Stiffness Damping Research Articles

Simplified seismic design procedure for steel MRF structure with nonlinear viscous dampers

This paper presents a simplified design procedure (SDP) for performance-based design of low-rise new steel MRF buildings with nonlinear viscous dampers. The SDP uses an effective stiffness and equivalent damping for a multi degree-of-freedom (MDOF) model of the MRF building, which is established using a linearized model of the damping system (damping devices and the associated bracing). The SDP is an integrated design process for the steel MRF and the damping system to achieve target performance objectives. The SDP is consistent with the analysis procedures in ASCE 7–16 for seismic design of conventional structures without dampers, however, differentiated from the analysis procedures for structures with dampers without the computation of effective period and effective damping ratio as a function of the ductility demand on the structure. The SDP was validated using nonlinear dynamic time history analyses (NDTHA) results for a 4-story example steel MRF building with nonlinear viscous dampers with two scenarios of damper arrangements in the building. The MRFs were designed for various base shear design strength levels (i.e., 100%, 75%, 60%, 50% and 40% of the required base shear design strength of ASCE 7–16), and nonlinear viscous dampers were sized and added to the MRFs to control the story drift response. The results presented in this paper show that performance objectives for the SDP can be selected and achieved using a MRF designed with smaller base shear design strength than a conventional MRF.

Nonlinear dynamic response of an isolation system with superelastic hysteresis and negative stiffness

The negative stiffness exhibited by bi-stable mechanisms together with the tunable superelasticity offered by shape memory alloy (SMA) wires can enhance the dynamic resilience of a structure in the context of vibration isolation. The effects of negative stiffness and superelastic damping in base-isolated structures are here explored by carrying out an extensive study of the nonlinear dynamic response via pathfollowing, bifurcation analysis, and time integration. The frequency-response curves of the isolated structure, with and without the negative stiffness contribution, are numerically obtained for different excitation amplitudes to construct the acceleration and displacement transmissibility curves. The advantages of negative stiffness, such as damping augmentation and reduced acceleration/displacement transmissibility, as well as the existence of rich bifurcation scenarios toward quasi-periodicity and chaos, are discussed.

Fault identification in cracked rotor-AMB system using magnetic excitations based on multi harmonic influence coefficient method

On-site estimation of multiple fault parameters has been performed in a rotor integrated with active-magnetic bearing (AMB) with a cracked shaft supported on flexible conventional bearings. In addition to external viscous damping (at flexible bearings), internal damping (at transverse crack) is considered to show its influence on the dynamics of the cracked system. The instability generated in the rotor system due to the effect of internal damping at high speed are reduced with the control action of the AMB. A Multiple Harmonic Influence Coefficient Method (MHICM) has been proposed that requires the full spectrum amplitude and phases of the rotor responses and excitation forces to obtain the fault parameters of the rotor. The additive crack stiffness, residual unbalances, and internal damping can be estimated in the operating condition with less information on the rotor system. The intensity of the fault parameters is required to be monitored periodically to identify the safe operating speed of the system. As the AMB is an integral part of the rotor system, the multi-harmonic excitation can be initiated without changing the physical condition of the system. To check the robustness of the algorithm, different percentages of random noise are added to the rotor responses.

Influence of Negative Stiffness Damper on Stay Cable with Neoprene Rubber Bushings

AbstractStay cables on cable-stayed bridges are inherently low-damped flexible structural members. In order to improve their energy-dissipating capacities, external dampers are installed to control...

Multiscale Analysis of High Damping Composites Using the Finite Cell and the Mortar Method

Metal lattice structures filled with a damping material such as polymer can exhibit high stiffness and good damping properties. Mechanical simulations of parts made from these composites can however require a large modeling and computational effort because relevant features such as complex geometries need to be represented on multiple scales. The finite cell method (FCM) and numerical homogenization are potential remedies for this problem. Moreover, if the microstructures are placed in between the components of assemblies for vibration reduction, a modified mortar technique can further increase the efficiency of the complete simulation process. With this method, it is possible to discretize the components separately and to integrate the viscoelastic behavior of the composite damping layer into their weak coupling. This paper provides a multiscale computational material design framework for such layers, based on FCM and the modified mortar technique. Its efficiency even in the case of complex microstructures is demonstrated in numerical studies. Therein, computational homogenization is first performed on various microstructures before the resulting effective material parameters are used in larger-scale simulation models to investigate their effect and to verify the employed methods.

