Hysteretic Damping Research Articles

Mitigation of Structural Vibrations of MDOF Oscillators by Modal Coupling Due to Hysteretic Dampers

In civil engineering, structural elements characterized by hysteresis are often encountered, such as materials with limited elastic fields, microsliding friction and elastomeric absorbers. Hysteretic nonlinearities produce a wide variety of dynamical phenomena, such as significant modal coupling, bifurcations and superabundant modes. This paper investigates nonlinear modal interactions in the dynamic response of a two-degree-of-freedom system (2DOF) with hysteretic elements. These phenomena are notably important in internal resonance conditions, where modal interactions produce strong modifications in the response with possible beneficial effects. In specific conditions, the transfer of energy between the two modes leads to a notable reduction in the maximum response amplitude; the exploitation of this feature to achieve vibration mitigation of the forced response is the main goal of the paper. Two configurations are investigated: the hysteretic element at the top (vibration damper) and the hysteretic element at the base (isolator). In both cases, several internal resonance conditions occur since, by increasing the excitation intensity, the frequencies of the hysteretic system change, as well as their ratio. Qualitative similar results are obtained, characterized by a transfer of energy between the two modes. For both configurations, the usefulness of exploiting these nonlinear phenomena in vibration mitigation has been shown.

Microstructural effects on dynamic response of rigid and flexible pavements to moving load under plane strain

Granular soils and asphalt concrete materials are characterized by microstructural effects due to their micro-stiffness and micro-inertia. In this work, an attempt is made to investigate if the material microstructure in rigid and flexible pavements affects their dynamic response to loads moving with constant speed under conditions of plane strain and linearity. The rigid pavement is modeled by a homogeneous isotropic and linearly elastic with viscous damping flexural plate resting on a homogeneous isotropic microstructured linear elastic with hysteretic damping half-pane. The flexible pavement is modeled by a layered half-plane with linear isotropic microstructured layers. The top (asphalt concrete) layer is viscoelastic, while the other layers are elastic with hysteretic damping. The dynamic response of both of the above rigid and flexible pavement models to a distributed over a finite length moving load is obtained by using the complex Fourier series approach in conjunction with compatibility and equilibrium at the plate/soil (for rigid pavements) and soil layers (for flexible pavements) interfaces. The so obtained analytical/numerical response solutions for rigid and flexible pavement problems, after verification, are employed for conducting parametric studies in order to assess the microstructural effects on the response of those pavements to moving loads. It was found, at least for the pavement cases considered here, that the presence of the stiff plate in rigid pavements and the viscoelastic top layer in flexible pavements reduce considerably microstructural effects on the pavement response, rendering them not so important for usual vehicle speeds. However, for vehicle speeds very close to the critical speed, microstructural effects become very important.

Optimization Analysis of Hysteretic Dampers Design Parameters on Seismic Performance of a Novel Self-Centering Prefabricated Concrete Frame

ABSTRACT To study the effect of the design parameters of dampers on seismic behaviors of the novel self-centering prefabricated concrete (SCPC) frame joint, eight pseudo-static loading tests with five sizes of dampers were conducted. Furthermore, three sizes parameters of dampers are applied on the seven-story prefabricated frames which are designed by the displacement-based method. Elastoplastic time-history analyses of three buildings are conducted at the DBE and MCE levels, respectively. Finally, the displacement-based seismic design method of the novel frame is implied to be effective, and the optimal design parameters of the proposed hysteretic damper for the novel SCPC frame are obtained.

Vertical distribution of seismic design load for seismically isolated buildings corresponding to diversity of seismic isolation devices

AbstractThis paper proposes a vertical distribution of seismic design load of seismically isolated buildings corresponding to diversity of seismic isolation devices such as hysteretic dampers and/or velocity‐dependent dampers. This proposed method is obtained from the relationship between response amplification caused by higher‐mode responses and key parameters such as Isolation ratio and Non‐linearity factor which evaluate structural characteristics of seismically isolated buildings. This response amplification is explained by nonlinear modal analysis with free‐free vibration mode. In addition, it is confirmed that this proposed method adapts to various model of seismically isolated buildings.

