Hysteretic Damping Research Articles

Complex mode superposition method of non-classically damped systems based on hysteretic damping model with frequency-dependent loss factors

For non-classically damped systems, it is easy to construct a damping matrix based on a hysteretic damping model. However, the damped natural frequency is non-physical, and the frequency response function is non-causal. These two drawbacks can be overcome by the hysteretic damping model with frequency-dependent loss factors. In this paper, a complex mode superposition method for non-classically damped systems based on the hysteretic damping model with frequency-dependent loss factors is proposed. Frequency-dependent loss factors of the natural frequencies are considered in the transient vibration response, while frequency-dependent loss factors of the external excitation frequencies are considered in the steady state vibration response. By decoupling complex modes in state space and physical space, non-proportional damping characteristics of hybrid structures can be effectively considered. Therefore, the proposed method can be used to calculate the time-domain dynamic responses of hybrid structures, whose loss factors are sensitive to frequency variation and have strong non-proportional damping characteristics. The time-domain dynamic responses of numerical examples are compared based on different mode superposition methods. Shaking table tests are performed on cantilever plates with different damping characteristics. The numerical and test results validate the proposed method. Moreover, the proposed method has a wide range of applications.

Reliability analysis of two archetype RC buildings with hysteretic dampers

The manuscript deals with a study on the performance/reliability analysis of steel hysteretic dampers designed for the seismic retrofit of RC frame structures at the Basic Design Earthquake, BDE (characterized by a 10 % probability of being exceeded over the reference lifespan, VR) for higher hazard levels, represented by a Maximum Considered Earthquake, MCE, with either 5 %/VR or 2.5 %/VR exceedance probabilities. Indeed, seismic codes prescribe that anti-seismic devices designed to satisfy the performance requirements at the BDE must be able to resist earthquakes of higher intensity. Therefore, γ-factors amplifying the design displacement or force must be considered for the design of the device capacity.The objective of the study consists in evaluating the over-demand caused on the steel dampers incorporated in dissipative bracing systems when passing from the BDE to the two higher hazard levels, and comparing this over-demand to the values of the corresponding γ-factors proposed in current codes. Dampers with various ductility factors are considered to include the majority of current hysteretic devices.The amplification factors recommended in the codes for hysteretic dampers are shown to be not suitable for guaranteeing the damper reliability; moreover, a dependence of the reliability of the retrofitted structures upon the ductility of the damped braces is highlighted.

Parametric study on a resilient hybrid steel-shape memory alloy yielding damper

A critical factor obstructing structural resilience is residual deformation after a damaging event. The search for a solution for removing residual deformation has led to the consideration of Shape Memory Alloys (SMAs) that can undergo large deformations and return to their original undeformed shape. This study focuses on an innovative hybrid yielding steel-SMA damper that uses monofilament wire loops. Because of numerous design parameters that affect the performance of this hybrid damper, this research aims to carry out a parametric study to optimize the damper’s performance. The study was conducted at the device level as well as a structural level. At the device level, the key design parameters, including SMA to steel ratio, max imposed strain, and the length of the elements, were evaluated. At the same time, the damper’s effect on the seismic performance of low, mid, and high-rise structures was investigated at the structural-level study. In the end, the results showed that using the damper in strong ground motions successfully reduced the maximum residual drift up to 71%, 97%, and 92% for low, mid, and high-rise structures, respectively. Therefore, it was concluded that the damper could add the self-centering ability to hysteretic dampers while maintaining satisfactory energy dissipation performance. Furthermore, some of the advantages claimed by the developers, including versatility in design and performance, adequate load resistance, and stable behavior, were also confirmed in this study.

The Effect of Landing Gear Dimension Variation on the Static Strength and Dynamic Response of Unmanned Aerial Vehicle (UAV)

This research discusses the static and dynamic analysis of the landing gear structure of an unmanned aerial vehicle (UAV). The dimensional study is conducted to investigate the effect of landing gear dimension variation on UAVs’ static strength and dynamic response. Static analysis was performed with Finite Element Method (FEM) software. The dynamic response of the UAV is analyzed using a single-degree-of-freedom vibration model. Based on the static analysis results, the landing gear stiffness and strength can be increased by increasing the width and decreasing the height, radius, and length of the landing gear structure. The energy dissipation in the dynamic analysis is described by hysteresis and viscous damping model. The dynamic response simulation results show that the increase in the stiffness of the landing gear leads to an increase in force transmission and acceleration of the UAV. Furthermore, the UAV response using the viscous damping model can accurately predict the system’s response with the hysteretic damping model for small damping conditions. However, the deviation was observed for large damping conditions.

