for small TLD fluid depths. The Bateman-Luke variational principle is employed to develop a system of coupled nonlinear ordinary differential equations which describe the fluid response when the tank is subjected to base excitation. Energy dissipation is incorporated into the model from the inclusion of damping screens. The fluid model is used to describe the response of a 2D structure-TLD system when the structure is subjected to external loading and the TLD tank geometry is irregular.Shake table experiments are conducted on a rectangular and chamfered tank subjected to unidirectional base excitation. Comparisons of the experimental and predicted sloshing forces and energy dissipation per cycle indicate that the model is able to predict the fluid response at fluid depth ratios greater than h/. L=0.10. Next, structure-TLD system tests are conducted and it is found that the model can predict the structural and TLD responses. The simulated and experimental results show that the TLD tank transfers energy between orthogonal structural sway modes. © 2013 Elsevier Ltd.


Hamelin J.A.,University of Toronto | Love J.S.,RWDI Inc. | Tait M.J.,McMaster University | Wilson J.C.,McMaster University
Journal of Fluids and Structures | Year: 2013

The amplitude-dependent damping associated with a tuned liquid damper (TLD) equipped with slat-type screens produces a device that performs optimally at a targeted response amplitude. Increasing the slat height produces a screen whose drag coefficient is dependent on the Keulegan-Carpenter number (KC), which may improve the TLD performance. This new type of TLD is modeled as an equivalent mechanical model with damping that is dependent on both KC and the response amplitude. An experimental shake table testing program is undertaken to study the influence of KC on the TLD response and to validate the model. A power fit is performed on the experimentally determined screen drag coefficient and KC values to express the drag coefficient as a function of KC and the steady flow drag coefficient. Predicted frequency response plots of sloshing forces and energy dissipation per cycle are in agreement with experimental results. A structure-TLD system model is developed to theoretically study the performance of this new TLD. Nonlinear shallow water wave theory is used to validate the output of the mechanical model. Results indicate that a KC-dependent screen drag coefficient produces a more robust TLD whose performance is maintained over a broader range of structural response amplitudes. © 2013 Elsevier Ltd.


Love J.S.,RWDI Inc. | Tait M.J.,McMaster University
Structural Control and Health Monitoring | Year: 2014

Tuned liquid dampers (TLDs) control the wind-induced vibrations of tall buildings using sloshing fluid. TLD tanks of complex geometry may be required in practice due to space limitations; however, their behaviour has not been considered in the literature. This study develops and experimentally validates a model to describe the structure-TLD interaction of a 2D system when the TLD tank geometry is complex. The equations of motion of the structure-TLD system are developed using Lagrange's equation. In general, the 2D structure-TLD interaction must be represented as a coupled four degree of freedom system. The model is validated using new structure-TLD system tests where the structure is subjected to 1D and 2D harmonic and random excitation. Two TLD tanks of complex geometry are considered; the first tank is anti-symmetric about both axes, whereas the second tank is symmetric about both axes. For the anti-symmetric tank, energy transfer between orthogonal structural sway modes and sloshing modes is significant; however, for the symmetric tank, this energy transfer is negligible. Experimental results indicate that the model adequately predicts the structural response; however, the nonlinear behaviour of the fluid response cannot be captured by the linearized model. © 2013 John Wiley & Sons, Ltd.


Love J.S.,RWDI Inc. | Tait M.J.,McMaster University
Journal of Vibration and Acoustics, Transactions of the ASME | Year: 2013

Tuned liquid dampers (TLDs) utilize sloshing fluid to absorb and dissipate structural vibrational energy, thereby reducing wind induced dynamic motion. By selecting the appropriate tank length, width, and fluid depth, a rectangular TLD can control two structural sway modes simultaneously if the TLD tank is aligned with the principal axes of the structure. This study considers the influence of the TLD tank orientation on the behavior of a 2D structure-TLD system. The sloshing fluid is represented using a linearized equivalent mechanical model. The mechanical model is coupled to a 2D structure at an angle with respect to the principal axes of the structure. Equations of motion for the system are developed using Lagrange's equation. If the TLD and structure are not aligned, the system responds as a coupled four degree of freedom system. The proposed model is validated by conducting structure-TLD system tests. The predicted and experimental structural displacements and fluid response are in agreement. An approximate method is developed to provide an initial estimate of the structural response based on an effective mass ratio. The results of this study show that for small TLD orientation angles, the performance of the TLD is insensitive to TLD orientation. © 2013 American Society of Mechanical Engineers.

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