A numerical model with high-accuracy and high-efficiency for the soil dynamic impedance of pile groups under vertical vibration

This paper develops a novel numerical model for the calculation of dynamic impedance of soil considering end-bearing pile groups under vertical vibration. The soil layer is treated as a linear viscoelastic material with hysteretic damping. The vertical displacement is assumed to be uniform in each individual pile in the groups at the same embedment depth. Using separation of variables and applying proper boundary conditions at the surface and rigid bedrock, the governing equation of soil layer in three-dimensional (3D) is first transformed into a two-dimensional (2D) Helmholtz equation in xy plane, where the solution in the vertical direction is obtained analytically. To solve this problem efficiently and accurately, the whole 2D unbounded soil is then divided into a finite interior domain and an infinite exterior domain. The finite domain is discretized using the finite element method (FEM) while an exact circular artificial boundary condition (ABC) is developed to model the infinite domain. Finally, the effect of pile group interaction on the dynamic impedance of soil is investigated considering various factors, e.g., dimensionless frequency, pile number, pile slenderness ratio and relative distance between piles.

Mechanical properties of shear-type hysteretic dampers supported by studs

The shear-type hysteretic damper of an energy-absorbing member reduces the damage to the main member, such as column or beam, by absorbing seismic energy as the shear deformation of steel. As a support element for connecting the damper to the structure, brace-type and stud-type systems are mainly used. In the stud support, the stress transmission mechanism to the damper is simple, and the degrees of freedom of the plane are higher than that of the other support types. For such a shear-type damper, an H-shaped cross-section with a panel made of a highly ductile material, such as a low-yield-point steel, is generally adopted. This study used a low-yield-point steel circular hollow-section damper, which was installed in the frame as a stud support form, and a case was used to receive the in-plane force. For the damper to function effectively in the frame, it was necessary to determine the elastoplastic mechanical properties of the damper and the dampers supported by the stud. The mechanical properties of the damper unit and damper system with the stud were examined by cyclic loading test. An H-shaped shear panel damper was used as the control group with almost the same full plastic shear strength, initial stiffness, and weight as the circular hollow-section damper and the cyclic loading test was conducted under the same conditions. The effectiveness of the low-yield-point steel circular hollow-section damper was examined as a shear-type hysteretic damper by comparing both. In addition, a nonlinear finite element analysis was performed to determine the influence of the initial stiffness on the damper supported by the stud.

Vibration Response of Timoshenko Beam-Foundation Interaction Model under Accelerated Moving Load

Simulation of an infinite Timoshenko beam subjected to accelerated moving load rested on the finite depth is assessed in this study. Then, the dynamic response of the infinite beam is illustrated on the various theoretical models, including the Winkler, Pasternak, and visco-elastic foundations. Furthermore, the effects of various damping, such as foundation damping, beam damping, and hysteretic damping (damping between soil grains), are also studied on the dynamic behavior of the beam. It has been worked out that the type of basement and its depth have a remarkable effect on the dynamic behavior. In addition, the load velocity will also cause a maximum displacement in the beam as the critical velocity approaches. The deflection of the beam on the basements increases when the velocity approaches the critical one, and the maximum displacement of the beam occurs under the load. Finally, it was seen that the presented diagrams for all three types of Winkler’s, Pasternak’s, and visco-elastic foundations follow the usual properties related to the critical velocity.