Some features of taking damping into account in calculating harmonic oscillations of linear systems

The problem of calculating harmonic oscillations of a linear damped system with inhomogeneous damping is considered. Along with the solution available in literature, which 
 requires the inversion of the matrix that determines the eigenvalues of the undamped system, the authors propose a new solution that does not require the inversion of the above mentioned matrix, but requires the inversion of the system damping matrix. The cases of hysteretic, viscous and mixed damping are considered. It is shown that the known solution gives an error near the resonance. At the resonance point, the result is not defined at all, and near the resonance it may be incorrect. An example of building the amplitude-frequency characteristic of a system with two mass tuned dynamic dampers and three peaks in the amplitude-frequency characteristic is given. The proposed formulas for calculating displacements are convenient for constructing the amplitude-frequency characteristics of damped systems with viscous, hysteretic and mixed types of damping.

Cyclic tests on two-leaf rubble stone masonry spandrels strengthened with CRM coating on one or both sides

The paper reports the results of an original experimental campaign carried out on full-scale, two-leaf rubble stone masonry spandrels retrofitted using the Composites Reinforced Mortar (CRM) technique, applied on one or both wall faces. The CRM system consisted of a mortar coating reinforced with Glass Fibre-Reinforced Polymer (GFRP) meshes and GFRP transverse connectors to promote the connection with the existing masonry. When the coating was applied on one side, additional transverse connectors, made of grout cores with embedded steel ties (artificial diatons), were also used. These elements further strengthened the connection between the coating and the masonry and connected the leaves of the multi-leaf stone masonry walls.The GFRP mesh in the mortar coating provided the walls with the capacity to resist tension: once the coating and the masonry cracked, the strengthened samples withstood higher distortions, exhibited increased ductility and developed very diffuse crack patterns before collapsing, yielding greater energy dissipation. Furthermore, the transverse connectors enabled the composite action of the CRM coating and the walls and, in the case of artificial diatons, prevented the separation of the masonry leaves.The resistance of the walls with the CRM coating on one and both sides was 2.8 and 3.4 times that of the plain samples, respectively; in both cases, the ultimate drift was more than five times larger than the reference, while the cumulative dissipated energy was more than 30 times. The equivalent hysteretic damping in the damaged state was 11–14% (for CRM on one side) and 8–9% (for both sides).

A Complex Mode Superposition Method Based on Hysteretic Damping Model for Mode Static Correction

Due to modal truncation, the dynamic responses calculated by the mode superposition method have some errors. In this paper, the source of truncation error of the complex mode superposition method for hysteretic damped systems with non-proportional characteristics is analyzed. It includes truncation errors of external excitation load and Hilbert transform term. With the increase of mode order, the ratio of excitation frequency to natural frequency gradually approaches zero. Combined with the expression of structural modal response caused by harmonic wave, the corresponding approximate expression of high-order modal response is obtained. Through quasi-static analysis, a complex mode superposition method of non-proportionally damped systems for mode static correction is proposed. Numerical examples show that when the ratios of the domain frequencies of the external excitation to the natural frequency of some high-order modes are small, the complex mode superposition method for mode static correction has a good effect.

Analysis of Damping Performance of Hysteretic Dampers of Buckling restrained Braced Type According to eccentricity of school buildings with Torsional irregularities

Analysis of Damping Performance of Hysteretic Dampers of Buckling restrained Braced Type According to eccentricity of school buildings with Torsional irregularities

The impact of seismic waves to evaluate the behaviour of a real case of damaged earth dam

ABSTRACT Many earth dams are damaged by shearing under seismic stresses effect. In Algeria, earthquake of 21 May 2003, of magnitude Mm = 6.9 on Richter scale, considered as the most violent for more than 20 years, occurred about 70 km east of Algiers’s capital, where a large number of structures were damaged in this region. The aim of this article is to present a numerical analysis of an earth dam in the province of Oum-Elboughi. The objective is to show the influence of compressive seismic waves and the effect of foundation deph on dam behavior .The stady was carried out using a 2D finite difference method (FDM) using the FLAC 2D calculation code. In this analysis, a soil nonlinear behaviour is provided by a combined Hardin/Drnevich hysteretic damping behaviour model with Mohr–Coulomb elasto-plastic model. Results that are presented in terms of deformations and shear stresses developed at the dam and dam foundation show that the most critical area is located on the downstream side of the dam. Increasing the foundation depth decreases the value of horizontal stress, while decreasing it increases the dam instability risk.

