Recent Advances in the Design of Structures with Passive Energy Dissipation Systems

A special issue of Applied Sciences (ISSN 2076-3417). This special issue belongs to the section "Civil Engineering".

Deadline for manuscript submissions: closed (31 January 2020) | Viewed by 54944

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Guest Editor
Department of Engineering, University of Messina, 98166 Messina, Italy
Interests: passive energy dissipation systems; random vibration theory; seismic design of structures

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Guest Editor
Department of Engineering, University of Messina, 98166 Messina, Italy
Interests: performance-based seismic design; seismic isolation; earthquake engineering; innovative structural control systems; limit-state behavior of reinforced concrete structures; strengthening techniques of reinforced concrete structures
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Guest Editor
Department of Disaster Mitigation for Structures, Tongji University, Shanghai 200092, China
Interests: structure vibration mitigation; isolation technology; soil structure interaction; ground motion

Special Issue Information

Dear Colleagues,

Passive vibration control plays a crucial role in earthquake engineering. Common solutions include seismic isolation and damping systems with various kinds of devices, such as viscous, viscoelastic, hysteretic, and friction dampers. These strategies have been widely utilized in engineering practice, and their efficacy has been demonstrated in mitigating damage and preventing the collapse of buildings, bridges, and industrial facilities. However, there is a need for more sophisticated analytical and numerical tools to design structures equipped with optimally configured devices. On the other hand, the family of devices and dissipative elements for seismic protection keeps evolving as a result of the growing performance demands and new progresses achieved in material science and mechanical engineering. As for emerging technologies, negative stiffness devices, self-centering devices, inerter-based systems, and energy sinks are just a few examples.

This Special Issue aims to collect contributions to the development and application of seismic protection strategies for structures, covering both traditional and innovative devices. In particular, the desired topics include, but are not limited to, experimental or theoretical investigations of high-efficient dampers and isolation bearings; optimization of conventional or innovative energy dissipation devices; performance-based or probability-based design of damped structures; application of nonlinear dynamics, random vibration theory, and modern control theory for the design of structures with passive energy dissipation systems; critical discussion of implemented isolation/damping technologies in significant or emblematic engineering projects.

Prof. Dr. Giuseppe Ricciardi
Dr. Dario De Domenico
Dr. Ruifu Zhang
Guest Editors

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Keywords

  • Seismic isolation
  • Energy dissipation devices
  • Tuned mass damper
  • Negative stiffness device
  • Inerter system
  • Damped structures

Published Papers (14 papers)

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Editorial

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6 pages, 185 KiB  
Editorial
Editorial for “Recent Advances in the Design of Structures with Passive Energy Dissipation Systems”
by Dario De Domenico, Giuseppe Ricciardi and Ruifu Zhang
Appl. Sci. 2020, 10(8), 2819; https://doi.org/10.3390/app10082819 - 19 Apr 2020
Cited by 2 | Viewed by 1764
Abstract
Civil engineering structures and infrastructures are inherently vulnerable to exceptional loads related to natural disasters, primarily earthquakes, tsunamis, strong winds, and floods [...] Full article

