Viscous Damping Research Articles

Calibration of Equivalent Viscous Damping Expressions for Displacement-Based Design and Application to RC Frames

Equivalent viscous damping plays a central role in displacement-based design procedures. In this paper, approaches for estimating the equivalent viscous damping of RC frame buildings are proposed. At first, the analytical formulation of Blandon and Priestley was analysed, and then a calibration of the coefficients of this formulation was performed. Compared with the work of Blandon and Priestley, a larger set of synthetic accelerograms, related to different types of soil and different intensities, and a wider range of the effective periods were considered. In particular, two different sets of parameters are proposed: the first is usable in the case of spectra obtained numerically (approach 1), and the second is usable in the case of code-based spectra and damping modification factor (approach 2). To test the performed calibration and to compare the considered formulations (i.e., the proposed and literature equations), the direct displacement-based design procedure has been applied to three case studies of reinforced concrete frame structures, and then pushover and nonlinear time-history analyses have been performed. The results show that the use of the calibrated parameters (for both the considered approaches) has determined more conservative results, in terms of design base shear and maximum drift from NLTH. Moreover, the average displacement profiles and the inter-storey drifts obtained from time-history analyses for the frames designed with the calibrated parameters match better the design profile.

Seismic behavior of an improved drilled flange connection for I-beam to CFST column

The use of cold-formed steel tubes in the concrete-filled steel tubular (CFST) columns makes the design of the moment connections between beams and CFST columns much more challenging. This is because setting the internal diaphragms in the CFST column to transfer the bending moment of the beam end becomes impossible, and thus new joints are needed. A novel joint was proposed in a previous study by the authors, where two end plates were used for the force transmission between CFST columns and beam flanges. Moreover, to satisfy the “weak member strong joint” requirement, the I-beams were reduced by drilling a series of circular holes in their flanges. However, most of the tested specimens failed by the unexpected rupture of the complete joint penetration (CJP) groove welds between the beam flanges and end plates. In this paper, three specimens are redesigned and tested, where modifications are made to improve their behaviors under the seismic load. In this test, the local buckling of beam flanges at the drilled sections was observed in all specimens, and two specimens failed due to the fracture at the drilled sections, while CJP weld fracture and significant bending of beam flanges both occurred at the failure of the rest specimen. The hysteresis curves of all specimens are fusiform, indicating their good energy dissipations (the maximum equivalent viscous damping coefficients between 0.35 and 0.40). The failure rotation angles are about 2.44–3.01, and the ductility coefficients are between 2.26 and 2.66. According to EC3, all specimens can be classified into the rigid and full-strength joints. Subsequently, the parametric analyses using the validated finite element model are carried out, where the effects of main parameters are investigated on the seismic behavior of the presented joint. This study brings insights into the moment connections between the steel beam and CFST column with the outer cold-formed section.

Multi-Directional Viscous Damping Absorbing Boundary in Numerical Simulation of Elastic Wave Dynamic Response

Numerical seismic wave field simulation is essential for studying the dynamic responses in semi-infinite space, and the absorbing boundary setting is critical for simulation accuracy. This study addresses spherical waves incident from the free boundary by applying dynamic equations and Rayleigh damping. A new multi-directional viscous damping absorbing boundary (MVDB) method is proposed based on regional attenuation. An approximate formula for the damping value is established, which can achieve absorbing the boundary setting by only solving the mass damping coefficients without increasing the absorbing region grid cells or depending on the spatial and temporal walking distance. The validity and stability of the proposed method are proven through numerical calculations with seismic sources incident from different angles. Meanwhile, the key parameters affecting the absorption of the MVDB are analyzed, and the best implementation scheme is provided. In order to meet the requirements of mediums with different elastic parameters for boundary absorption and ensure the high efficiency of numerical calculations, the damping amplitude control coefficients k can be set between 1.02 and 1.12, the thickness of the absorbing region L is set to 2–3 times of the wavelength of the incident transverse wave, and the thickness of the single absorbing layer is set to the size of the discrete mesh of the model Δl.

