Single Degree Of Freedom Structure Research Articles

Testing, Modelling, and Performance Evaluation of a Rotary Eddy-Current Damper with Inherent Nonlinear Damping Characteristics for Structural Vibration Control

This paper investigates the inherent nonlinear damping characteristics of a rotary eddy-current damper (RECD) and evaluates its vibration control performance on a single-degree-of-freedom (SDOF) system subjected to harmonic and seismic excitations. First, a RECD prototype was manufactured to experimentally identify its intrinsic nonlinear eddy-current damping characteristics. A magic formula model is then proposed to characterize the relationship between the eddy-current damping force and the velocity of the RECD, and its applicability in depicting the nonlinear damping characteristics of the RECD is evaluated by comparing with the electromagnetic finite-element (FE) model and the commonly used Wouterse’s model. Moreover, by comparing the experimental and analytical frequency–domain responses of an SDOF structure equipped with a RECD, the applicability of the magic formula model in evaluating the structural vibration control performance of the RECD is further verified. Finally, the control performance of the RECD for an SDOF structure subjected to earthquake ground motions is numerically evaluated and compared. Results show that the eddy-current damping force of the RECD presents obvious nonlinear characteristics with increasing velocity, and the proposed magic formula model can adequately depict the nonlinear eddy-current damping characteristics of the RECD. Moreover, the RECD exhibits superior structural control performance under harmonic and seismic excitations.

Phản ứng động đất của các hệ nhị tuyến tính đàn - dẻo và tự tâm định dưới tác dụng của các chuyển động nền do động đất xa và gần

This study presents seismic response of single degree of freedom (SDOF) elasto-plastic and self-centering systems under far and near-fault ground motions. These parameters was conducted to determine the influence on SDOF structure response in term of ductility, absolute acceleration, absorbed energy, strength ratio and strength reduction factor. It was found that maximum ductility for bilinear elasto-plastic systems was qualitatively similar to self-centering hysteretic systems, by adjusting the value of α and β, a self-centering hysteretic systems could be made qualitatively better than bilinear elasto-plastic systems in term of ductility. With respect to the absorbed energy, the self-centering hysteretic systems always less than comparable bilinear elasto-plastic systems. A three 3-story steel frame Self-Centering Brace Frame (SCBF) was designed according AISC seismic provison to validate of response of single degree of freedom self centering systems. 20 far field earthquake groundmotion are used for analysing of three 3-story steel frame SCBF under DBE (Design Based Earthquake) and MCE (Maximum Considerded Earthquake) level by using computer program PISA3D. The maxmimun value of interstory drift are under 1% and 2%, while residual drift are small.

Damage Spectra of SDOF Structures Under Tsunami Actions Considering the Nonlinear Dynamic Analysis Method

This paper studies the damage spectra of single-degree-of-freedom (SDOF) systems for tsunami loading. The 2011 Tohoku tsunami wave traces are computed and obtained by adopting the Cornell Multi-grid Coupled Tsunami (COMCOT) model and are further verified by the Tohoku Tsunami Joint Survey (TTJS) data. The tsunami response analyses of SDOF systems are conducted taking into account the dynamic analysis method. The classical ductility damage is considered as the damage performance. The damage spectra are computed for five force reduction factors and 791 tsunami loadings. The effects of inundation depths, hysteretic model, post-yield stiffness ratio, [Formula: see text], viscous damping ratio, [Formula: see text], are explored and interpreted scientifically and statistically. The results demonstrate that the effect of the hysteretic model, force reduction factor, R, post-yield stiffness ratio, [Formula: see text], viscous damping ratio, [Formula: see text], on the damage of the structure is evident. Comparison with the static method and influence analysis of structural damping indicate the necessity for the application of the dynamic method. A simplified predictive formulation is developed for the evaluation of structural damage for tsunami loadings.

Investigation of optimum tuned mass damper parameter according to stroke capacity

During major earthquakes, civil structures may collapse due to vibration that has a frequency close to the frequency content of the structure. Because of this, control systems have also been proposed for building structures. These systems can be active ones that are controlled by electronic devices or passive ones that are tuned mechanical systems. Passive tuned mass dampers (TMDs) include mass, stiffness element and damping element and these are tuned around the frequency of the structure. For optimum tuning and the complex nature of the mathematics under random vibrations, metaheuristic algorithms are needed to be used. In the presented study, TMDs are optimized via Jaya algorithm. The control system was optimized for displacement minimization of the structure. Additionally, the stroke amount of the system was limited. The stroke capacity factor was investigated for wide limits between 0.5 and 4 for normalized stroke according to the maximum displacement of the structure. The investigation was done for a single degree of freedom structure for a general conclusion. It is observed that the stroke limit did not affect performance and optimum parameters after 2.75. The small values of the stroke limit have significantly different optimum period. <w:LsdException Locked