Research

Jump to: Editorial

30 pages, 724 KiB  
Article
Distributed Passive Actuation Schemes for Seismic Protection of Multibuilding Systems
by Francisco Palacios-Quiñonero, Josep Rubió-Massegú, Josep M. Rossell and Hamid Reza Karimi
Appl. Sci. 2020, 10(7), 2383; https://doi.org/10.3390/app10072383 - 31 Mar 2020
Cited by 4 | Viewed by 2217
Abstract
In this paper, we investigate the design of distributed damping systems (DDSs) for the overall seismic protection of multiple adjacent buildings. The considered DDSs contain interstory dampers implemented inside the buildings and also interbuilding damping links. The design objectives include mitigating the buildings [...] Read more.
In this paper, we investigate the design of distributed damping systems (DDSs) for the overall seismic protection of multiple adjacent buildings. The considered DDSs contain interstory dampers implemented inside the buildings and also interbuilding damping links. The design objectives include mitigating the buildings seismic response by reducing the interstory-drift and story-acceleration peak-values and producing small interbuilding approachings to decrease the risk of interbuilding collisions. Designing high-performance DDS configurations requires determining convenient damper positions and computing proper values for the damper parameters. That allocation-tuning optimization problem can pose serious computational difficulties for large-scale multibuilding systems. The design methodology proposed in this work—(i) is based on an effective matrix formulation of the damped multibuilding system; (ii) follows an H approach to define an objective function with fast-evaluation characteristics; (iii) exploits the computational advantages of the current state-of-the-art genetic algorithm solvers, including the usage of hybrid discrete-continuous optimization and parallel computing; and (iv) allows setting actuation schemes of particular interest such as full-linked configurations or nonactuated buildings. To illustrate the main features of the presented methodology, we consider a system of five adjacent multistory buildings and design three full-linked DDS configurations with a different number of actuated buildings. The obtained results confirm the flexibility and effectiveness of the proposed design approach and demonstrate the high-performance characteristics of the devised DDS configurations. Full article
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13 pages, 3955 KiB  
Article
Shared Tuned Mass Dampers for Mitigation of Seismic Pounding
by Rajesh Rupakhety, Said Elias and Simon Olafsson
Appl. Sci. 2020, 10(6), 1918; https://doi.org/10.3390/app10061918 - 11 Mar 2020
Cited by 16 | Viewed by 3241
Abstract
This study explores the effectiveness of shared tuned mass damper (STMD) in reducing seismic pounding of adjacent buildings. The dynamics of STMDs is explored through numerical simulations of buildings idealized as single and multiple degree of freedom oscillators. An optimization method proposed in [...] Read more.
This study explores the effectiveness of shared tuned mass damper (STMD) in reducing seismic pounding of adjacent buildings. The dynamics of STMDs is explored through numerical simulations of buildings idealized as single and multiple degree of freedom oscillators. An optimization method proposed in the literature is revisited. It is shown that the optimization results in two different solutions. The first one corresponds to the device being tuned to one of the buildings it is attached to. The second solution corresponds to a very stiff system where the TMD mass hardly moves. This solution, which has been described as an STMD in the literature, is shown to be impractical due to its high stiffness and use of a heavy stationary mass that plays no role in response mitigation but adds unnecessary load to the structure. Furthermore, it is shown that the second solution is equivalent to a viscous coupling of the two buildings. As for the properly tuned solution, i.e., the first solution, sharing the device with an adjacent building was found to provide no added benefits compared to when it is placed on one of the buildings. Based on results from a large set of real earthquake ground motions, it is shown that sharing a TMD mass with an adjacent building, in contrary to what is reported in the literature, is not an effective strategy. Full article
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19 pages, 1950 KiB  
Article
Motion-Based Design of Passive Damping Systems to Reduce Wind-Induced Vibrations of Stay Cables under Uncertainty Conditions
by Javier Naranjo-Pérez, Javier F. Jiménez-Alonso, Iván M. Díaz, Giuseppe Quaranta and Andrés Sáez
Appl. Sci. 2020, 10(5), 1740; https://doi.org/10.3390/app10051740 - 03 Mar 2020
Cited by 4 | Viewed by 2562
Abstract
Stay cables exhibit both great slenderness and low damping, which make them sensitive to resonant phenomena induced by the dynamic character of external actions. Furthermore, for these same reasons, their modal properties may vary significantly while in service due to the modification of [...] Read more.