Experimental verification of a translation model of linear transfer function of ultrasonic vibrations with nonlinear wave modulation for detection of contact-type failures

Contact-type failures, such as the crack closure at the tip of a fatigue crack, closed delamination of composite materials, and loosening of bolted joints, are difficult to detect through nondestructive inspections using linear ultrasonic waves or vibrations. When low-frequency vibrations, such as environmental disturbances, operating vibrations, and vibrations excited by actuators, are applied to a structure with contact-type failure, the contact condition of the failure surface fluctuates in synchronization with the low-frequency vibration. The amplitude and phase of ultrasonic waves or vibrations through contact-type failure with fluctuating contact conditions are modulated in synchronization with low-frequency vibrations, that is, realizing nonlinear wave modulation. Previous reports have presented evaluation and localization methods of contact-type failure using amplitude and phase demodulation signals. In this study, amplitude and phase demodulations were affected by the change in the viscous damping of a structure. Therefore, the essence of nonlinear wave modulation was considered to be the fluctuation of the natural frequencies. In this study, a visualization experiment of the fluctuation of natural frequencies caused by nonlinear wave modulation was conducted. The time-varying transfer function was reconstructed by measuring the amplitude and phase demodulation signals with the change in the excitation frequency. Moreover, the translation model of the transfer function of the ultrasonic vibration with nonlinear wave modulation was evaluated.

Development and verification of real‐time hybrid simulation with deep learning‐based nonlinear numerical substructure

AbstractReal‐time hybrid simulation (RTHS) provides an effective approach for assessing structural responses under dynamic excitation. However, performing RTHS with a complex nonlinear numerical substructure is challenging, as computations must be completed within predefined time steps. In this study, a RTHS framework which contains a rate‐dependent experimental substructure and a nonlinear numerical substructure has been proposed and verified. An OpenSees model was constructed to simulate a three‐story, one‐bay steel building with viscous dampers at each floor and was used to generate the training dataset through a large number of nonlinear time‐history analyses. A Recursive Long Short–Term Memory (LSTM) neural network model was trained to predict the nonlinear structural responses using ground acceleration and time‐delayed damper force located at the first story. Hence, the Recursive‐LSTM model served as a surrogate model for the numerical substructure, implicitly incorporating delay compensation for the experimental substructure. After the training was completed, offline testing was performed to realize the stability of the RTHS framework. Then, online RTHS with a virtual damper taken as the experimental substructure was conducted to further confirm the feasibility and accuracy. Afterwards, a nonlinear rotary fluid viscous damper (RFVD) was fabricated as the actual experimental substructure, whose dynamic response was not considered in training the Recursive‐LSTM model. Finally, RTHS with the RFVD was completed successfully and stably, demonstrating the capability of a well‐trained Recursive‐LSTM model to serve as a nonlinear numerical substructure incorporating constant delay compensation for RTHS. The potential of the proposed RTHS framework is worth further studies in the future.

Evaluation of viscous damper on the vibration transmission to the piping system and the support structure exposed to sinusoidal vibration in vertical, horizontal, and lateral directions.

Viscous dampers have been shown to be a potential solution to addressing piping vibration problems. The primary objective of this study is to confirm the ability of viscous dampers in addressing piping vibration problem in a piping system at different supporting structural stiffness. The piping systems were fabricated and arranged horizontally, vertically, and axially with respect to the direction of the input vibration force. Input force was applied to the piping system using an electromagnetic shaker. A sinusoidal vertical vibration at a 5 Hz frequency (21 mm/s RMS) was applied at one end of the piping system. The use of viscous damper was varied from no viscous damper to one, two and three dampers. Results showed that having three viscous dampers installed caused the piping vibration at point P2 showed the maximum reduction in vibration of up to 80% for three axes, respectively. For the case of structural vibration, the measurement results showed that point S1 experienced the highest vibration exposure before the installation of the viscous dampers, in all axes. With the three viscous dampers installed, the maximum vibration reduction for the sinusoidal vibration test case at point S1 were 86% and 91% for the x- and z-axes, respectively. In conclusion, viscous dampers able to reduce both the piping and structural vibration in multiple axes. This study also highlights the importance of positioning dampers in reducing piping vibration and vibration transmitted to the structure, with reduction up to 90% amplitude for sinusoidal input and 80% for random input.

