Viscous Damping Research Articles

ON THE USE OF THE GENERAL BANDWIDTH METHOD TO IDENTIFY DAMPING IN MDOF SYSTEMS

The general bandwidth (GeB) method is one of the methods used for viscous damping identification of structures. In this method, approximate and exact formulas have been studied to estimate the damping ratio from frequency response function (FRF) of the single degree-of-freedom (SDOF) system. However, the applicability of these formulas to estimate the damping in multi degree-of-freedom (MDOF) systems has not been analyzed in detail. This article studies the influence of modal parameters on the accuracy of the GeB method used to identify the viscous damping ratios in MDOF systems. The results compared with the formulas based on the half-power bandwidth (HPB) method show that the GeB method has good efficiency and wide identification range.

Strengthening of reinforced concrete beam-column joints by means of fastened C-FRP ropes

The efficiency of using C-FRP ropes as external superficial reinforcement to strengthen beam-column connections in reinforced concrete structures with regard to seismic requirements is investigated experimentally. The method is an easy-to-apply, effective method for locally increasing the load-bearing capacity of beam-column connections in existing buildings. To strengthen the beam, external C-FRP ropes are placed in slots along each side of the beam at the top and bottom. The test results with test specimens on a scale of 1:1 in undamaged condition (JA0) and in strengthened condition after pre-damage (JA0b) are analysed and compared. From the comparative representation of the hysteresis reactions, it is concluded that the strengthened test specimens show an improved hysteresis reaction in all cases examined compared to the corresponding test specimens without strengthening. Comparisons of the damage index values and the equivalent viscous damping values obtained from the test results are also presented and commented on in order to enable objective and well-founded conclusions to be drawn. It can be concluded that the use of C-FRP ropes as external reinforcement is suitable as an efficient and easy-to-handle strengthening technique in all cases investigated.

Self-centering dual rocking core system with viscous dampers in additional rocking sections

To mitigate the high mode effects and reduce the force requirements of the structural members in the multi-story self-centering dual rocking core (SDRC) system, this paper proposes the multiple self-centering dual rocking core system with viscous dampers in additional rocking sections (MSDRCV system). The sketch and ideal working mechanisms of the MSDRCV system are interpreted. The additional rocking sections are set to decrease the force requirements of structural members and viscous dampers are included to mitigate high mode responses of the additional rocking sections, introducing seismic performance enhancement. Comparative analyses on a 9-story MSDRCV system with viscous dampers in rocking sections, a 9-story multiple self-centering dual rocking core system without viscous dampers in rocking sections (MSDRC system) and a 9-story SDRC system were carried out. The MSDRCV and MSDRC system can realize the reduction of the force demands in structural members in contrast to the SDRC system. Nevertheless, the high mode responses caused the uncontrollable displacement concentration in the MSDRC system and hence aggravated the seismic performance under rare seismic events. The analysis results in the frequency domain confirmed that the viscous dampers in the MSDRCV system can efficiently control the high-mode responses. The effects of the design parameters of the viscous dampers on the peak responses of the MSDRCV systems were comprehensively studied via parametric analyses. The results offer guidance for the viscous dampers design.

A novel slit damper configuration to enhance ductility and seismic behavior of concentrically braced frames

Steel slit dampers are the specific type of metallic yielding dampers used for the structural passive control. They are constructed by introducing a series of openings or slits in a steel plate to control the seismic behavior of structures. These dampers absorb energy through shear yielding, flexural yielding, or a combination of both. In this paper, a new form of steel slit damper is introduced and examined. The novel damper, called the Zipper-shaped Slit Damper (ZSD), is composed of two nested boxes connected through high-strength bolts. There are several steel strips in an external box and L-shaped profiles to prevent out-of-plane buckling, maximize flexural capacity, and ensure optimal lateral force distribution. Additionally, L-shaped profiles are welded to the ends of the steel strips. To assess the structural capacity and seismic behavior, ZSD is modeled in three dimensions using ABAQUS finite element software. The model is first validated against experimental results and then subjected to cyclic nonlinear static analysis, comprising 15 models with different width-to-thickness and height-to-width ratios of steel strips. The failure index (FI), based on equivalent plastic strain, is employed to predict the moment of failure. The results obtained from the FI were analyzed, and the analysis was limited until the moment of the first failure. On average, the novel damper demonstrated improved durability with an increase in the height-to-width ratio, resulting in enhanced ductility up to 8.75. Additionally, within each width -to-thickness ratio group, a 0.5 unit increase in this ratio corresponded to a reduction of approximately 10 % in energy dissipation efficiency. The equivalent viscous damping in the models averaged 42 %. The analysis indicated that all models exhibited stable hysteresis cycles and had high ductility and energy dissipation. Also, considering the obtained results, it can be concluded that the ZSD, due to its replaceable components, ease of construction, and easy installation, can be utilized in concentrically braced frames. Mechanical models, as well as stiffness and force relationships for design and implementation in braced frames, are presented. The findings provide valuable insights for the utilization of this innovative damper in seismic-resistant structural systems.