Duration and damping for ground motion characterization in frequency‐domain damage estimation of SDOF structures

AbstractIn estimating the damage to a single‐degree‐of‐freedom (SDOF) structure due to multiple earthquake events, it may be convenient to use a frequency‐based approach, in which the anticipated ground motions are characterized through power spectral density functions (PSDFs) compatible with the specified design spectra for those motions. Since a spectrum‐compatible PSDF corresponds to a fictitious stationary ground motion process of a specified duration, the duration of this process should preferably be same as the length of the stationary segment in the actual ground acceleration process for a meaningful computation of the stochastic response. On assuming the strong‐motion segment of a given ground motion to represent its stationary segment, the nonstationarity of the strong‐motion segment is evaluated for the existing strong‐motion duration definitions. It is found that the Trifunac‐Brady definition is the most reasonable strong‐motion duration definition in respect of consistently giving the longest strong‐motion segment with least nonstationarity. Further, a spectrum‐compatible PSDF can be used for estimating the stochastic response of a linear system, provided the system has the same damping ratio as that of the design spectrum from which the PSDF has been computed. This causes errors in estimating the peak response of an equivalent linear system due to its damping ratio being higher than the initial damping ratio of the nonlinear system. To address this, an empirical expression is developed for the modified damping ratio of a linear system, which would lead to the correct peak response of the system on using the PSDF obtained from the 5%‐damping design spectrum.

Design of Optimal Passive Tuned Mass Damper with Static Output Feedback and Updating Iterative Procedure

In this study, the optimal design issue of a passive tuned mass damper (TMD) was transformed into the nonsparse control gain matrix optimization problem, and a general passive TMD optimization design method to minimize structural mean square responses or impulse response is therefore proposed. The proposed optimization procedure combines the static output feedback (also known as direct output feedback) algorithm and the updating iterative procedure. The proposed method can be applied to variant design scenario, whether the main structure is single-degree-of-freedom (SDOF) or multidegree-of-freedom (MDOF) structures, undamped or damped structures, subjected to wind disturbances or earthquake excitations. In addition, the proposed method is capable to consider the excitation shaping filter, so the design results are more suitable for practical application. The design procedure of the proposed method is presented, and all the required weighting matrices are introduced and derived in detail. Firstly, the SDOF structures are used as the main structure to demonstrate the correctness of the proposed method. The numerical simulation results verify that the obtained optimal design parameters of TMD were found identical to some cases which contain the analytic solution. The accuracy and feasibility of the proposed design method are confirmed. Finally, a passive TMD is optimally designed for a 5-story MDOF structure subjected to Kanai–Tajimi spectrum comparable earthquakes and a 60-story high-rise MDOF structure subjected to Davenport spectrum comparable wind loads for demonstration.

Shared vibration absorbers for connected SDOF structures

This paper considers the response reduction of structures connected with shared vibration absorbers. The response of two single-degree-of-freedom (SDOF) structures next to each other are minimized by a connected mass damper as an absorber. The optimum values of the damper’s properties are obtained by using metaheuristic algorithms. The objective function is taken as the H2 norm of the regulated outputs, where the regulated outputs are taken as displacements of both structures. To simplify the problems, the stiffness and damping properties of the absorber are taken the same. Genetic algorithms are used to optimize the absorber parameters. Two cases are considered in the numerical examples. The first case is when we have twin buildings, in which each structure’s mass, stiffness, and damping are the same. The second case is when the structure stiffnesses are different, one is the stiff structure, and another is the flexible one. Several dampers’ constraints are considered to see the possibilities of the connected absorber to reduce the structural responses. The simulations of the structures subjected to four selected ground excitations were carried out to show the absorbers’ performance in reducing the structures’ response with different percentages of reductions.

On energy dissipation or harvesting of tuned viscous mass dampers for SDOF structures under seismic excitations