An indirect bridge frequency identification method using dynamic responses of high-speed railway vehicles

The identification of bridge frequencies using dynamic responses of moving vehicles has been studied by many researchers, however, most of them assume that the vehicle moves at a relatively low speed. In the application of high-speed railway bridges, the bridge span is typically short and the train always moves at a very high speed, which implies that the duration of the vehicle traveling on the bridge is very short and the signal recorded from the vehicle is not long enough for signal processing to extract the bridge frequency. The present study proposes a new method to identify the bridge frequency from vehicles moving at a high speed by combining the responses of multiple vehicles. The theoretical analysis is conducted using the simple vehicle-bridge interaction (VBI) model. By subtracting the acceleration responses of adjacent vehicles at the same position on the bridge, the residual vehicle responses were obtained and combined, which eliminated the additional driving frequencies and avoided its interference on the bridge frequency identification. Numerical simulations are then conducted to verify the proposed method, which shows that by combining the acceleration of several vehicles to extend the overall duration of the signal, the frequency resolution can be improved and the bridge frequency can be successfully identified using vehicles travelling at a high speed. The influence of track irregularity, vehicle speed, bridge stiffness, and bridge damping on the identification results has also been studied. In addition, a multi-degree-of-freedom vehicle model is used to further verify the proposed method.

A novel structural seismic protection system with negative stiffness and controllable damping

In this paper, an innovative controllable negative stiffness system (CNSS) integrating adaptive negative stiffness and controllable damping characteristics is proposed to realise desirable vibration protection and improve adaptability, hence being effective to various earthquakes. The force-displacement relationship of the CNSS is derived as the forward model to describe its nonlinear properties. Three representative control algorithms, i.e., Linear Quadratic Regular (LQR) control, H∞ control and Sliding Mode (SM) control, are utilised for the CNSS to attain optimal control force. Based on the Takagi-Sugeno-Kang (TSK) Fuzzy inference system optimised by Non-Dominated Sorted Genetic Algorithm II (NSGAII), a novel inverse model is proposed accordingly to obtain input current according to the required control force and real-time system responses. To demonstrate the feasibility and efficiency of the CNSS for structural seismic protection, a numerical case study is conducted on a three-storey building model with CNSS installed on its first floor. Four scaled benchmark earthquakes are employed as excitations for the case study. Ten evaluation criteria are adopted to assess and verify the performance of the CNSS, and comparisons are made with that of uncontrolled and passive controlled systems. The numerical results indicate that the proposed CNSS can significantly improve the vibration control performance on all evaluation criteria simultaneously in comparison with the other two conventional systems. In addition to having good suppression effects on peak floor displacement and peak inter-storey drift, the CNSS with the SM controller demonstrates superior performance on mitigating peak structure shear and peak acceleration response of the first floor.

Identification and semi-active control of structures with abrupt stiffness degradations

This paper presents for variable stiffness tuned mass dampers (VS-TMDs) a vibration control algorithm combined with a nonlinear system identification method. The objective of the proposed approach is the control of multistory shear frame structures, which exhibit abrupt stiffness degradations. A stiffness variable control (SVC) algorithm is developed to control the stiffness of the VS-TMD, which is based on the mitigation of the potential energy of the structure. For the identification of the system parameters, an adaptive unscented Kalman filter (A-UKF) scheme is utilized. The paper describes the theoretical background of the proposed approach with its governing equations and conducts performance studies on a semi-actively controlled 2-story shear frame structure. Harmonic, white noise and earthquake excitation scenarios including seismic aftershock effects are investigated. Sensitivity studies are conducted. With the proposed approach, the abrupt stiffness changes of the structure are detected and the damper stiffness is adapted successfully. The results show that the SVC together with the A-UKF clearly outperforms the passive TMD control.

An experimental study on a self-centering damper based on shape-memory alloy wires

This experimental study investigates the behavior of a proposed damper based on austenite Nitinol wires. The damper’s design is so that the wires are always in tension under both tensile and compressive forces. Also, the damper can employ steel wires as a hybrid to enhance the performance of the damper. Steel wires can be employed in parallel with the SMA wires and in the same manner. Therefore, SMA and steel wires are stretched simultaneously in the hybrid damper state. This experimental study includes the process of training the wires and the main cyclic tests with different strain rates which leads to the extraction of the hysteresis curves of the proposed damper. A thermal study is also conducted on the employed shape-memory alloy (SMA) wires during the cyclic loadings. The results indicate that the increase of loading frequency causes the SMA wires to heat; thus, the inner area of the hysteresis curve decreases, resulting in diminished damping capacity. Also, the damper stiffness and the residual strain are increased by using the steel wires. The proposed SMA damper is employed for seismic control of a three-story steel frame to evaluate its efficiency. The results reveal that the residual drift ratios of the controlled structure are significantly decreased.