Assessment of cyclic deformation and critical stress amplitude of jointed rocks via cyclic triaxial testing

Jointed rock specimens with a natural replicated joint surface oriented at a mean dip angle of 60° were prepared, and a series of cyclic triaxial tests was performed at different confining pressures and cyclic deviatoric stress amplitudes. The samples were subjected to 10,000 loading-unloading cycles with a frequency of 8 Hz. At each level of confining pressure, the applied cyclic deviatoric stress amplitude was increased incrementally until excessive deformation of the jointed rock specimen was observed. Analysis of the test results indicated that there existed a critical cyclic deviatoric stress amplitude (i.e. critical dynamic deviatoric stress) beyond which the jointed rock specimens yielded. The measured critical dynamic deviatoric stress was less than the corresponding static deviatoric stress. At cyclic deviatoric stress amplitudes less than the critical dynamic deviatoric stress, minor cumulative residual axial strains were observed, resulting in hysteretic damping. However, for cyclic deviatoric stresses beyond the critical dynamic deviatoric stress, the plastic strains increased promptly, and the resilient moduli degraded rapidly during the initial loading cycles. Cyclic triaxial test results showed that at higher confining pressures, the ultimate residual axial strain attained by the jointed rock specimen decreased, the steady-state dissipated energy density and steady-state damping ratio per load cycle decreased, while steady-state resilient moduli increased.

Steady-state dynamic response analysis of single-degree-of-freedom dual frame-wall resilient system

A mixed dual frame-wall resilient system, composed of a high-strength moment-resisting steel frame (HS-MRF) and self-centering steel plate shear walls (SC-SPSWs), was proposed to address the issue of frame expansion. To study the steady-state dynamic responses of the structural system, an analytical solution of a single-degree-of-freedom nonlinear oscillator under harmonic excitation was solved using the method of averaging. The steady-state responses of HS-MRF, self-centering frame and steel plate shear wall that are represented by the bilinear, self-centering and pinching hysteresis, respectively, were studied individually, followed by a full system study. A stability analysis was also carried out to evaluate the behaviour of the singular points. The results show that the hysteretic damping in the bilinear system can significantly reduce the resonance, and the responses are always stable. Jump phenomenon occurs in the self-centering system, and increasing the post-yield stiffness can reduce the nonlinearity, thus decreasing the resonance and unstable region. Unbounded resonance responses appear in the pinching system under large excitation but can change to jump behaviour under small excitation. A left-unbounded unstable region was also found when the unloading force is small. In the combined-hysteresis system, increasing the portion of bilinear hysteresis has negligible effects on the resonance but can reduce the nonlinearity under lower excitation intensities. However, under higher intensities, increasing bilinear hysteresis can significantly decrease peak responses and reduce both the jump and unbounded phenomena. The unstable regions also strongly depend on the ratio of hysteretic models. These findings shed light on the inherent dynamic properties of the dual frame-wall system and suggest that a well-design can achieve a favourable seismic performance.

Practical negative stiffness device with viscoelastic damper in parallel or series configuration for cable damping improvement

Negative stiffness mechanism has been found able to improve damping performance of dampers on a stay cable which otherwise is limited by the damper installation distance from a cable end. This study provides a practical negative stiffness device (NSD) with adjustable negative stiffness and experiments are performed to validate the negative stiffness effect. The NSD is then combined with a viscoelastic damper in parallel or series for cable damping improvement. Explicit design formulas are derived for optimal design with a target enhancement effect in damping considering the damper described respectively using the Kelvin model and the linear hysteretic damping model. The formulas are verified by analytical and numerical solutions. Parametric analyses show damping enhancement effects of the NSD and it is found more efficient when combined with a damper in series because both deformation amplitudes of the damper and the NSD are further increased in this configuration. Subsequently, case studies are carried out based on two cables of the Sutong Bridge respectively with a shear-type viscous damper and a high damping rubber damper. The results show that the designed NSD can fulfill practical requirements. Particularly, a 100% increase in damping can be achieved by the presented NSD when combined with the damper installed on a cable of 546.9 m long.

