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Mechanical models for shear behavior in high damping rubber bearings
Abstract and Figures
High damping rubber bearings have been in use for seismic isolation of buildings worldwide for almost
30 years now. In the present work, a brief introduction to the process leading to their manufacturing is
first given. Next, a series of novel 1D mechanical models for high damping rubber bearings is proposed,
based on the combination of simple and well-known rheological models. These models are calibrated
against a set of harmonic tests at strain amplitudes up to 200%. Extension of the models to bidirectional
horizontal motion and to time-varying vertical loads is the subject of ongoing work
Figures - uploaded by George D. Manolis
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... Similarly, Markou and Manolis proposed several combined models to achieve the large strain modeling of elastomeric bearings. These models combine nonlinear spring, elastoplastic, and hysteretic element, but more than 10 shape parameters are needed in the models [24]. Other studies also focused on improving the traditional Bouc-Wen model to depict the strength degradation behavior of LRBs [25] and Sliding-LRBs [26]. ...
... The original hysteretic component z 2 (t) and modified value K R ⋅m⋅z 2 (t) is shown in Fig. 5(b). The hysteretic component z 2 (t) is added and combined in parallel withz 1 (t), and z 2 (t) is introduced in the generalized model to represent the large strain stiffness and match the "unloading" behavior of the hysteretic curves [24]. This target is achieved by obtaining a best-fit approach of the shape control parameters (α 2 ,β 2 ,γ 2 , and m). ...
Lead rubber bearings (LRBs) have been widely used in seismic isolation systems to mitigate earthquake damage in regions characterized by high seismic intensity. However, effective isolation is achieved at the expense of largely concentrated displacement in the isolation layer. Past experimental studies have confirmed that rubber stiffening and degradation properties are essential for LRBs at large cyclic strains. That is, accurately simulating the complex nonlinear behavior of LRBs is significant to evaluate the performance of isolated structures under strong earthquakes. Nevertheless, most LRB models in engineering practice cannot capture the strong nonlinear properties and the existing models for elaborate modeling are not widely used due to the complicated shape parameters. For this reason, the present study proposes a generalized Bouc–Wen model that can reasonably reflect the large strain stiffening and strength degradation properties of rubber. The traditional Bouc–Wen model of LRBs was introduced first. Subsequently, a generalized Bouc–Wen model of LRBs that is capable of simulating the observed large cyclic behavior with reasonable accuracy was developed. The model was further verified by the experimental results of LRBs with different design parameters under various loading conditions. Moreover, time history analyses were conducted to evaluate the earthquake responses of the single-degree-of-freedom system with the traditional Bouc–Wen and generalized Bouc–Wen model. Comparison proves that the two bearing models can closely estimate the peak deformation and shear force in minor and moderate earthquakes. By contrast, the generalized model can accurately capture the LRB properties under large cyclic strain that can restrain the bearing deformation but possibly increase the shear force significantly under strong earthquakes.
... In recent years, rubber isolation bearings have undergone new changes and developments. Considerable efforts have been invested in the development of new rubber isolation bearings [10][11][12][13][14][15][16][17][18]. Compared to ordinary natural rubber isolation bearings and lead-core rubber isolation bearings, high-damping rubber isolation bearings ( Figure 3) have plenty of advantages over the both, such as a simple structure, stable mechanical performance, strong energy dissipation capacity, large stiffness before yielding, environmental protection, etc., that make it an excellent choice for base-isolated structures [16]. ...
... Cross-section of high-damping rubber isolation bearing[13]. ...
At present, high-damping rubber materials, widely used in the field of engineering seismic isolation, generally have the problems such as narrow effective damping temperature range, low damping loss factor and strong temperature dependence, which lead to prominent dependence of temperature and load conditions of the isolation performance of high-damping rubber isolation bearings. Research and development of high-performance high-damping rubber materials with broad effective damping temperature range, high damping loss factor and weak temperature dependence are very urgent and necessary to ensure the safety of the seismic isolation of engineering structures. This paper mainly reviews the recent progress in the research and development of high-damping rubber materials using nitrile butadiene rubber (NBR), epoxidized natural rubber (ENR), ethylene propylene diene rubber (EPDM), butyl rubber (IIR), chlorinated butyl rubber (CIIR), and bromine butyl rubber (BIIR). This is followed by a review of vulcanization and filler reinforcement systems for the improvement of damping and mechanical properties of high-damping rubber materials. Finally, it further reviews the constitutive models describing the hyperelasticity and viscoelasticity of rubber materials. In view of this focus, four key issues are highlighted for the development of high-performance high-damping rubber materials used for high-damping rubber isolation bearings.