How to model vibration damping in complex materials and structures

Damping is perhaps the most challenging aspect of any model where damping is relevant. For example, an accurate damping model is often important when modeling vibration of metamaterials, vehicles, and machinery. Mass density is easily and accurately calculated from simple measurements of weight and volume. Elastic moduli are easily and accurately calculated from simple measurements of stress and strain. Large databases of mass density and elastic moduli are readily available and accurate for most materials. But damping is elusive. Many models have been proposed in many different research communities. Published numerical values for the parameters are in short supply. But the choice of damping model may dramatically affect the predicted response. The damping model is likely to make the difference between a useful result and a useless result. This presentation seeks to collect and summarize knowledge related to damping to help us model damping more accurately and more efficiently. The three most common models of damping are reviewed. These are material damping, viscous damping, and Coulomb damping. For each, an analysis is presented that begins with the fundamental assumptions and ends with the inclusion of the damping mechanism in finite element models. [Work supported by ONR under Grant N00014-22-1-2785.]

English

English

Structures incorporating damping devices: Are we correct in our design thinking?

The use of discrete damping devices in New Zealand buildings is increasing as designers seek to limit damage to both architectural and structural building elements in moderate earthquakes. The overall damping of the structure becomes a combination of inherent material damping, hysteretic damping from yielding of building elements at specific locations and damping from discrete devices. For over 60 years, engineers have used simplified analysis procedures (e.g., modal response spectrum analysis) to predict building response under seismic actions. The design of structures incorporating viscous dampers requires a paradigm shift in approach as the force each damper resists is a function of the relative velocity between its ends. Popular pseudo-static design methodologies promote the use of a viscous strut in the analysis model to represent them. However, it is incorrect to use elastic, mode-based analysis for a structure incorporating damping devices and relying on significant inelastic behaviour. This paper elucidates the complex mechanics of damper-structure interaction by reviewing some of the established classical, modal‑based, simplified analysis techniques used in seismic design. A series of numerical investigations demonstrate how these techniques are usually invalid for structures that incorporate viscous dampers because they violate the laws of physics. The reason why mode-based techniques are invalid is explored with reference to the imaginary components of the natural modes of vibration and the effect on them of significant inelasticity within the structure. The dynamic characteristics of viscous dampers challenge conventional design approaches such as displacement-based design. This paper establishes that nonlinear time-history analysis is the only meaningful way of predicting the dynamic response of a structure incorporating viscous dampers when significant inelastic behaviour of the structure is expected.

Damping enhancement of nodal modes for stay cables using a single-sided pounding tuned mass damper (SS-PTMD)

Extra long stay cables, owned characteristics of light weight and low damping, may produce large-amplitude vibrations in modes with relatively high frequencies under a moderate wind speed. Installing a transverse fluid viscous damper near the cable anchorage to add maximum damping to the first few cable modes is a traditional method to improve the cable modal damping ratio. However, the installation location of the damper may be coincide with the nodal point of some high vibration modes, and diminishing the damping effect to a large extent. To tackle this nodal mode issue, a single-sided pounding tuned mass damper (SS-PTMD), which exhibits superior control performance over a conventional tuned mass damper (TMD), is adopted to enhance the damping ratio of nodal modes. The coupled equations of motion of a cable equipped with a SS-PTMD are established, and impact force between damper mass and the cable are considered by a impact force model. Free pounding tests are performed to study the pounding behavior with different viscoelastic (VE) material layers and various types of pounding strikers. Numerical simulations are carried out to investigate the damping enhancement and vibration mitigation effect of the SS-PTMD on the cable under various loading cases, including harmonic and simulated turbulent wind excitations. Field performance validations of the SS-PTMD is performed on a cable numbered A10 of the Dongting Lake Bridge. The results from free pounding tests show that the selection of the VE material layers and strikers can greatly affect the pounding behavior of the SS-PTMD. The Numerical simulation of the coupled cable-SS-PTMD system reveals that the SS-PTMD can effectively enhance the damping ratio of the target mode by a SS-PTMD with only 1.08% mass ratio. The numerical results show that SS-PTMD is effective in mitigating the high-oder nodal mode vibration of the cable. Field tests show that after the installation of SS-PTMD, the 2nd-mode modal damping ratio of the cable increases from 0.15% to 1.8%.