Stay cables exhibit both great slenderness and low damping, which make them sensitive to resonant phenomena induced by the dynamic character of external actions. Furthermore, for these same reasons, their modal properties may vary significantly while in service due to the modification of the operational and environmental conditions. In order to cope with these two limitations, passive damping devices are usually installed at these structural systems. Robust design methods are thus mandatory in order to ensure the adequate behavior of the stay cables without compromising the budget of the passive control systems. To this end, a motion-based design method under uncertainty conditions is proposed and further implemented in this paper. In particular, the proposal focuses on the robust design of different passive damping devices when they are employed to control the response of stay cables under wind-induced vibrations. The proposed method transforms the design problem into a constrained multi-objective optimization problem, where the objective function is defined in terms of the characteristic parameters of the passive damping device, together with an inequality constraint aimed at guaranteeing the serviceability limit state of the structure. The performance of the proposed method was validated via its application to a benchmark structure with vibratory problems: The longest stay cable of the Alamillo bridge (Seville, Spain) was adopted for this purpose. Three different passive damping devices are considered herein, namely: (i) viscous; (ii) elastomeric; and (iii) frictions dampers. The results obtained by the proposed approach are analyzed and further compared with those provided by a conventional method adopted in the Standards. This comparison illustrates how the newly proposed method allows reduction of the cost of the three types of passive damping devices considered in this study without compromising the performance of the structure. Full article
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17 pages, 4669 KiB  
Article
Study of Lead Rubber Bearings for Vibration Reduction in High-Tech Factories
by Shen-Haw Ju, Cheng-Chun Yuantien and Wen-Ko Hsieh
Appl. Sci. 2020, 10(4), 1502; https://doi.org/10.3390/app10041502 - 22 Feb 2020
Cited by 9 | Viewed by 6244
Abstract
This paper studies the seismic and micro vibrations of the high-tech factory with and without lead rubber bearings (LRBs) using the three-dimensional (3D) finite element analysis. The soil-structure interaction is included using the p-y, t-z, and Q-z nonlinear soil springs, while the time-history [...] Read more.
This paper studies the seismic and micro vibrations of the high-tech factory with and without lead rubber bearings (LRBs) using the three-dimensional (3D) finite element analysis. The soil-structure interaction is included using the p-y, t-z, and Q-z nonlinear soil springs, while the time-history analysis is performed under seismic, wind, or moving crane loads. The finite element results indicate that the moving crane does not change the major ambient vibrations of the factory with and without LRBs. For a normal design of LRBs, the high-tech factory with LRBs can decrease the seismic base shear efficiently but will have a much larger wind-induced vibration than that without LRBs, especially for the reinforced concrete level. Because micro-vibration is a major concern for high-tech factories, one should use LRBs with a large initial stiffness to resist wind loads, and use a small final LRB stiffness to reduce the seismic load of high-tech factories. This situation may make it difficult to obtain a suitable LRB, but it is an opportunity to reduce the seismic response without increasing the micro-vibration of high-tech factories. Full article
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18 pages, 7178 KiB  
Article
Numerical Study on Hysteretic Behaviour of Horizontal-Connection and Energy-Dissipation Structures Developed for Prefabricated Shear Walls
by Limeng Zhu, Lingmao Kong and Chunwei Zhang
Appl. Sci. 2020, 10(4), 1240; https://doi.org/10.3390/app10041240 - 12 Feb 2020
Cited by 79 | Viewed by 7427
Abstract
This study proposed a developed horizontal-connection and energy-dissipation structure (HES), which could be employed for horizontal connection of prefabricated shear wall structural system. The HES consists of an external replaceable energy dissipation (ED) zone mainly for energy dissipation and an internal stiffness lifting [...] Read more.
This study proposed a developed horizontal-connection and energy-dissipation structure (HES), which could be employed for horizontal connection of prefabricated shear wall structural system. The HES consists of an external replaceable energy dissipation (ED) zone mainly for energy dissipation and an internal stiffness lifting (SL) zone for enhancing the load-bearing capacity. By the predicted displacement threshold control device, the ED zone made in bolted low-yielding steel plates could firstly dissipate the energy and can be replaced after damage, the SL zone could delay the load-bearing and the load-displacement curves of the HES would exhibit “double-step” characteristics. Detailed finite element models are established and validated in software ABAQUS. parametric analysis including aspect ratio, the shape of the steel plate in the ED zone and the displacement threshold in the SL zone, is conducted. It is found that the HES depicts high energy dissipation ability and its bearing capacity could be obtained again after the yielding of the ED zone. The optimized X-shaped steel plate in the ED zone exhibit better performance. The “double-step” design of the HES is a potential way of improving the seismic and anti-collapsing performance of prefabricated shear wall structures against large and super-large earthquakes. Full article
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17 pages, 5870 KiB  
Article