Concept and performance testing of an all-steel miniature dual stiffness damper

The double-stage yield buckling-restrained braces gradually play a role in different floors, so as to control the structural deformation pattern and hinder the weak-story collapsing. In this study, a novel all-steel damper called the miniature dual stiffness damper (MDSD) was proposed, which had the advantages of simple assembly and low cost. A series of tests was performed under quasi-static test to address the hysteretic behavior of MDSDs with different stiffness ratios of the large yield segment to the small yield segment, Kyl/Kys. The test results demonstrated that MDSDs had a stable hysteretic behavior, and the dual stiffness can be achieved by yielding successively in small and large yield segments. The second stiffness of the MDSD increased with the increase of Kyl/Kys when the elastic stiffness of the small yield segment kept unchanged. The low-cycle fatigue life of the MDSD was negatively correlated with the strain of the small yield segment. An in-series stiffness model for the MDSD was presented. The theoretical hysteretic curves of MDSDs were further obtained based on the proposed stiffness model, and a good accuracy was achieved.

Glued-in CFRP and GFRP rods in block laminated timber subjected to monotonic and cyclic loading

Current advances in timber engineering with the use of timber at longer spans necessitate the use of high performance joints. Glued-in rods exhibit high axial load capacity and stiffness and are suitable for such applications. FRP rods can increase their durability and fire performance but ways to produce progressive failure mechanisms are necessary to enhance their resilience. In this study CFRP and GFRP rods glued in block laminated timber with epoxy are investigated under both monotonic and cyclic loading. Joints with constant glue-line thickness and variable bond-line geometry are studied to induce progressive resin failure mechanisms. A stepped wedge shaped geometry with varying glue-line thickness and a mirrored version were investigated. The effect of elastic modulus (CFRP vs GFRP) and glue-line thickness on the bond strength, stiffness and material viscous damping are explored. CFRP rods exhibit 11% higher axial load capacity under monotonic loading but GFRP rods exhibit higher bond stiffness at the serviceability stage. The cyclic loading does not discount the bond performance and results in higher stiffness due to viscoelastic creep deformation. An increase in glue-line thickness results in higher axial withdrawal capacity and viscous material damping. Specimens with a wedge shaped bond-line exhibit superior mechanical performance. An FEA model is presented for a variable bond-line geometry and the numerical results agree well with the experimental findings.

Enhanced performance of airfoil-based piezoaeroelastic energy harvester: numerical simulation and experimental verification

This paper performs the detailed simulation analyses of airfoil-based piezoaeroelastic energy harvester with two degrees of freedom self-induced plunge-pitch motions, for exploring the flow field characteristic and enhancing the harvesting performance. The designing of the harvester for achieving flutter is first accomplished, finite element model is then built and simulation analyses are performed, and a prototype of the harvester system is finally fabricated. The obtained simulation results are in good agreement with the experimental and theoretical values. The effects of the key structural parameters of the harvester on flow field, aeroelastic vibration, and harvesting performance are numerically investigated. The results demonstrated that the structural parameters of the harvester determine primarily flutter onset of velocity, and consequently affect the dynamic behavior and harvesting performance. The harvester system takes place flutter and occurs limit cycle oscillations after flutter onset of velocity, which is suitable for harvesting energy. The smaller pitch structural stiffness coefficient and the more moderate both plunge stiffness and pitch damping coefficients are, the better aeroelastic vibration and output performance can be captured. A maximum output voltage of 29.08 V and output power of 3.382 mW can be harvested when the linear and cubic structural stiffness coefficients in pitch are 2.5 N·m and 100 N·m at 14 m/s, respectively, which corresponds to the power density of 21.138 mW/cm3 and demonstrates the superior harvesting performance over others. This work provides a significant guidance for designing the more efficient airfoil-based piezoaeroelastic energy harvester utilized in unmanned aerial vehicles.

High‐performance vibration isolation technique using passive negative stiffness and semiactive damping

AbstractAmong active, semiactive, and passive vibration isolation methods, active control can provide the best isolation performances. However, high‐energy consumption hinders its wide applications in civil engineering field. This paper proposes a novel vibration isolation technique based on a passive negative stiffness spring (NSS) and a semiactive device (SAD), aiming to achieve an active isolation performance by using a low‐power semiactive technique. Due to its nature of negative potential energy, an NSS enables the semiactive isolation system to provide negative transient power flow that injects power into the structure and avoids the clipping phenomenon of semiactive control forces. Consequently, the combined NSS and SAD isolation system can perfectly generate the theoretical control forces calculated by an active control algorithm and achieve a considerably improved semiactive isolation performance. The prospects and performance advantages of the proposed NSS and SAD isolation system are validated through a series of numerical simulations of single‐degree‐of‐freedom and multi‐degree‐of‐freedom structures excited by various types of ground motions and a benchmark building model excited by seismic ground motions.