The Seismic Response Evaluation of an Existing Multi-span Reinforced Concrete Highway Bridge in the Presence of Linear and Nonlinear Viscous Dampers

AbstractIt’s crucial to keep bridges safe and operational all the time. Before or after an earthquake, they may require immediate seismic retrofitting. In this situation, adopting both isolation systems and viscous dampers could be used as a solution. Therefore, the seismic performance of a RC bridge with linear and nonlinear viscous dampers at both pier tops and abutments is investigated. The selected bridge model is the Incesu Bridge in Artvin province in north–eastern Turkiye. In the bridge model, elastomer bearings (EBs) and viscous dampers (VDs) are added to the abutments and the tops of the piers (i.e., the bridge deck connection points). The results revealed that the maximum bending moment of two piers could be significantly reduced compared with the case where the pier’s tops are fixed to its deck. However, a large level of a viscous damper coefficient added to a bridge could cause structural damage to its deck under a strong design earthquake.

Simplified design of nonlinear damper parameters and seismic responses for long-span cable-stayed bridges with nonlinear viscous dampers

Simplified design of nonlinear damper parameters and seismic responses for long-span cable-stayed bridges with nonlinear viscous dampers

Improving the Step Response of Flexible Systems in the Presence of Real Nonminimum Phase Zeros

Abstract It is well known that real nonminimum phase (RNMP) zeros impose a tradeoff between the settling time and undershoot in the step response of flexible systems. Existing methods to alleviate this tradeoff predominantly rely on various advanced control strategies without delving into a broader mechatronic approach that combines physical system and control system design. To address this gap, this article proposes a proportional viscous damping-based physical system design in combination with feedback control and prefilter design. First, the effect of proportional viscous damping on RNMP zeros of flexible systems is established to propose a damping strategy that pushes all the RNMP zeros further away from the imaginary axis. Then, a step-by-step mechatronic system design process is presented to apply this damping strategy along with a full-state feedback control strategy and prefilter to a multi-degree-of-freedom (DoF) flexible system. The application of this design process yields simultaneous improvement in the settling time and undershoot in the step response of this flexible system.

Visco-Hyperelastic Constitutive Modeling for High-Damping Rubber Materials During Combined Quasi-Static Compression–Cyclic Shear Deformation Process

High-damping rubber materials utilized in high-damping rubber isolation bearings are frequently subjected to multiple deformations during the occurrence of earthquakes. Typically, large combined compression–shear deformations of the material could potentially cause compressive shear damage to rubber bearings. During this process, visco-hyperelastic properties of rubber materials will greatly change, which would significantly impact the seismic performance of rubber bearings. Thus, to give out a deep insight into their variations, it is necessary and urgent to develop a high-performance numerical method to investigate this process. This paper proposed a visco-hyperelastic constitutive modeling approach for high-damping rubber materials based on the experimental assessment of combined quasi-static compression–cyclic shear deformation process. Within the thermodynamic framework, the Clausius–Duhem inequality associated with the intrinsic dissipation of the material was firstly derived in accordance with the Lagrangian formulism. Then, stress–strain relations were obtained upon considering the occurrence of entropy production due to viscous dissipation. In the model, Stumpf–Marczak strain energy density function, which satisfies the Baker–Ericksen (B–E) inequality, was harnessed to describe the hyperelasticity of the material. By introducing higher orders of strain and strain rates and taking their couplings into account, a generalized viscous dissipation potential was proposed to capture nonlinear strain and strain rate-sensitivity effects of the material. To identify constitutive parameters, the deformation gradient was particularized for the combined quasi-static compression–cyclic shear deformation process. And, an inverse identification procedure was carried out at different levels of compression stress. The prediction results revealed that the proposed model exhibits remarkable prediction ability and adaptivity for different rubber materials during this process. Several new insights were highlighted on the variations of visco-hyperelastic characteristics of high-damping rubber materials with respect to the compression stress. The accuracy of the model was further validated by design parameters including initial shear modulus, secant shear modulus and equivalent viscous damping factor. This work could provide a fundamental guideline for the optimization and reliability analysis of high-damping rubber isolation bearings used in the field of seismic engineering.