Seismic Response Mitigation of Base-Isolated Buildings
by Mohammad Hamayoun Stanikzai, Said Elias and Rajesh Rupakhety
Appl. Sci. 2020, 10(4), 1230; https://doi.org/10.3390/app10041230 - 12 Feb 2020
Cited by 15 | Viewed by 5373
Abstract
Earthquake response mitigation of a base-isolated (BI) building equipped with (i) a single tuned mass damper at the top of the building, (ii) multiple tuned mass dampers (MTMDs) at the top of the building, and (iii) MTMDs distributed on different floors of the [...] Read more.
Earthquake response mitigation of a base-isolated (BI) building equipped with (i) a single tuned mass damper at the top of the building, (ii) multiple tuned mass dampers (MTMDs) at the top of the building, and (iii) MTMDs distributed on different floors of the building (d-MTMDs) is studied. The shear-type buildings are modeled by considering only one lateral degree of freedom (DOF) at the floor level. Numerical approach of Newmark’s integration is adopted for solving the coupled, governing differential equations of motion of 5- and 10-story BI buildings with and without TMD schemes. A set of 40 earthquake ground motions, scaled 80 times to get 3200 ground motions, is used to develop simplified fragility curves in terms of the isolator maximum displacement. Incremental dynamic analysis (IDA) is used to develop simplified fragility curves for the maximum target isolator displacement. It is found that TMDs are efficient in reducing the bearing displacement, top floor acceleration, and base shear of the BI buildings. In addition, it was noticed that TMDs are efficient in reducing the probability of failure of BI building. Further, it is found that the MTMDs placed at the top floor and d-MTMDs on different floors of BI buildings are more efficient in decreasing the probability of failure of the BI building when compared with STMD. Full article
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22 pages, 9797 KiB  
Article
Experimental Campaign of a Low-Cost and Replaceable System for Passive Energy Dissipation in Precast Concrete Structures
by Álvaro Mena, Jorge Franco, Daniel Miguel, Jesús Mínguez, Ana Carla Jiménez, Dorys Carmen González and Miguel Ángel Vicente
Appl. Sci. 2020, 10(4), 1213; https://doi.org/10.3390/app10041213 - 11 Feb 2020
Cited by 3 | Viewed by 3168
Abstract
This research develops a new low-cost energy dissipation system, capable of being implemented in residential structures in developing countries with high seismic activity, in which the current solutions are not economically viable. These residential structures are entirely made of precast concrete elements (foundations, [...] Read more.
This research develops a new low-cost energy dissipation system, capable of being implemented in residential structures in developing countries with high seismic activity, in which the current solutions are not economically viable. These residential structures are entirely made of precast concrete elements (foundations, walls, and slabs). A solution is developed that consists of a new connection between a precast foundation and a structural wall, which is capable of dissipating almost all the seismic energy, and therfore protecting the rest of the building from structural damage. To validate the solution, a testing campaign is carried out, including a first set of “pushover” tests on isolated structural walls, a second set of “pushover” tests on structural frames, and a final set of seismic tests on a real-scale three-storey building. For the first and second set of tests, ductility is analyzed in accordance with ACI 374.2R-13, while for the third one, the dynamic response to a reference earthquake is evaluated. The results reveal that the solution developed shows great ductility and no relevant damage is observed in the rest of the building, except in the low-cost energy dissipation system. Once an earthquake has finished, a precast building implemented with this low-cost energy dissipation system is capable of showing a structural performance level of “immediate occupancy” according to ACI 374.2R-13. Full article
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21 pages, 10787 KiB  
Article
A Multi-Degree of Freedom Tuned Mass Damper Design for Vibration Mitigation of a Suspension Bridge
by Fanhao Meng, Jiancheng Wan, Yongjun Xia, Yong Ma and Jingjun Yu
Appl. Sci. 2020, 10(2), 457; https://doi.org/10.3390/app10020457 - 08 Jan 2020
Cited by 13 | Viewed by 5116
Abstract
This paper proposes a synthetic approach to design and implement a two-degree of freedom tuned mass damper (2DOFs TMD), aimed at damping bending and torsional modes of bridge decks (it can also be applied to other types of bridges like cable-stayed bridges to [...] Read more.
This paper proposes a synthetic approach to design and implement a two-degree of freedom tuned mass damper (2DOFs TMD), aimed at damping bending and torsional modes of bridge decks (it can also be applied to other types of bridges like cable-stayed bridges to realize the energy dissipation). For verifying the effectiveness of the concept model, we cast the parameter optimization of the 2DOFs TMDs conceptual model as a control problem with decentralized static output feedback for minimizing the response of the bridge deck. For designing the expected modes of the 2DOFs TMDs, the graphical approach was introduced to arrange flexible beams properly according to the exact constraints. Based on the optimized frequency ratios, the dimensions of 2DOF TMDs are determined by the compliance matrix method. Finally, the mitigation effect was illustrated and verified by an experimental test on the suspension bridge mock-up. The results showed that the 2DOFs TMD is an effective structural response mitigation device used to mitigate the response of suspension bridges. It was also observed that based on the proposed synthetic approach, 2DOFs TMD parameters can be effectively designed to realize the target modes control. Full article