Efficiency of energy dissipators in the seismic response of buildings

This paper aims to study the efficiency of energy dissipators, both fluid viscous and hysteretic, to improve the seismic responses of buildings. To quantify the ability of energy dissipators to reduce seismic responses, a series of time history analyzes were carried out on simplified models of buildings. Said simplified models consist of masses and springs with linear and elastic behavior whose properties are obtained from a shear beam model, joined by link elements with non-linear behavior to simulate energy dissipators. The main study parameters that were considered are the fundamental period of the structure without seismic control devices and the objective reduction factor. Likewise, a procedure is proposed for the dimensioning of the hysteretic dampers that will be incorporated into a building. On the other hand, the main building of the Lima airport was used as a case study, for which two alternatives are proposed, each one with a different type of energy dissipator, but both designed to have similar performance. Finally, the reductions obtained by both the simplified models and three-dimensional models are compared. It is concluded that the simplified models allow a fast and acceptable prediction of the levels of reduction of the seismic response in buildings that incorporate energy dissipators.

A Calculation Method for Determining the Number of Truncated Modes Based on Hysteretic Damping Model

A Calculation Method for Determining the Number of Truncated Modes Based on Hysteretic Damping Model

A steel hysteretic damper for seismic design and retrofit of precast portal frames

In this paper a steel hysteretic damper is proposed which can be installed at the beam-column joint of precast concrete structures and can greatly improve the seismic performance of these structures. The damper is made of a few steel plates with reduced sections placed in parallel, which yield under in-plane bending caused by joint rotation and dissipate energy induced by seismic activity. As less attention has been paid to seismic performance evaluation and design of precast portal frames, a procedure for design and performance estimation is established based on the available theoretical formulation and is verified by comparing their results with those obtained by analysis. The efficiency of the proposed damper is investigated by retrofitting a portal frame and evaluating its seismic performance before and after retrofit. The results show that the developed damper can significantly reduce the maximum interstory drift ratio and prevent the global collapse of the structure, which is of particular interest in practice. The hysteretic behavior and the energy dissipation capability of the frame are compared before and after the retrofit. It is observed that most of the seismic energy is dissipated by the dampers installed in the retrofitted frame, which protects the frame against seismic damage.

Tuned mass systems with the Bouc-Wen and a hybrid hysteresis

Tuned-mass-dampers are extensively used in physical systems in order to reduce the dynamic response of the primary structures. The damping in a tuned-mass-damper system plays a significant role. In many engineering systems, we see damping is hysteretic in nature. Tuned-mass systems with nonlinear hysteretic damping are mathematically challenging. In this paper, tuned mass systems with rate-independent hysteresis are studied. In particular, first we study tuned mass systems with the famous Bouc-Wen model, and then we study tuned mass systems with the Bouc-Wen model and a recently developed scalar hysteresis model in parallel. Numerical approaches are used to study the dynamic responses of the systems. The sine sweep responses show two resonance peaks. The sine sweep responses indicate the amplitude versus frequency of the systems. The numerical results obtained for two different hysteretic dampers are compared.

Performance-based design of steel frames with self-centering modular panel

The self-centering modular panel (SCMP) is an emerging seismic resilient lateral force-resisting system. This paper intends to develop a performance-based design (PBD) method for steel buildings equipped with the SCMPs based on the concept of direct displacement-based design methodology. The theoretical hysteretic model of the SCMP consisting of the post-tensioned frame (PTF) and four replaceable hysteretic dampers (RHD) is proposed and validated in this paper. Based on the proposed theoretical hysteretic model, the equation for the equivalent damping ratio of the steel buildings with SCMP is developed and the PBD method is proposed. The 3-story and 6-story steel frames equipped with the emerging SCMP are established through the developed PBD procedure. Static analyses were performed to investigate the nonlinear responses of the established buildings. Twenty ground sequences were chosen and scaled to evaluate the seismic responses of the designed steel frames subjected to different seismic intensity levels through nonlinear dynamic analyses. The results of the research show that steel structures equipped with SCMPs established through the developed PBD procedure can display the expected hysteretic behavior and performance under earthquakes. The designed buildings can achieve excellent post-earthquake recoverability by keeping the residual displacement in each story less than 0.5% even under earthquakes with MCE intensity.