... 54 However, experiments results of many practical materials like asphalt, acrylic polymers, and rubber exhibit significant energy dissipation with no or minor dependence of the energy dissipation on the deformation frequency. 55 By using such material, it is not difficult to manufacture frequency independent dampers (FID) such as the sandwich type shown in 56 and high damping rubber damper for cables. 57 To describe the dynamic behavior of this FID, the classical linear hysteretic damper model is usually used as follows 45 ...
Damped outrigger system is effective for improving energy dissipation for tall buildings. However, conventional damped outrigger (CDO) system with viscous damping has two limitations: (i) its maximum damping ratio cannot be improved when outrigger/column stiffness is inadequate; (ii) different modes achieve their maximum damping ratios at different outrigger damping values, and thus the dampers cannot be optimized to simultaneously reduce vibrations of multiple modes of concern to their minimum. In this paper, a purely frequency-independent negative stiffness damped outrigger (FI-NSDO) system is proposed by combining frequency-independent damper (FID) and negative stiffness device (NSD). The damped outrigger with FID can achieve the maximum damping ratio for all modes as compared to frequency-dependent damper like viscous damper. As the NSD has the features of assisting and enhancing motion and frequency-independence, the utilization of NSD will considerably improve the maximum damping ratios when outrigger/column stiffness is inadequate and maintain the frequency-independent feature of the whole system. Therefore, the FI-NSDO has the capability of simultaneously increasing the damping ratios of all target modes to their maximum values. Analysis in frequency domain and time domain, demonstrate that the proposed FI-NSDO performs better in controlling the multi-mode vibration of seismic responses.
... Some of the representative phenomena of these devices are shown in Fig. 1, which include a large critical damping ratio (10-20% [4]), stiffening at large strains, anisotropic damage, and isotropic hardening. Several numerical models have been proposed to simulate the static and dynamic behavior of HDRBs [5][6][7][8][9][10][11]. However, a limited number of them consider bidirectional shear coupling or anisotropic damage. ...
Seismic isolation has become increasingly popular due to the excellent performance observed in buildings during past earthquakes. The seismic response of isolated structures to earthquake input is strongly controlled by the force-deformation constitutive behavior of the isolators. High Damping Rubber Bearings (HDRBs) are one of the most widely manufactured and used isolation systems in practice. Because of the large shear flexibility, the stress-strain constitutive behavior of the elastomeric material controls the overall behavior of the device. Thus, the behavior of HDRBs is highly nonlinear and characterized by the same phenomena as the elastomeric material, which is challenging to model analytically. Consequently, this article describes a simple but sufficiently accurate numerical model for simulating the bi-directional shear behavior of HDRBs under large shear deformations. A brief description of the experimental test data of HDRBs is presented, as well as the importance of including the observed phenomena in the numerical model proposed. The mathematical formulation of the proposed model is summarized, based on a hyperelastic spring and dissipative element connected in parallel. The former considers anisotropic degradation (scragging and Mullins effect), while the latter includes the isotropic hardening phenomenon. The proposed model was validated using experimental results of bi-directional shear tests of cylindrical disks of high damping natural rubber, unidirectional shear cyclic tests, and a bi-directional shear loading history applied to an HDRBs. Since the proposed model is capable of simulating the bi-directional cyclic behavior of HDRBs by considering anisotropic degradation instead of the classical isotropic behavior, which improves the numerical predictions, it can be used in dynamic analyses of buildings isolated with HDRBs.KeywordsHigh damping rubberBase isolationNonlinear responseBidirectional shearSeismic isolation
... In the conventional seismic design, structural damage is only allowed at specific components (e.g. bridge columns) to dissipate energy during strong earthquakes [1][2][3][4][5][6][7][8][9][10][11][12]. In order to reduce damage to bridge structures, especially substructure systems, in the past three decades, with the concept of seismic isolation, various devices have been employed to protect structures against earthquake forces and improve structural resilience. ...