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15 pages, 6823 KiB  
Article
Experimental Investigation on the Mechanical Properties of Curved Metallic Plate Dampers
by Jie Zheng, Chunwei Zhang and Aiqun Li
Appl. Sci. 2020, 10(1), 269; https://doi.org/10.3390/app10010269 - 30 Dec 2019
Cited by 86 | Viewed by 3925
Abstract
This study proposes a novel curved steel plate damper to improve the seismic performance of structures. The theoretical analysis of the curved plate damper was carried out deriving formulas of key parameters of the curved plate damper including elastic lateral stiffness, yield strength, [...] Read more.
This study proposes a novel curved steel plate damper to improve the seismic performance of structures. The theoretical analysis of the curved plate damper was carried out deriving formulas of key parameters of the curved plate damper including elastic lateral stiffness, yield strength, and yield displacement. Moreover, a cyclic loading test of four sets of specimens was conducted, and the hysteretic performance, ductility, energy dissipation performance, and strain of the specimens were studied. The results showed that the initial stiffness of the damper was large, no obvious damage was observed, and the hysteresis loop was full. The tested dampers had good deformation and energy dissipation performance. The stress variable rule of the damper was obtained by stress analysis, where the plastic deformation at the end of the semi-circular arc was large. The formula for various parameters of the damper was compared with experimental and numerical results; thus, the value of the adjustment coefficient was determined reasonable. Meanwhile, the rationality of the finite element model was also verified. Full article
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19 pages, 13889 KiB  
Article
Displacement-Dependent Damping Inerter System for Seismic Response Control
by Zhipeng Zhao, Ruifu Zhang, Yiyao Jiang, Dario De Domenico and Chao Pan
Appl. Sci. 2020, 10(1), 257; https://doi.org/10.3390/app10010257 - 29 Dec 2019
Cited by 15 | Viewed by 3714
Abstract
Various inerter systems utilizing velocity-dependent damping for vibration control have been developed. However, a velocity-dependent damping element may exhibit relatively poor performance compared to a displacement-dependent damping element (DDE) of equivalent damping ratio, when the structural deformation is small in the early stage [...] Read more.
Various inerter systems utilizing velocity-dependent damping for vibration control have been developed. However, a velocity-dependent damping element may exhibit relatively poor performance compared to a displacement-dependent damping element (DDE) of equivalent damping ratio, when the structural deformation is small in the early stage of the seismic response. To address this issue, the advantage of DDE in generating a larger control force in the early stage of excitation is promoted here and enhanced by a supplemental inerter-spring-system, thus realizing a proposed novel displacement-dependent damping inerter system (DDIS). First, the influence of various DDIS-parameters is carried out by resorting to the stochastic linearization method to handle non-linear terms. Then, seismic responses of the DDIS-controlled system are evaluated in the time domain taking the non-linearity into account, thus validating the accuracy of the stochastic dynamic analysis. Several design cases are considered, all of which demonstrated damping enhancement and timely control achieved by the DDIS. The results show that the energy dissipation as well as reduction of structural displacement and acceleration accomplished by the proposed system are significant. DDIS suppresses structural responses in a timely manner, as soon as the peak excitation occurs. In addition, it is demonstrated that interactions among the inerter, spring, and DDE, which constitute the damping-enhancement mechanism, lead to a higher energy-dissipation efficiency compared to the DDE alone. Full article
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26 pages, 11804 KiB  
Article
Wind-Induced Response Control of High-Rise Buildings Using Inerter-Based Vibration Absorbers
by Qinhua Wang, Haoshuai Qiao, Dario De Domenico, Zhiwen Zhu and Zhuangning Xie
Appl. Sci. 2019, 9(23), 5045; https://doi.org/10.3390/app9235045 - 22 Nov 2019
Cited by 40 | Viewed by 4039
Abstract
The beneficial mass-amplification effect induced by the inerter can be conveniently used in enhanced variants of the traditional Tuned Mass Damper (TMD), namely the Tuned Mass-Damper-Inerter (TMDI) and its special case of Tuned Inerter Damper (TID). In this paper, these inerter-based vibration absorbers [...] Read more.