Analisis Perbandingan Fluid Viscous Damper dan Fixed Base Terhadap Beban Siklik dengan Finite Element

The geographical location of Indonesia, which is very at risk of earthquake disasters, requires the planning of building structures that are resistant to earthquake risks, one of which is by using base isolators. A base isolator system can improve structural performance by dissipating earthquake energy with its flexibility character to increase the vibration period. One type of base isolator is the Fluid Viscous Damper (FVD), which can be applied to high-rise buildings that often experience destruction during earthquakes. This research aims to determine the energy dissipation and ductility of fixed base structures and structures using FVD with finite element method using ABAQUS application. The object of analysis of this study uses a two-story portal with a steel structure. The results of this study obtained the characteristics of the two building models are semi-ductile, but there are differences in the ductility value between the two models. Based on the calculation results, the deviation ductility value that occurs in the fixed base building model is 2.624. Meanwhile, the deviation ductility of the FVD building model is 4.104. The use of FVD can increase the ductility value by 22%. The dissipation that can be done by the fixed base building model is 0.119, and the energy dissipation value for the building model with FVD is 0.156. Using FVD can increase energy dissipation in the analyzed model by 13.45%.

Seismic design and performance assessment of a retrofitted building with tuned viscous mass dampers (TVMD)

Vibration control technologies have been widely implemented for the seismic retrofitting of buildings in high seismic regions. Among various vibration control devices, the tuned viscous mass damper (TVMD) has proven effective in mitigating both lateral inter-story drifts and floor accelerations. This paper presents the seismic design and performance assessment of a retrofitted structure located in a highly seismic area. The existing masonry building is being retrofitted into a steel frame-jacketed masonry wall interacting structural system installed with TVMDs. A simplified iterative design process is proposed for the tuning design of TVMDs used in the retrofitted structure, which is based on the fixed-point method. The seismic responses of the buildings are calculated using non-linear dynamic analysis in OpenSees. Applying the FEMA P-58 approach, the seismic performance of the buildings as measured by the repair cost and repair time is evaluated. The findings reveal that the majority of the structural damage is focused within the masonry walls, coupling beams, and non-structural components. Use of TVMDs results in reduced maximum inter-story drifts that when subjected to very rare earthquake (VRE) shaking are up to approximately 40% lower in both transverse and longitudinal directions compared with the uncontrolled structure. Owing to the effective control of seismic damage to both structural and non-structural components, the TVMD-equipped structure achieves a 42% reduction in median repair cost and a 46% reduction in median repair time at VRE compared with the uncontrolled building. The seismic performance assessment results also illustrate the advantages of TVMD control compared with conventional viscous dampers.

Enhancing Seismic Resilience: Evaluating Buildings with Passive Energy Dissipation Strategies

Structures are recommended to be designed and constructed with the integration of structural health monitoring techniques to ensure that they can dissipate a large amount of energy without considerable damage when subjected to earthquakes. Hysteretic (H), friction (F), viscous (V), and viscoelastic (VE) dampers were employed in this study to observe the response of buildings using the commercially available software ETABS. The effect of different dampers along with configurations on three prototype concrete buildings (3, 5, and 10-storey) was studied by performing a time history analysis. Initially, the response of the buildings was observed in terms of storey drifts, base shear, and displacement without using dampers, while gradually increasing the damping ratio from 0 to 40%. Subsequently, the response of the buildings was evaluated in terms of displacements and base shear using various types of dampers with different configurations. The analysis results demonstrated that the effectiveness of viscous and viscoelastic dampers is higher for 3 and 5-storey buildings, while friction and hysteresis dampers are more suitable for 10-storey buildings. This information enables informed decisions regarding the performance and maintenance of dampers, contributing to the overall resilience and durability of structures in seismic events.

Parameter Identification of Space Manipulator's Flexible Joint

It is considered to use a manipulator mounted on a satellite in order to perform active debris removal missions. Space manipulator control system needs to take the dynamic model of the satellite-manipulator system into account because of the influence of the manipulator motion on the position and attitude of the satellite. Therefore, precise modelling of the space manipulator dynamics as well as parameter identification are needed in order to improve the credibility of the simulation tools. In this paper we presented the identification of the flexible-joint space manipulator model based on dynamic equations of motion. Experiments were performed in emulated microgravity environment using planar air bearings. The arbitrarily selected joint-space trajectory was performed by the manipulator’s control system. The experiments were repeated multiple times in order to analyze the identification method sensitivity. The identification is based on Simulink SimMechanics model. Thus, the procedure can be used for any space manipulator without the need of obtaining analytical relations for dynamic equations each time. Including joint flexibility and spring viscous damping in the dynamic model allowed to reflect the experimental measurements better than the reference model could. Identified parameters of the flexible joint have values of the same magnitude as corresponding real system parameters.