In this paper, a novel metal rubber bearing is proposed as an alternative to the conventional rubber bearings for small- and medium-span highway bridges to solve the aging-related issues of conventional rubber bearings such as chemical degradation and erosion. The bearing is made of porous metal wire by coiling, weaving and cold-pressing to specific shapes. A shear test program is then described on two metal rubber bearings of stainless steel wire with different densities in order to identify the characteristics of hysteretic curves. The effects of shear strain, compressive stress, loading frequency and repeated loading cycles on the hysteretic behavior were investigated. It was found that the lateral hysteretic curves are approximately in bilinear shape, which consists of an initial elastic stage and a post-yield stage. The equivalent damping ratio of the tested bearings was around 20% at 25% shear strain levels and meanwhile increased with the strain levels, indicating an appreciable energy dissipation capacity. In addition, stiffness degradation was observed for the hysteretic curves beyond a certain deformation limit due to the plastic deformation caused by wire delamination and bearing bulging. However, beyond this limit, the bearing could still work as a unit with stable hysteretic behavior. These characteristics make the metal rubber bearing a great candidate for the conventional rubber bearings. It was also found that the hysteretic behavior is related with a variety of parameters such as density, loading frequency and compressive stress. Finally, it was found that the Bouc-Wen model with appropriate input parameters representing the mechanical properties can accurately simulate the hysteretic curves of the proposed bearings.
The dynamic behavior of isolated structures is strongly controlled by the force–deformation constitutive behavior of the isolators. Among the different types of existing isolation devices, High Damping Rubber Bearings (HDRBs) are commonly used in practice, which behavior is highly non-linear and difficult to model analytically. Consequently, this article proposes a simple, but sufficiently accurate, mathematical model for simulating the non-linear shear behavior of HDRBs under large deformations, and an estimation procedure for its parameter values using the geometrical features and mechanical characteristics of the device. First, we briefly describe the phenomena observed in the experimental test data, as well as other phenomena not observed within the range of experimental deformations. Then, the mathematical formulation is presented, which is based on the consideration of two components connected in parallel, a hyperelastic spring and a dissipative component. The governing equation for the former is derived from the expanded formulation of the Mooney–Rivlin model for isotropic hyperelastic materials, and the latter from a Bouc-Wen model with hardening. A novel model is included to account for stiffness degradation, including scragging and Mullins effects, which is developed from experimental data of 924 tested devices. The proposed model fits well the experimental test results of HDRBs with different geometric features and material properties. Based on the evolution laws for the different variables, the model can be successfully used in structural dynamic analysis. To facilitate model calibration, a statistical estimation procedure is proposed to reduce the 17 force–deformation constitutive model parameters of the isolator to 9 unknown parameters, which are computed from the geometric features of the device and mechanical characteristics of the rubber material. This makes the calibration of the force–deformation constitutive model parameters feasible. The estimation procedure successfully predicts the behavior of an average device within a batch of HDRBs, showing good agreement with two different experimental datasets.
In this study, a seismic isolator placed on the base of a structure was optimized under various earthquake records using an adaptive harmony search algorithm (AHS). As known, the base-isolation systems with very low stiffness provide a rigid response of superstructure, so it was assumed that the structure is rigid and the base-isolated structure can be considered as a single-degree of freedom structure. By using this assumption, an optimization method that is independent of structural properties but specific to the chosen earthquake excitation set is proposed. By taking three different damping ratio limits and isolator displacement limits, the isolator period and damping ratio were optimized so that the acceleration of the structure was minimized for nine cases. In the critical seismic analysis performed with optimum isolator parameters, the results obtained for different damping ratios and isolator periods were compared. From the results, it is determined that isolators with low damping ratios require more ductility, and as the damping ratio increases, further restriction of the movement of the isolator increases the control efficiency. Thus, it is revealed that increasing the ductility of the isolator is effective in reducing the total acceleration in the structure.
In the present study, a new core-and-filler system was proposed to use in elastomer bearings as a substitution to hazardous lead core while improving the performance of base isolators. The proposed system utilizes steel core and filler consists of either granular or polymer materials in relation to this proposal, both pure sand and epoxy are used as filler. Special design procedure for the proposed bearing was developed to determine the required dimension for elastomeric bearing under considered design loads according to the code of practice.
The finite element model of the designed elastomeric bearing was developed to evaluate performance of the proposed bearings under design condition through nonlinear dynamic analysis. Then, parametric study was conducted to simulate various material properties and loading conditions that may occur during the manufacturing and service life of base isolation.
Substantial improvement in performance of proposed bearing with core-and-filler system was observed in comparison to the lead rubber bearing. By reducing the volume of sand filler, the damping bearing of proposed sand and steel core mechanism can be improved. By manipulating the sand packing condition during manufacturing, improvement in term of effective stiffness is achievable. Trilinear constitutive curve for fully sand filled bearing revealed that, the increment in effective stiffness of bearing is higher for the shear strains more than 150%. Therefore, the core-and-filler system with full sand filler provides superior resistance against high shear strain in comparison to the lead-core rubber bearing, and achieve the purpose of limiting lateral displacement.