A novel bi-directional rail variable friction pendulum-tuned mass damper (BRVFP-TMD)

The shape of hysteretic loops for a friction pendulum system transforms when excited by bi-directional motion, which exhibits unexpected dynamic behavior compared with unidirectional motion. Therefore, a novel bidirectional rail variable friction pendulum-tuned mass damper (BRVFP-TMD) with two independent rails that satisfied the purpose of bidirectional structural response control and provided a full bidirectional friction force was proposed. The variable friction arrangement was applied to the rails so that the BRVFP-TMD could be accomplished with a linear hysteretic damping property that is contributed by the displacement-dependent variable friction force. Using unidirectional harmonic excitations with attack angle as bi-directional loading, illustrations were created to investigate the control effect of traditional pendulum friction TMDs with a spherical sliding surface. This demonstrated the collapse of hysteretic loops of traditional pendulum friction TMDs and superiority of BRVFP-TMD in terms of mechanism. For the BRVFP-TMD with a lightly damped structure, the optimizations of the fixed-point theory were accessed to obtain the closed-form solutions of the optimal parameters of the BRVFP-TMD. Numerical verifications based on bidirectional motions were conducted to evaluate the performance of the BRVFP-TMD. The bidirectional earthquake results indicated stable and excellent performance of the BRVFP-TMD in terms of either frequency response reduction or friction energy dissipation efficiency. Meanwhile, bidirectional wind-induced vibrations confirmed the correctness of the optimization and the stable robustness of the optimized BRVFP-TMD.

The Magnetoelastic Contribution to the Steel Internal Damping.

In this paper, the steel internal damping due to both the thermoelastic and the magnetoelastic phenomena has been investigated through a formulation based on thermodynamical potential joints with a hysteretic damping model. With the aim of focusing on the temperature transient in the solid, a first configuration has been considered, which is characterized by a steel rod with an imposed alternating pure shear strain in which only the thermoelastic contribution was studied. The magnetoelastic contribution was then introduced in a further configuration, in which a steel rod in free motion was subjected to torsion on its ends in the presence of a constant magnetic field. A quantitative assessment of the influence of the magnetoelastic dissipation in steel has been computed according to the Sablik-Jiles model by giving a comparison between the thermoelastic and the prevailing magnetoelastic damping coefficients.

Testing of Damaged Single-Bay Reinforced Concrete Frames Strengthened with Masonry Infill Walls

Despite achieving consensus and having current knowledge on the behaviour and contribution of masonry infill walls, there remain unresolved issues regarding their nonlinear behaviour as a method for strengthening existing reinforced concrete (RC) frames with effective modifications, primarily infills and the interconnection of infills and frames. The challenge for safely and economically designing frames with competent walls is to utilise the stiffening benefits while ensuring that the increased lateral forces and reduced drift capacity do not hinder performance. This study aims to investigate the potential of using masonry infill to strengthen previously slightly damaged RC frames. Experimental tests were conducted on previously slightly damaged RC frame specimens infilled with vertically hollowed-clay and solid-clay masonry units, connected to the frame elements using traditional methods (i.e., avoiding the use of modern composite materials). These strengthened infilled frame structures were subjected to constant vertical and cyclic lateral loading, which revealed improved stiffness, strength, and damping characteristics, enhancing their overall behaviour. As the main novelties, the study found that when damaged RC frames were strengthened with masonry infill walls, their performance resembled that of undamaged infilled RC frames. The strengthened infilled frame structures exhibited enhanced stiffness, strength, and hysteretic damping. The increase in stiffness was observed regardless of the type of masonry units and the strengthening technique employed. However, the improvements in strength and hysteretic damping were influenced by the specific masonry units, particularly their robustness, and the chosen reinforcement method.