Response-spectrum-based design method for active base-isolated buildings with viscous dampers and hysteretic dampers

Active control has been applied to base-isolated buildings to achieve high control performance. A base-isolated building with active control has many design parameters, such as parameters of the superstructure, isolator, viscous dampers, and hysteretic dampers. The conventional control-system design uses trial-and-error approaches to select these design parameters and numerical simulations to estimate the responses of the system, causing a limited design outlook. In this study, we presented a spectrum-based design method for active base-isolated buildings with both viscous and hysteretic dampers for selecting the parameters of the isolator, viscous damper, steel hysteretic damper, and controller. The presented method estimates the maximum responses and maximum control force of the control system only using response spectra of the design earthquake wave, thus eliminating trial-and-error approaches and numerical simulations. Numerical design examples were also used to show the details of the design procedure and the validity of the presented method.

The numerical calculation method based on equivalent frequency-independent time-domain damping model

In order to realize the time-domain analysis based on hysteretic damping model, the frequency-independent time-domain damping model of single degree of freedom (SDOF) system is constructed. Based on the assumed relationship of vibration responses, the equivalent frequency-independent time-domain damping model in complex domain and real domain are proposed. The characteristic that the dissipated energy in each cycle is not related to the vibration frequency of external excitation is retained for the two equivalent damping models. Combined with Newmark- β method, the corresponding numerical methods are obtained. The numerical examples show that the free vibration responses are stably convergent based on equivalent damping models. The numerical results of vibration responses of SDOF system due to earthquake wave have high calculation accuracy. Compared with equivalent frequency-independent time-domain damping model in real domain, the computational accuracy of equivalent frequency-independent time-domain damping model in complex domain is higher, and the computational efficiency is lower.

Seismic design and numerical assessment of shape memory alloy-restrained rocking precast concrete bridge columns

This paper introduces a class of shape memory alloy (SMA)-restrained rocking (SRR) bridge columns and numerically evaluates their response under lateral loading. SRR columns are low-damage precast concrete columns that are connected to their adjacent substructure components through two series of unbonded links, namely, SMA links and energy dissipation (ED) links. The SMA links, which are prestressed and made of superelastic Nitinol, provide the rocking joints with self-centering and dissipate a moderate amount of energy. The ED links, which are made of mild steel and are replaceable, supplement the hysteretic energy dissipation provided by the SMA links. The rocking joints are protected against concrete damage via steel jacketing and end steel plates. Following the introduction of three SRR column design variations, a displacement-based procedure is proposed for their effective seismic design. Nonlinear 3D finite element models are then developed to investigate the performance of the proposed columns under monotonic and cyclic lateral loading. Finally, a parametric study is conducted to examine the effective ranges of two major design parameters of SRR columns. The findings illustrate that the proposed SRR columns are capable of meeting their targeted performance objectives, i.e., avoiding damage under the displacement demands induced by a 2475-year seismic event, as well as providing significant self-centering and hysteretic damping.

Evaluating the efficiency of supplementary rebar system in improving hysteretic damping of self-centering rocking walls

Evaluating the efficiency of supplementary rebar system in improving hysteretic damping of self-centering rocking walls

Seismic optimization of variable friction pendulum tuned mass damper with hysteretic damping characteristic

A variable friction pendulum-tuned mass damper (VFP-TMD) with hysteretic damping characteristics was proposed. The mechanism of the proposed VFP-TMD demonstrated linear behavior and nonlinear properties. Further, the fully nonlinear (FN) and partial linear (PL) equations of motion of the structure with the VFP-TMD system were derived. The VFP-TMD demonstrated stable and excellent seismic mitigation capacities and stroke limitation functionality. Based on the fixed-point theory, the closed-form exact solutions to design parameters of an undamped structure with a VFP-TMD system subjected to the ground motion were presented for different performance indices. The parametric studies showed that optimal designed VFP-TMD can be perfectly tuned in the frequency domain, which proved the applicability of closed-form solutions. To better understand VFP-TMD with hysteretic damping, constant friction pattern and multi-stage variable friction pattern were proposed for comparison. In contrast with constant friction and multi-stage variable friction, VFP-TMD with hysteretic damping characteristic was significantly optimized by the closed-form solutions. To verify the effectiveness of the closed-form solutions on VFP-TMD, twenty sets of real earthquake records were conducted which exhibited the superiority of linear variable friction patterns on seismic mitigation simultaneously. Results showed that the optimized VFP-TMD had an “infinitely large bandwidth”, which enabled it to reach its full potential according to the excitation amplitude.