Damage-aware structural control based on reinforcement learning

This contribution presents a semi-active control technique intended for mitigation of structural vibrations. The control law is derived in a repeated trial-and-error interaction between the control agent and a simulated environment. The experience-based training approach is used which is the defining feature of the machine learning techniques of reinforcement learning (RL). In particular, a specific modification of the Deep Q Learning (DQN) approach is applied. The involved artificial neural network not only approximates the expected reward of the control (which defines the control action and quantifies its performance), but additionally keeps track of structural damages. This requires a specific architecture, which allows the network to be damage-aware, and a specific training procedure, where the memory pool preserved for the RL stage of experience replay is populated with not only the observations, control actions, and rewards, but also with the momentary status of structural damage. Such an approach explicitly promotes the damage-awareness of the control agent. The proposed technique is tested and verified in a numerical example of a shear-type building model subjected to a seismic excitation. A tuned mass damper (TMD) with a controllable level of viscous damping is used to implement the semi-active actuation, and the optimally tuned classical TMD provides the reference response.

SINGLE-DEGREE-OF-FREEDOM VIBRATION ISOLATION SYSTEM WITH ONE ADDITIONAL SUPPORT

Vibration isolation is one of the most effective methods for reducing vibration levels of supporting structures when installing vibroactive equipment (active vibration isolation) or vibration levels of vibro-sensitive objects relative to foundation vibration levels (passive vibration isolation). Damping devices utilizing high-speed fluid flow through apertures have found wide applications in shock vibration isolation and vibration isolation systems in aerospace and defense sectors. Recent research has led to the development of viscous fluid dampers (VFDs) for use in civil engineering, particularly in earthquake-prone areas. Scientists conducted experiments aimed at determining the ability of viscous fluid dampers to reduce damages and displacements of structures without increasing stresses. Mathematical models have been developed and are applied in vibration isolation systems. When vibroactive equipment is installed on building and structure support systems, vibrations with sufficiently high vibration parameters may occur, potentially leading to loss of load-bearing capacity. In such cases, vibration isolation is considered one of the most effective methods for reducing these vibration levels. In this study, a calculation method has been developed, and calculation dependencies and algorithms for calculating vibration protection systems with nonlinear characteristics (additional support connections, viscous fluid damper) have been derived for both single-degree-of-freedom and two-degree-of-freedom systems. The research involved an analysis of normative and scientific-technical literature on the subject: types, structural solutions, calculation, and analysis of vibration protection systems. The main method selected was based on the use of transfer functions of linear systems (the non-traditional "normal form" method). Calculations were performed using computer mathematics systems- Matlab.

Global existence and exponential decay for a swelling porous-heat system subject to a distributed delay

In this article, we consider a swelling porous-heat system with viscous damping and distributed delay term. It’s well-known in the literature that the thermal effect only lacks exponential stability. For that, we need to add another damping mechanism to stabilize exponentially the system. However, we prove, based on the energy method, that the combination of viscous damping and thermal effect provokes an exponential stability in the presence of distributed delay irrespective of the wave speeds of the system.

Testing novel hybrid inter-module joints for steel modular buildings under cyclic load

To bridge the gap between the unrealised disassembly and reuse potential of volumetric modular buildings and the lack for seismic resilience, a hybrid inter-module connection employing a high-damping rubber bearing was proposed to reduce the inelastic deformation in the members of the volumetric module. The cyclic behaviour of the proposed connection was previously investigated at connection level through validated proof-of-concept FEA, reflecting promising damping and re-centring capabilities. In this study, six in-plane cyclic loading tests on inter-module joints with the novel, hybrid inter-module connection were carried out to investigate the connection’s influence on the cyclic behaviour of steel modular buildings under lateral load at joint level. The tests focused on the contribution of the laminated elastomeric bearing to the joint’s lateral behaviour and the effect of different bolting assemblies on the working mechanism of the hybrid connection system. The standard FEMA/SAC loading sequence was employed on single-span, meso-scale joint prototypes with axial and in-plane lateral loading applied to the top post. The results showed that the hybrid IMJs exhibited nonlinear, multi-stage hysteretic responses, governed by the bending resistance of the bolting assembly and the stiffness of the intra-module connection. The aseismic performance of the joints was characterised by residual drifts below the permissible limit of 0.5 % up to 2 % drift ratio and high equivalent viscous damping during the low-amplitude cycles. Overall, the tests demonstrated the feasibility of the proposed connection with respect to the mitigation of damage in the structural elements of the volumetric modules after an earthquake, as proved by the low inelastic deformation recorded up to 4 % drift ratios.