A Novel Enhanced Torsional Eddy Current Damper for Fixed-Axis Rotation Control of Rigid Bodies

The control of angular velocities in the fixed-axis rotation of rigid bodies is crucial for ensuring the safety and functionality of civil structures and mechanical systems. In this research, a novel enhanced torsional eddy current damper (ETECD) is proposed to effectively control the angular velocities of rigid bodies within confined installation spaces. At first, an estimation approach is developed to determine the damping coefficient of the eddy current damper (ECD) within limited installation space. Furthermore, we utilize a gearbox to enhance the damping performance of the ECD in confined spaces. To establish the framework for the design of the proposed ETECD, the motion equation and solution of the rotating body are derived. By analytically presenting the approximate solution for the responses of a rotating body with a torsional viscous damper, the required range of the torsional damping coefficient is derived. This range ensures compliance to velocity restrictions under linearly angle-related torques, guiding the design of the ETECD. The ETECD, comprising two cylindrical torsional eddy current dampers (ECDs) and a motion-amplified gearbox, is designed and tested for a rotating body. Numerical examples and experimental tests are carried out to validate the performance of the proposed ETECD. The calculated damping coefficients and predicted control performance in the numerical examples agree well with the experimental results. Notably, under the minimum and maximum torques, the terminal angular velocity (TAV) of the rotating body can be significantly reduced by 70.76% and 58.99%, respectively. The proposed work emphasizes the potential of the ETECD as an effective and economic method in reducing angular velocities for rotating bodies.

Impact of Sources of Damping On the Fragility Estimates of Wind Turbine Towers

Abstract Fragility estimates in wind turbine towers have been investigated but the the effect of damping on fragility has not been studied. While damping can often be small, it can come from different sources for a wind turbine. This paper demonstrates that even for small levels of equivalent viscous damping, a combination of sources can have a significant impact on the estimate of the fragility of a wind turbine in operational conditions. The widely studied 5MW reference wind turbine is considered for this study. The fragility analysis is performed considering the tower fore-aft displacement and acceleration responses. The impact of different sources of damping on fragility is estimated and ranked to qualitatively understand the impact of damping on the lifetime performance of the tower and develop approximate estimates of their quantitative changes.

Experimental investigation of a novel high performance multi-walled carbon nano-polyvinylpyrrolidone/silicon-based shear thickening fluid damper

A novel high performance multi-walled carbon nano-polyvinylpyrrolidone/silicon-based shear thickening fluid (MWCNTs-PVP/SiO2-STF), abbreviated and subsequently referred to as MPS-STF, is developed in this paper. The rheological properties of the MPS-STF are investigated, and the viscosity model of MPS-STF is established. Furthermore, the MPS-STF based viscous fluid damper (MPS-STF-VFD) is designed according to the rheological characteristics of the novel fluid. The impact of loading frequencies, displacement amplitudes and the numbers of piston holes on the dynamic performance of the damper is studied through sophisticated multiple cases loading tests using MTS facility. The test results show that the loading frequency, displacement amplitudes and the number of piston holes have great influence on the rheological properties of MPS-STF. This directly affects the maximum damping force and heat dissipation capacity of MPS-STF-VFD. Finally, the mechanical model of the damper is established based on the principle of fluid mechanics. The simulation results agree well with the experimental data. The high damping performance of the MPS-STF-VFD can be achieved based on the characteristics of the modified fluid. Relevant results reported in this paper can provide an important solution for the development and application of damping technology in engineering structures.