Seismic design framework for steel structures with hysteretic and viscous dampers

Mixed-use of viscous and hysteretic dampers is considered an effective way to control the seismic responses of nonlinear building structures; however, the existing damper capacity design methods were mainly constructed based on a single type of damper. In this study, a displacement-based design method is proposed to determine the capacities of the two types of dampers simultaneously. The equivalent stiffness of the added component and the primary structure at the target drift is considered vital factors. Based on the assumption that the equivalent stiffness is proportional to the shear force, the stiffness of the added component can be derived, which further determines the capacity of the dissipative damper. The seismic control design and nonlinear time history analysis were performed on ten-story steel moment frame buildings with different structural parameter settings, and six scenarios of damper arrangement were compared. It was demonstrated that the proposed procedure could derive a design scheme for an arbitrary damper arrangement to achieve a relatively uniform story drift in structure. The fragility analysis was further performed to compare the seismic control effect of various damper arrangement schemes for comprehensively understanding their performance.

Dynamics of plates resting on layered transversely isotropic poroelastic media under moving loads

This paper investigates the dynamic interaction between a plate and multi-layered transversely isotropic (TI) hysteretically damped poroelastic media under a moving rectangular load. Following Kirchhoff's thin plate theory, the plate deflection is derived utilizing the Fourier series expansion and the integral transform technique. The governing equation for the layered TI hysteretically damped poroelastic media is formulated through the standard hysteretic damping model and Biot's theory. The solution for the plate-soil dynamic interaction in the wavenumber domain considering the plate-soil interface condition is obtained by the extended precise integration method (PIM) for the layered TI saturated porous media. This solution can be further converted into the spatial domain by the inverse transform technique. We have verified the efficiency and accuracy of the proposed method. Several numerical examples are presented to investigate the influences of the plate thickness, plate modulus ratio, surface layer, speed of the moving load, and hysteretic damping of the solid skeleton on the dynamic behaviors of the plate on layered TI poroelastic media.

Mechanical characteristics of circular hollow section damper under bidirectional cyclic loading

During earthquake events, hysteretic dampers installed on the elevations composed of the columns and beams of structural frames can resist forces in any direction other than the in-plane direction because of the three-dimensional behavior of buildings and the interrelationship between the dampers and the adjacent members. Circular hollow section dampers (CHSDs), which form a type of steel hysteretic dampers, can be employed as seismic devices because they provide equal structural performance in any horizontal direction according to the geometrical characteristics of the cross-sectional shape. However, the cumulative hysteretic characteristics of CHSDs for multidirectional behavior remain unelucidated; therefore, an empirical review is needed. This study experimentally analyzed the cumulative hysteresis behavior of a CHSD repeatedly loaded sequentially in two horizontal directions (bidirectional cyclic loading). The results obtained were compared with previous experimental results under unidirectional cyclic loading conditions. The comparative analysis using empirical data revealed that the hysteretic curve of the CHSD under bidirectional cyclic loading maintained a relatively constant strength increase ratio and effective stiffness along with a stable spindle shape until the damper reached the ultimate state despite the continuous change in the loading direction. Further, compared with the unidirectional cyclic loading condition, the CHSD under bidirectional cyclic loading exhibited similar structural trends considering the damper aspect ratio and material influence. Moreover, the total accumulated plastic deformation in each loading direction was approximately the same as the cumulative plastic deformation caused by unidirectional cyclic loading.