Cyclic Behavior of Beam–Column Pocket Connections in GFRP-Reinforced Precast Concrete Assemblages

This paper presents details of an experimental program evaluating the behavior of six half-scale glass fiber–reinforced polymer (GFRP) reinforced concrete beam–column precast members connected together through pocket connections, which are subjected to cyclic loading. The novel beam–column connection was constructed by incorporating either epoxy resin or tensioned or untensioned GFRP rock bolts in conjunction with different-sized pocket connections. The effects of an additional connection bar between the column and beam components in the connection, as well as the confinement of the concrete around the pocket region, were also investigated. An innovative test setup was designed so that the beam–column joint could rotate without restraint provided by the supports. All specimens were tested under an incrementally increasing cyclic load. The load-carrying capacity, deformational behavior, failure modes, energy dissipation, and hysteretic damping were all recorded and evaluated. All specimens failed as a result of column failure within the pocket connection region. This was attributed to the relative rotational flexibility of the column with respect to the beam, owing to the low elasticity of the epoxy resin used in the pocket region, and hence the stress concentration at the column ends within the pocket area. According to the results, a pocket connection containing GFRP reinforcement providing confinement around the embedded area yielded the highest capacity, ductility, and energy dissipation under cyclic loading. The connection containing a GFRP bolt, regardless of whether or not the bolt was prestressed, did not significantly improve the performance of the connection. The findings presented here can be used for the design of precast elements reinforced with GFRP bars. Of particular relevance is application to jetties and other offshore concrete infrastructure where steel reinforcement (because of corrosion issues) needs to be replaced with GFRP reinforcement.

RETRACTED ARTICLE: Dynamic analysis of structures installed hysteretic dampers with hardening post-yielding stiffness using connection element method

RETRACTED ARTICLE: Dynamic analysis of structures installed hysteretic dampers with hardening post-yielding stiffness using connection element method

EVALUATION METHOD FOR CUMULATIVE PLASTIC DEFORMATION OF HYSTERETIC DAMPERS INSTALLED IN SMRF

By yielding under small inter-story deformation, hysteretic dampers installed to a response control structure absorb seismic energy and effectively control the damage to the frame. When designing such a structure, it is important to estimate the maximum deformation and the cumulative plastic deformation of the dampers against ground motions. Especially in the early stage of design, simple methods are useful for the preliminary study of determining the characteristics of the dampers. In this research, the shortcomings of the existing simple methods are discussed and a new method is proposed. Its accuracy and applicability are investigated using numerical examples.

Novel design procedure for steel hysteretic dampers in seismic retrofit of frame structures

An energy-based design procedure for sizing dissipative bracing systems equipped with steel hysteretic dampers is proposed for application to the seismic retrofit of frame structures. The procedure is based on the following assumptions: it is not iterative, as it provides a direct estimation of the steel dissipater sizes; the stiffening effects of dampers reduce displacements below prefixed limits; their damping effects reduce displacements and stress states to keep the response of structural members within their safe domains up to medium-to-high levels of the input seismic action. The procedure is articulated in three steps: seismic assessment analysis in current state and definition of the elastic properties of the bracing system to be installed in the structure; design of the dampers; verification of the seismic performance of the structure in retrofitted conditions. A demonstrative case study concerning a precast reinforced concrete frame school building is offered to explicate the practical application of the procedure, as well as to evaluate the enhancement of its response generated by the intervention. The latter consists in incorporating a dissipative bracing system equipped with triangular-shaped added damping and stiffness (T-ADAS) steel hysteretic devices. The two limit hypotheses assumed in the computational analyses for the roof beam-to-column connections of the building, i.e. hinges or fixed-ends, allow to discuss how the fundamental period of the structure in current conditions affects the parameters involved in the sizing process of the T-ADAS dampers.

Computational Comparison of Performance of Different Steel Plate Shear Yielding Dampers

The computational modeling of hysteretic dampers is a powerful tool for design, allowing us to predict and optimize damper performance. In this research, a numerical model, based on Chaboche’s nonlinear kinematic hardening constitutive law, was implemented. The parameters of this law were identified and validated by inverse analysis, based on the macro-hysteretic response of the hexagonal honeycomb steel damper. The validated model was applied to simulate the cyclic loading behavior of five proposed steel plate shear yielding dampers (SPSYDs), which were then used to compare the hysteretic performance in terms of effective stiffness, effective damping, and energy dissipation capacity. The parametric analysis of design variables performed on the SPSYDs demonstrated that the plate depth does not modify the effective damping, and the thickness is the most significant factor affecting the maximum displacement, dissipation energy and endurance cycles. The comparison of the performance of the dampers allowed us to establish design guidelines for the SPSYDs, which allow the device to be adjusted with the requirements of the building in which it is installed.