In the past decade, tuned viscous mass dampers (TVMD) have been demonstrated as effective seismic resistant dampers. However, theoretical study on energy dissipation or energy harvesting of the TVMD has rarely been investigated, particularly, whether or not its optimal passive vibration control and energy dissipation maximization are consistent remains questionable. Here, from the theoretical perspective, we present an analysis of energy dissipation or energy harvesting of the TVMD in terms of damping power or output power, respectively. We derive the closed-form solutions of the average damping power of a single-degree-of-freedom (SDOF) structure-TVMD system under white-noise base excitations or seismic excitations modeled by the Kanai-Tajimi spectra, which is verified against the Monte Carlo simulations. Based on the closed-form solutions, the influences of the TVMD parameters, site conditions, and structural dynamic characteristics on the average damping power are analyzed via a parametric study. Theoretical results indicate that structural damping, site condition, structural period, frequency ratio, and inertance-to-mass ratio have a significant impact on the damping power or dissipated energy. In addition, the TVMD dissipates much more energy at a soft-soil site than at a stiff-soil site. At a stiff-soil site, the TVMD dissipates more energy for a short-period structure than for a long-period structure, however, at a soft-soil site, the law is the opposite. The study also presents the theoretical upper bound of the output power of an energy-harvesting TVMD. Particularly, results also illustrate that the maximization of TVMD energy dissipation is not consistent with the optimal passive vibration control. This study may shed light on the TVMD studies for seismic response control or energy harvesting purposes in the years to come.

Experimental study of model-free vibration control based on a virtual controlled object considering parameter uncertainty of actuator

This study experimentally verifies robustness of a model-free vibration controller based on a virtual controlled object (VCO) considering parametric uncertainty of actuator. A proof-mass actuator, which can be modeled as a single-degree-of-freedom (SDOF) system, is used. A VCO, which is defined as an SDOF structure, is introduced between a real controlled object and the actuator model. The parameters of the VCO are determined so as to achieve model-free vibration control. A state equation to derive the model-free controller is constructed using the two-degree-of-freedom (2DOF) structure composed of the actuator model and the VCO. The parametric uncertainty of the actuator is quantitatively characterized in the 2DOF structure. The mixed [Formula: see text] control theory is used to design a model-free controller. The vibration suppression performance and robustness to the actuator uncertainty of the proposed method are validated by experiments. Simulation studies are also conducted to enhance the validity of the experimental results. As a result, the proposed damping method exhibits good damping performance and strong robustness to the actuator uncertainty and characteristic changes in controlled object.

Damage boundaries on shock response spectrum based on an elastic single-degree-of-freedom structural model

Damage boundary based on a single-degree-of-freedom (SDOF) structural model under shock environment is studied in the present paper. Shock environment applied to the SDOF structure is characterized by different shock-waveforms. For an SDOF model with small damping, its shock damage boundary consists of three characteristic lines intersecting at a point, i.e. the isodamage absolute acceleration asymptote, pseudo velocity horizontal line and relative displacement asymptote in different frequency regimes. The upper and lower damage bounds on 4-coordinate pseudo velocity shock response spectrum (PVSRS) graph are proposed, which are associated with generic shock-waveforms with sufficiently large and small shock-waveform coefficients, respectively. The validity of the upper and lower damage bounds proposed in this study is demonstrated using an idealized mass-plate model with pins subjected to shock loads characterized by various shock-waveforms. Particularly, the lower damage bound underpins the use of PVSRS ‘damage metric’ as a rule-of-thumb in various engineering fields. It also shows that the proposed method is suitable for real shock environment.

Optimization of Seismic Base Isolation System Using Adaptive Harmony Search Algorithm

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.

Mitigation of Flow-Induced Vibration of Steel Catenary Risers with Pounding Tuned Mass Damper

Steel catenary risers (SCR) have been widely used in the offshore oil industry. This paper proposes using a novel vibration control device, i.e., the pounding tuned mass damper (PTMD), to mitigate the flow-induced vibration of an SCR. The numerical model of the SCR and the PTMD has been established in ANSYS. The soil-pipe interaction is simulated by nonlinear springs based on p-y curves. A single degree of freedom structure is utilized to verify the PTMD model established in ANSYS using APDL. Afterwards, numerical studies are carried out to validate the vibration control performance of the proposed PTMD and to investigate the influence of mass ratio and the location of the PTMD. The numerical results imply that the PTMD is very effective in reducing the displacement of the SCR under different oceanic conditions. The vibration control effectiveness will increase with the increase in mass ratio. The maximum vibration reduction is achieved when the PTMD is located at the place where the largest amount of motion takes place.

Insight into energy dissipation behavior of a SDOF structure controlled by the pounding tuned mass damper system

AbstractThe purpose of this paper is to present an innovative insight into the behavior and energy dissipation mechanism of a single‐degree‐of‐freedom (SDOF) structure controlled by pounding tuned mass damper (PTMD). In this study, a shake table test was conducted to investigate energy response of the SDOF structure incorporated with PTMD and subjected to seismic excitations. Moreover, SDOF structure and the updated analytical structural pounding force model based on viscoelasticity of materials have been investigated for parametric studies, including dynamic parameters of the primary structure, properties of PTMD, and characteristics of the earthquake records. The influence of these parameters has been discussed in details in this paper. The results showed that energy can be dissipated by PTMD as well as via the three traditional ways of TMD. The energy dissipated by PTMD keeps increasing during excitation, which is similar to the process of energy dissipated by damping mechanism. Furthermore, energy dissipated by damping and PTMD are nearly equal, and the two types of energy dissipation predominate the behavior of the system. Hysteretic, recoverable elastic strain and kinetic energy of the controlled structure diminish to very low level during earthquakes.