Investigation of the effect of curvature on the local mass flux of evaporating droplets using a phase field method

Droplet evaporation, a fundamental process with wide-ranging applications, involves complex physical mechanisms that significantly influence mass transfer rates and droplet lifetimes. Despite its significance, the influence of droplet deformation induced by capillary forces on local saturation conditions and its subsequent impact on phase change have received limited attention. This study delves into the impact of capillary-induced droplet deformation on local saturation conditions and its subsequent effect on phase change within a quiescent vapor environment. Contrary to most analytical and numerical studies that impose temperature and heat flux conditions at the vapor–liquid interface, our investigation employs direct numerical simulations based on the thermal Navier–Stokes–Korteweg model, capturing the dynamics of the droplet and its interface without relying on ad-hoc interface conditions. Our findings demonstrate that droplet deformation induces free oscillatory motion, which, although not significantly altering droplet lifetime due to viscous damping, leads to non-uniform mass fluxes along the droplet interface. We observe that areas of higher curvature are associated with increased local pressure and reduced temperatures, a discrepancy primarily attributed to evaporative cooling. This effect is further elucidated through an analysis of pressure and energy fluxes, revealing that regions of high curvature experience significant heat consumption, driving evaporative cooling and creating temperature gradients along the interface. Conversely, areas with negative curvature exhibit a reverse trend, indicating the complex interplay of capillarity, deformation, and phase change in droplet evaporation. Our results highlight the intricate relationship between droplet deformation, local pressure, mass flux, and temperature, underscoring the necessity for improved modeling of these factors in future studies on droplet evaporation dynamics.

Seismic design of reinforced concrete buildings equipped with viscous dampers using simplified performance-based approach

Passive control systems, such as Fluid Viscous Dampers (FVDs), have gained significant consideration in the design of earthquake-resistant structures. However, simple analysis and design methods are scarce for more practical and feasible implementation. This study provides a simplified procedure for performance-based seismic design of Reinforced Concrete (RC) special moment resisting frame using nonlinear FVDs. It adopts an extended performance-based design approach, focusing on maximum displacement along with floor acceleration to control the overall behavior of the structure. The fundamental principle of the method is to achieve the fully stressed (effect of FVDs on response indices) design approach to place dampers, which is attained by placing dampers among the storeys where drifts exceed the pre-decided performance limits. Further, a uniform damage distribution concept is followed to maximize the dampers' capacity. This study examines a rectangular-shaped RC SMRF with dampers to get the required performance when subjected to design basis and maximum considered earthquake levels. To check the efficacy, the proposed method is contrasted with a practical design method and a standard placement method employed in previous studies for RC structures with dampers. The analysis shows that the structure meets the performance targets of the design basis and the maximum considered level of earthquake hazards using the proposed step-by-step procedure. The comparison with the other two methods confirmed that the structure with dampers improved seismic behavior with the suggested process. Structural engineers can refer to the proposed method for the design of RC buildings with FVDs.

Experimental study on the seismic enhancement of brick masonry spandrels using a single-sided composite reinforced mortar coating

AbstractThe paper reports on four cyclic tests of brick masonry spandrels in reference state and strengthened state. The tests were carried out on full-scale, H-shaped masonry panels to investigate the coupling role of the spandrel in connecting two piers in a historical masonry wall subjected to in-plane lateral actions. Two 250-mm-thick solid-brick masonry samples were tested—one single-leaf, the other two-leaves masonry. Both samples were tested before and after strengthening by applying a Composite Reinforced Mortar (CRM) coating on one surface. The CRM coating consisted of a lime mortar coating (nominal thickness = 30 mm), reinforced with mesh made of Glass Fibre-Reinforced Polymer (GFRP) that was anchored to the wall by GFRP transverse connectors. For the double-leaf masonry, there were additional transverse connectors made of steel bars in concrete cores (artificial diatones) to prevent masonry leaves separation and to improve the bonding of the CRM coating to the masonry. The test responses are compared in terms of crack pattern, failure mode, resistance, displacement and energy dissipation capacity. The tests showed the effectiveness of the proposed CRM system, which increased the spandrel resistance by 33% and 125% in the single—and double-leaf masonry, respectively, with the ultimate drift being 3.2% (one order of magnitude greater than for the unstrengthened reference samples). Data on energy dissipation and the equivalent viscous damping are also collected and compared. Importantly, the presence of the reinforcing mesh and the composite action of the coating and the wall changed the damage evolution and response mechanism, which resulted in a much better seismic response.