Experimental Study on Seismic Performance of Composite Shear Wall with Horizontal Connection and Frame

Prefabricated concrete shear-wall structures are a primary form of prefabricated concrete construction. In this paper, the seismic performance of precast shear walls with frames is studied by experimental methods. The failure characteristics, hysteretic performance, energy dissipation capacity, stiffness degradation, and ductility of the shear wall are mainly analyzed. The results indicate that incorporating various frames into concrete shear walls can significantly enhance the traditional single seismic defense line. The maximum differences between the positive and negative initial stiffnesses of the framed shear wall are 32.6% and 29.7%, respectively. The maximum differences between the positive and negative ductility coefficients compared to the ordinary reinforced concrete shear wall are 15.7% and 20.7%, respectively. The maximum difference in equivalent viscous damping compared to the ordinary reinforced concrete shear wall is 26.5%.

Seismic responses evaluation of tall tubular structures using viscous dampers in outriggers under far fault excitations

Seismic responses evaluation of tall tubular structures using viscous dampers in outriggers under far fault excitations

A proposed model to investigate the dynamic response of stay cables with viscous damper

Viscous dampers commonly mitigate structural vibrations, and various models exist to capture their nonlinear behavior. This article proposes a Hysteretic Maxwell model obtained by evolving the standard Maxwell model to effectively integrate the hysteresis effect. The model entails only a limited number of parameters. The optimized model parameters are identified by fitting model predictions with reported experimental measurements. A numerical case study is conducted, focusing on the longest stay cable of the Rades-La Goulette cable-stayed bridge. Simulation results emphasize the significant improvement of the proposed model over its predecessor, showcasing reductions in both free and forced first-mode vibrations.

Forced vibration analysis of a beam-plate system coupled through multiple nonlinear single-freedom-degree systems

A beam-plate coupling system is widely used in the construction of different frameworks across industries according to engineering application requirements. In this paper, a nonlinear single-degree-of-freedom structure is introduced as a coupling element between the beam and the plate. Therefore, a coupling system connected through a plurality of the nonlinear single-degree-of-freedom structures is proposed with exposure of its operational mechanism and the dynamic behavior analysis as required. The nonlinear coupled governing equations of the beam-plate system with series nonlinear energy sinks are established according to the Hamilton principle and solvable by the Galerkin truncation method. Meanwhile, the nonlinear characteristics of transverse vibration of the coupling system are studied for discussing the effect of nonlinear stiffness on a low-frequency response of the beam-plate system. Further, the transverse vibration of the system may vary with changes in the nonlinear stiffness, the external viscous damping, and the motion mass of the nonlinear single-degree-of-freedom structures. Accordingly, the variations along with these factors are investigated. The results indicate that a reasonable nonlinear single-degree-of-freedom structure can have a significant influence on the transverse vibration characteristics of the beam-plate system.

Optimizing Viscous Damper Placement for Stochastic Performance of Buildings with Plan Asymmetry

Optimized viscous dampers mitigate the dynamic response of building with plan asymmetry. Previous research efforts limit the optimization method to time domain requiring time history analyses to optimize damper placement for plan eccentricity-induced torsional response combined with translational response. This can consume high computational effort and lead to the variability in the ground motion selection. To expedite the optimization process while taking ground motion variability into account, this study will offer a novel criterion based on stochastic performance. This technique will skip the traditional approach of employing time history analyses and will take frequency domain variability into account. Through given distance between the center of mass (CM) and the target frame, the study establishes the stochastic criterion for the response at the perimeter of the building where the maximum torsional-translational response occurs. This allows the optimization methods to generate high quality solution with less computational efforts compared to traditional approach (i.e. time domain-based optimization). It is noteworthy that the proposed criterion is applicable to extensive kinds of responses (e.g. peak floor acceleration, story shear and etc.) once the geometric relationship is given. The proposed criterion as the objective function is compared against their counterpart in time domain through a case study. The case study is based on a reinforced concrete (RC) moment-resisting-frame (MRF) building with two-way asymmetric plan and adopts Element Exchange Method (EEM) to optimize the damper placement. The effectiveness of optimized design based in frequency domain and time domain is evaluated for their total running time and maximum peak interstory drift against a suite of ground motions. The result showed that the proposed criterion can offer the improvement against the traditional approach in terms of solution quality (i.e. performance in time domain and frequency domain) and computational efforts (i.e. total running time for optimization).