Application of proposed elastomeric bearings in the 5-story building as base isolator has been proven the effectiveness and suitability of implementing bearing with core and fully filled sand and also with epoxy filler as alternative isolator to the lead core elastomer bearings.
Recent earthquakes have enforced the engineering community to design seismically more efficient buildings through the energy dissipation systems. For this purpose, this paper investigates the seismic behavior of a high-rise building with a series of base isolation systems. Firstly, a 20-storey steel frame is selected as a fixed-base building, and then equipped with lead rubber bearings (LRBs). In the modelling of LRB, isolation period is alternatively varied as 4, 4.5, and 5 sec to evaluate the effectiveness of the isolator characteristic on the seismic performance of the high-rise base-isolated buildings. The seismic responses of the fixed-base and base-isolated buildings evaluated through a series of time-history analyses are performed using natural ground motion records. The analysis results are compared using engineering demand parameters such as storey displacement, isolator displacement, relative displacement, roof drift, interstorey drift ratio, absolute acceleration, base shear, base moment, input energy, and hysteretic curve. It is revealed that adjusting the isolation period in the design of LRB improved the seismic performance of the base-isolated high-rise steel buildings.
This tutorial introduces the CMA Evolution Strategy (ES), where CMA stands for Covariance Matrix Adaptation. The CMA-ES is a stochastic, or randomized, method for real-parameter (continuous domain) optimization of non-linear, non-convex functions. We try to motivate and derive the algorithm from intuitive concepts and from requirements of non-linear, non-convex search in continuous domain.
In 2003-2004 two four-story reinforced concrete buildings belonging to IACP (SR) were seismically retrofitted by hybrid base isolation. The base isolation system for each building, consisted of 12 high-damping rubber bearings (HDRB) and 13 flat lowfriction sliding bearings (LFSB). Within the bearing supply two HDRB were kept for later testing. One of the two bearings was tested at the University of Basilicata on 11th and 12th December 2014. The present report summarizes the results of the tests.
In the present work, we investigate the response of a hybrid base isolation system under earthquake excitation. The physical parameters of the hybrid base isolation system are identified from dynamic tests performed during a parallel project involving two residential buildings in the town of Solarino, Sicily, using the well-established optimization procedure 'covariance matrix adaptation-evolution strategy' as dynamic identification algorithm in the time domain. The base isolation system consists of high damping rubber bearings and low friction sliding bearings. Two separate models are employed for the numerical simulation of the high damping rubber bearing component, namely a bilinear system and a trilinear system, both in parallel with a linear viscous damper. In addition, a linear Coulomb friction model is used to describe the behavior of the low friction sliding bearing system. Analytical solutions are provided, in compact form, for all possible phases of motion of the hybrid base isolation system under earthquake excitation. A series of numerical simulations are carried out to highlight the behavior of the considered hybrid base isolation system under different excitation and site conditions.
multilayer rubber bearings as vibration isolation bearings;multilayer rubber bearings in mechanical and automotive engineering;equipment isolation from vibration via anti-vibration;vibration isolation in concert halls, Benaroya Concert Hall in Seattle;seismic isolation and multilayer rubber bearings;Los Angeles City Hall, a 28-story steel frame building;bearings for Hearst Memorial Mining Building, University of California;base-isolated four-story reinforced concrete building and UNIDO-sponsored program
A fractional derivative Zener (FDZ) model connected in parallel with a linear viscous damper and a Coulomb friction slider is used to numerically simulate the mechanical behavior of a base isolated (BI) building tested under free vibration conditions in Solarino, Sicily. This hybrid BI system comprises high damping rubber bearings in combination with low friction sliding bearings. A comparison study of the present model with previous ones appearing in the literature, namely the bi-linear and the tri-linear models defined in the time domain, is carried out here. Furthermore, the linear viscoelastic solid, namely the classical Zener model, is also implemented and evaluated. The rheological models representing all the above BI systems are analyzed and, for the first time, the rheological formulation for the tri-linear model is presented. The present comparison study shows that the FDZ model is capable of describing the complex nonlinear response of BI systems.
Design Example for a High-Damping Rubber Bearing Design Example for a Lead-Plug Bearing
An Introduction to Rubber Technology. Southampton: Rapra Technology Limited
- A Ciesielski
Ciesielski A. An Introduction to Rubber Technology. Southampton: Rapra Technology Limited; 1999.