On the structure dynamic response of a coastal structure subject to the dam break induced surge impact pressure

ABSTRACT Detailed laboratory datasets of the dam break-induced surge impact pressures measured by Lobovský et al. are analyzed, upon which the dynamic amplification factors (DAF) of the single degree of freedom structures with different natural periods are calculated to quantify the dynamic responses of the measured total pressure series, the decomposed impulsive and quasi-steady pressure series based on the Hilbert-Huang transform algorithm. The maximum DAFs of the measured total and decomposed impulsive pressure series increase with the decrease of structure natural periods, while those of the decomposed quasi-steady pressure series show no relation with structure natural periods. The impulsive pressure is more influential to structures with small natural periods, whereas the quasi-steady pressure plays a predominant role regarding structures with large natural periods. Due to the resonance effect, the oscillatory pressure can significantly increase the maximum DAFs and delay its occurrence time of the measured total pressure series for structures with small natural periods. Nevertheless, the damping effect can generally decrease the DAFs of structures and therefore the resonance effect. Considering the damping coefficient varies from 0 to 0.1 in reality, increase of the maximum DAF induced by resonance is non-negligible for structures with small damping and short natural period.

Clutching inerters enhanced tuned mass dampers for structural response mitigation under impulsive and seismic excitations

Inerters, a type of two-terminal inertial elements, have significantly enhanced the performance of conventional control devices. The clutching inerters are especially appealing since they take energy away from the structural system without transferring back. In this study, a clutching inerter enhanced tuned mass damper (TMDCI) is proposed. First, the formation of the TMDCI is described based on a tuned mass damper inerter and two clutching flywheels. Then, the equations of motion are derived for the TMDCI on a single-degree-of-freedom (SDOF) primary structure. Subsequently, the modal properties of the TMDCI system are revealed by examining the steady-state responses under harmonic ground excitations. Afterward, performance analyses are conducted for the TMDCI on SDOF and three-DOF steel structures when subjected to initial velocities. The frequency robustness and parametric sensitivity of the TMDCI are evaluated on the SDOF structure, whereas practical concerns regarding the hosting location and stiffness demand of the TMDCI are addressed on the three-DOF structure. Finally, the seismic performance of the TMDCI is investigated on the three-DOF structure under a suite of earthquakes. The results show that the TMDCI exhibits a large damping effect which can reduce responses in both the structure and device and maintain strong robustness against frequency uncertainties. This study demonstrates the great potential of TMDCIs as an effective and affordable control strategy for the seismic protection of structures.

Exploration of the Nonlinear Effect of Pendulum Tuned Mass Dampers on Vibration Control

Understanding the nonlinearity of pendulum tuned mass dampers (PTMDs) under large-amplitude vibration is important to enhance control performance. Here, the nonlinear effects of PTMDs on vibration control of a single-degree-of-freedom (SDOF) system under harmonic excitation are explored. The nonlinear governing equations of the linear SDOF structure coupled with the PTMD are formulated. The results obtained via the method of harmonic balance under various excitation amplitudes are compared with those obtained employing the linearized system. It is shown that the effects of PTMD nonlinearity can be ignored when the PTMD rotation angle is below about 9°. Upon increasing the excitation amplitude, remarkable differences are observed between the nonlinear and linear frequency response functions (FRFs). Large mass ratios of PTMD are found to lead to reduced PTMD motion and attenuated nonlinear effects. A parametric study is performed to find the optimal parameters of the nonlinear PTMD under various excitation amplitudes. The results indicate that the optimal tuning frequency ratio increases significantly with excitation amplitudes, whereas the optimal damping is less sensitive to excitation amplitudes. Finally, a 61-m-high steel chimney structure subjected to harmonic and random wind loadings is investigated to verify the proposed PTMD design method.