The dynamic behaviour of flexible oscillators rocking and sliding on concentrated springs

AbstractThis study presents the Flexible Rocking Model on Concentrated Springs (FRMCS), developed to investigate 2D laterally flexible oscillators rocking and sliding on deformable support media during ground excitations. In this model, concentrated vertical springs and viscous dampers simulate the contact forces from support medium at the corners of the body; the tensionless vertical contact element is linear in compression. Horizontal concentrated springs and linear viscous dampers simulate the frictional behaviour at the corners; the constitutive law for the springs models elastic deformations and sliding (according to Coulomb's friction law). With these elements, FRMCS can model the response of a rocking body which can experience sliding and free‐flight phases of motion. The consideration of the flexibility of the support medium enables the evaluation of the forces exerted by the support medium on the structure during an impact. In this study, the FRMCS response is first compared to a previous model where the support medium deformability and the effects of sliding and free‐flight are ignored. Then, the responses of four configurations, which feature either stiff or soft lateral springs and stiff or soft high‐grip support media, are examined under the influence of pulse excitations. Finally, to understand the potential influence of sliding, a configuration with a low‐grip support medium is explored. The comparative influence of lateral flexibility and support medium deformability and sliding is quantified with stability diagrams and various response spectra, describing structural force and moment demands.

Study on Vibration Reduction Effect of the Building Structure Equipped with Intermediate Column–Lever Viscous Damper

Generally speaking, the traditional lever amplification damping system is installed between adjacent columns in a building, which occupies a significant amount of space in the building. In contrast to amplification devices in different forms, the damper displacement of the intermediate column damper system is smaller, and the vibration reduction efficiency is lower. In light of these drawbacks, this study proposes a new amplification device for energy dissipation and vibration reduction, which is based on an intermediate column–lever mechanism with a viscous damper (CLVD). Initially, a specific simplified mechanical model of CLVD is derived. Subsequently, an equivalent Kelvin mechanical model of CLVD is derived to intuitively reflect CLVD’s damping and stiffness effect. The damping ratio added by CLVDs to the structure is calculated according to that model; the additional damping ratio and additional stiffness are utilized to calculate the displacement ratio Rd and shear force ratio Rv of the structure with CLVDs to the structure without CLVDs. Rd and Rv are introduced to evaluate the vibration reduction effect of the structure with CLVDs, and the effects of various parameters (such as intermediate column position, beam’s bending line stiffness, lever amplification factor, damping coefficient, and earthquake intensity) on Rd and Rv are analyzed. The results indicate that when the ratio of the distance from the intermediate column to the edge column to the span of the beam is 0.5, CLVD owns the optimal vibration reduction effect. Increasing the beam’s bending line stiffness is beneficial for CLVD to control structural displacement and shear force; when the leverage amplification factor is too large, the CLVD provides the structure with stiffness as the main factor, followed by damping. Additionally, when the ratio of the displacement amplification factor to the geometric amplification factor satisfies fd/γ = 1/21−0.5α, the CLVD has the optimal displacement control effect on the structure. After that, measures are provided to optimize the CLVD in different situations in order to effectively control the inter-story displacement and the story shear force of the structure. Consequently, a nine-story frame is taken as an example to elaborate the application of CLVDs in the design for energy dissipation and vibration reduction. The results reveal that the CLVD scheme adopting the proposed optimization method can effectively enhance the displacement amplification ability of CLVDs, resulting in an additional damping ratio of up to 12%. At the same time, the inter-story displacement was reduced by almost 40% under fortification earthquakes. Through the research in this study, designers can obtain a new choice in structural vibration reduction design.

Performance analysis of a novel single-flywheel resettable-inertia damper with eddy-current damping

The clutching inertia model presents an ideal Bang-Bang control approach, but it is challenging to realize practically through passive means. In this paper, a single-flywheel resettable-inertia damper (SRID) is proposed on the basis of the clutching inertia model. This device is implemented with a rack-and-pinion system, a right-angle gearbox system, and a flywheel-mounted eddy-current damping system. Initially, a mechanical analysis model of this device is established according to its working mechanism. Subsequently, comparative analyses are performed on the performance of SRID in a single degree-of-freedom (SDOF) structure compared to viscous dampers (VDs) subjected to harmonic and seismic excitations. The results show that the SRID can achieve a comparable control effect as VDs with a much smaller need for the damping coefficient, reflecting a damping amplification effect over 100 times. The SRID is effective in controlling peak displacement and absolute acceleration responses, especially for long-period structures. Moreover, the control performance is significantly improved with increasing magnetic induction intensity.