The beneficial mass-amplification effect induced by the inerter can be conveniently used in enhanced variants of the traditional Tuned Mass Damper (TMD), namely the Tuned Mass-Damper-Inerter (TMDI) and its special case of Tuned Inerter Damper (TID). In this paper, these inerter-based vibration absorbers are studied for mitigating the wind-induced response of high-rise buildings, with particular emphasis on a 340 m tall building analyzed as case study. To adopt a realistic wind-excitation model, the analysis is based on aerodynamic forces computed through experimental wind tunnel tests for a scaled prototype of the benchmark building, which accounts for the actual cross-section of the structure and the existing surrounding conditions. Mass and stiffness parameters are extracted from the finite element model of the primary structure. Performance-based optimization of the TMDI and the TID is carried out to find a good trade-off between displacement- and acceleration-response mitigation, with the installation floor being an explicit design variable in addition to frequency and damping ratio. The results corresponding to 24 different wind directions indicate that the best vibration mitigation is achieved with a lower installation floor of the TMDI/TID scheme than the topmost floor. The effects of different parameters of TMD, TMDI and TID on wind-induced displacement and acceleration responses and on the equivalent static wind loads (ESWLs) are comparatively evaluated. It is shown that the optimally designed TMDI/TID can achieve better wind-induced vibration mitigation than the TMD while allocating lower or null attached mass, especially in terms of acceleration response. Full article
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17 pages, 5289 KiB  
Article
Theoretical Study on a Cable-Bracing Inerter System for Seismic Mitigation
by Liyu Xie, Xinlei Ban, Songtao Xue, Kohju Ikago, Jianfei Kang and Hesheng Tang
Appl. Sci. 2019, 9(19), 4096; https://doi.org/10.3390/app9194096 - 01 Oct 2019
Cited by 17 | Viewed by 2705
Abstract
In this paper, cables are proposed to connect the inerter and main frame for translation-to-rotation conversion, i.e., the cable-bracing inerter system (CBIS), with a magnified mass and enhanced damping effect. This novel configuration has the benefits of deformation relaxation at the connecting joints, [...] Read more.
In this paper, cables are proposed to connect the inerter and main frame for translation-to-rotation conversion, i.e., the cable-bracing inerter system (CBIS), with a magnified mass and enhanced damping effect. This novel configuration has the benefits of deformation relaxation at the connecting joints, easy installation, and an adaptive layout for nonconsecutive-story deployment. Dynamic motion equations were established for a single degree-of-freedom (SDOF) model equipped with a CBIS. The influence of dimensionless parameters, such as inertance-mass ratio, stiffness ratio and additional damping ratio on vibration mitigation were studied in terms of displacement response and force output. A single objective and multiple objective optimal design method were developed for a CBIS-equipped structure based on a performance-oriented design framework. Finally, the mitigation effect was illustrated and verified by a numerical simulation in a time-domain. The results showed that a CBIS is an effective structural response mitigation device used to mitigate the response of structural systems under earthquake excitation. Using the proposed optimization method, CBIS parameters can be effectively designed to satisfy the target vibration control level. Full article
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16 pages, 4114 KiB  
Article
Free Vibration of a Taut Cable with Two Discrete Inertial Mass Dampers
by Zhihao Wang, Fangfang Yue and Hui Gao
Appl. Sci. 2019, 9(18), 3919; https://doi.org/10.3390/app9183919 - 18 Sep 2019
Cited by 16 | Viewed by 2630
Abstract
Recently, inertial mass dampers (IMDs) have shown superior control performance over traditional viscous dampers (VDs) in vibration control of stay cables. However, a single IMD may be incapable of providing sufficient supplemental modal damping to a super-long cable, especially for the multimode cable [...] Read more.
Recently, inertial mass dampers (IMDs) have shown superior control performance over traditional viscous dampers (VDs) in vibration control of stay cables. However, a single IMD may be incapable of providing sufficient supplemental modal damping to a super-long cable, especially for the multimode cable vibration mitigation. Inspired by the potential advantages of attaching two discrete VDs at different locations of the cable, arranging two external discrete IMDs, either at the opposite ends or the same end of the cable is proposed to further improve vibration mitigation performance of the cable in this study. Complex modal analysis based on the taut-string model was employed and extended to allow for the existence of two external discrete IMDs, resulting in a transcendental equation for complex wavenumbers. Both asymptotic and numerical solutions for the case of two opposite IMDs or the case of two IMDs at the same end of the cable were obtained. Subsequently, the applicability of asymptotic solutions was then evaluated. Finally, parametric studies were performed to investigate the effects of damper positions and damper properties on the control performance of a cable with two discrete IMDs. Results showed that two opposite IMDs can generally provide superior control performance to the cable over a single IMD or two IMDs at the same end. It was also observed that attaching two IMDs at the same end of the cable had the potential to achieve significant damping improvement when the inertial mass of the IMDs is appropriate, which seems to be more promising than two opposite IMDs for practical application. Full article
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