A Framework with reduced computational burden for Seismic Fragility Assessment of Reinforced Concrete Buildings in High-Intensity Seismic Zones

The current research is targeted to develop the analytical fragility relationships of reinforced concrete (RC) buildings in high-intensity seismic zones by considering the effects of higher structural modes to reduce the computational effort. A new framework is presented in the study to assess the vulnerability in terms of the fragility relationships that can consider the modal response of individual modes in a building structure. The developed methodology considers the uncoupled modes of a structure employing a nonlinear single degree of freedom structures and defines distinct limit states for each mode separately. By using the presented methodology, the response of higher modes can be incorporated in the fragility assessment. For elucidation, a two-story reinforced concrete (RC) school building structure is selected from seismic zone 4 of Pakistan. In the first place, its vulnerability is assessed by developing fragility relationships using dynamic response history analysis of full three Dimensional nonlinear analytical models, subsequently, the fragility relationships are developed using the presented methodology by considering the first two modes of the structure. Afterward, a comparison has been made between the developed fragility curves from both of the methodologies. The results prove the effectiveness, swiftness, and the simplicity of the established methodology for carrying out the vulnerability assessments without compromising any accuracy. The developed framework reduces the computational time of one calculation cycle from 72 h for conventional methods to merely 4 h using a regular computer.

Evaluation of Soil–Structure Interaction in Structure Models via Shaking Table Test

Modeling the soil–structure interaction (SSI) in seismic design involves the use of soil response curves for single-degree-of-freedom (SDOF) structures; however, real structures have multiple degrees of freedom (MDOF). In this study, shaking-table-derived p-y curves for SDOF and MDOF superstructures were compared using numerical analysis. It was found that an MDOF structure experienced less displacement than an SDOF structure of the same weight, but the effect of increasing the DOF decreased at greater pile depths. Numerical analysis results estimated using the natural periods and mass participation rates of the structures were similar to those of shaking table tests. Abbreviations: finite element: FE; frequency response function: FRF; multiple degrees of freedom: MDOF; single degree of freedom: SDOF; soil–structure interaction: SSI.

Study on Pounding Response of Adjacent Inelastic SDOF Structures Based on Dimensional Analysis

The dimensional analysis method is applied to study the pounding response of two inelastic single-degree-of-freedom (SDOF) structures under simplified earthquake excitation. The improved Kelvin pounding model is used to simulate the force and deformation of the collider during the contact process. Using bilinear interstory resistance model to simulate the inelastic characteristics of SDOF structures, the expression of dimensionless pounding force and the dimensionless equation of motion during the pounding process are deduced. When dimensionless parameters are used to represent the colliding equation of adjacent inelastic SDOF structures, the variables affecting the pounding response of the adjacent structures are reduced from 14 to 11, which can clearly reflect the rules during the pounding process. The correctness and superiority of the improved Kelvin model are verified by comparing the pounding responses between the improved Kelvin model and Kelvin model. The pounding response of the two inelastic SDOF structures with improved Kelvin model is illustrated in the form of spectra, and the self-similarity of pounding response of the two inelastic SDOF structures is revealed. The effects of structural parameters on the pounding response are analyzed. The results show that the effects of mass ratio, frequency ratio, and initial spacing between the adjacent inelastic SDOF structures on the pounding response of the left-side structure (with smaller mass and stiffness) are closely related to the division of spectral regions. For the right-side structure with larger mass and stiffness, the amplification of pounding on structural response increases with the increase of mass ratio Π m and decreases with the increase of frequency ratio μ and structural spacing Π d .

A Double Shape Memory Alloy Damper for Structural Vibration Control

Shape memory alloy (SMA) dampers are widely investigated passive control systems for structural vibration mitigation. However, the damping robustness of conventional austenite SMA dampers may be affected by environmental temperature. In this study, an innovative double SMA damper (DSD) system is presented to improve the temperature robustness of the SMA dampers. In the proposed system, double SMA hysteretic elements with different phase transition temperatures are arranged in parallel, where the SMA element with lower transition temperature behaves as austenite under room temperature, and the other with higher transition temperature behaves as martensite. To study the vibration control effect, both single-degree-of-freedom (SDOF) and multiple-degree-of-freedom (MDOF) structures with DSD systems are employed. The thermal and mechanical behaviors of the SMA elements and the working principle of DSD are also introduced. Thereon, the equivalent linearization method for SMA’s output force and the motion-governing equations for SDOF structure with DSD are derived. Moreover, parametric studies are conducted to investigate the performance of the proposed DSD system in both frequency and time domains. Also, numerical analysis for the MDOF structure with DSD systems is carried out to illustrate the trend in response reduction with an increasing number of degrees of freedom. The analytical results show that the DSD can mitigate the structural seismic response more effectively than the conventional one with acceptable residual deformation, and is capable of delaying the degradation of SMA’s energy dissipation capacity. Less SMA material is required for the proposed DSD to fulfill the same mitigation requirement, and it is suitable for general applications for temperature robustness.