The effect analysis of the stiffness changes of a Traditional Fishing Boat Foundation on Vibration Amplitude

The ship with the outboard engine is intended to make it easier for fishers to operate and maintain. However, the magnitude of the vibration due to the excitation of the engine during operation adversely affects the surrounding structures. It is evidenced by measuring the vibration amplitude of more than 0.02 mm at several points around the ship engine foundation. This study aims to reduce these vibrations by changing the canal's dimensions as a foundation and using damping rubber as the simplest solution. The analysis was carried out by calculating the vibration parameters of 2 types of machines, SR1110 and S1100. The numerical method is used to calculate the vibration's amplitude by varying the value of channel stiffness and rubber damping on the machine foundation. Supporting data is obtained by measuring the vibration amplitude at several points around the foundation. The magnitude of the previous vibration amplitude is 0.078 mm for the SR1110 type and 0.069 mm for the S1100 type, which exceeds the limit still. The amplitude is reduced by changing the foundation's dimensions and using a rubber damper (c). With the new foundation dimensions, the amplitude for the diesel engine type SR1110 becomes 0.0245 mm and type S1100 becomes 0.0238 mm. Increased stiffness and the addition of rubber succeeded in reducing the vibration amplitude by a significant value. The amplitude was reduced by 69% for the SR1110 engine type and 65% for the S1100 engine type within the allowable limit of less than 0.02 mm to 0.03 mm based on Barkan's observation results.

Resetting passive stiffness damper with passive negative stiffness device for seismic protection of structures

The objective of the present study is to investigate a new energy dissipation system that combines the positive stiffness of the resetting passive stiffness damper (RPSD) with the negative stiffness of a passive negative stiffness device (PNSD). The displacement-based adjustable stiffness and energy dissipation (D-BASED) system can be designed to have independent damper stiffness and energy dissipation. Equations for modeling the RPSD and PNSD components of the D-BASED system are presented, along with an approach for designing the PNSD component. The results of laboratory experiments on a small-scale prototype D-BASED system are provided for validation of the concept. Numerical simulations are performed for the D-BASED system installed in the isolation layer of a five-story base-isolated building subject to a suite of near-field earthquake ground motions. The performance of the D-BASED system with the same net stiffness, but different levels of energy dissipation, is compared with that of the RPSD alone. It is shown that increasing the RPSD- and PNSD-component stiffness in the D-BASED system results in a reduction in the peak base drift compared to the RPSD, while limiting the building story drifts. Furthermore, it is shown that increasing the RPSD- and PNSD-component stiffness generally does not lead to an increase in the peak total force transmitted to the foundation. The D-BASED system is also found to yield smaller peak story drifts and foundation forces compared to a passive linear fluid viscous damper for a long-period base-isolated building.

Research on dynamic behavior and traffic management decision-making of suspension bridge after vortex-induced vibration event

Long-span suspension bridges are susceptible to wind loads due to their lightweight, low stiffness, and small structural damping. Recently, two large-span suspension bridges in China that closed for several months due to COVID-2019 experienced large-scale and continuous vortex-induced vibration shortly after reopening to traffic, and the traffic was closed again for safety consideration, which has aroused widespread concerns in society. To provide a reference for owners and related decision-making departments whether to restore the traffic, this article intends to explore the impact mechanism of traffic loads on the dynamic behavior of suspension bridges. First, two mechanical models for suspension bridges considering traffic loads and structural damping are proposed in this article. Then, based on the extended dynamic stiffness method, the explicit expressions of modal damping ratio in the two models are derived for the first time. Subsequently, Wittrick–Williams algorithm is employed to solve the frequency equation to obtain the modal frequency of the structure that considers the effect of traffic loads. A numerical case is studied to inspect the influence of traffic loads on the structural dynamic characteristics. Moreover, field monitoring data of accelerations of a suspension bridge are utilized to demonstrate the reasonability and accuracy of the approach proposed. Analysis shows that the theoretical results are consistent well with the measured ones, which indicates the traffic loads will affect the dynamic characteristics of the suspension bridge, thus reducing the modal frequency and increasing the modal damping ratio. Besides, the measured results further explain that the contribution of traffic loads to the structural damping is significant, which has a positive effect on preventing and eliminating vortex-induced vibration response. Some interesting and enlightening conclusions are also obtained in this article.

The Characteristics of Rotordynamic Forces generated by Mechanical Seals

Evaluating rotordynamic reaction force caused by whirl excitation is very effective technique in order to investigate the dynamic properties of the mechanical seal. Especially, it is easy to understand the stability of the rotating component by investigating rotordynamic tangential force. In this paper, the stability of the mechanical seal was discussed by measuring the rotordynamic tangential force depending on the whirl frequency. Judging from the result, the mechanical seal used for this study has stable performance that the tangential force always acts against whirling direction at 1,000 rpm of rotational speed and up to 30 Hz of whirl frequency. Furthermore, whirl frequency ratio and effective damping were calculated using cross-coupled stiffness and direct damping which were obtained by solving quaternary linear equations after whirl excitation test. Whirl frequency ratio was always bellow 1.0, and effective damping was also always positive at all frequencies. Those results indicate that the mechanical seal definitely generate the force to stabilize this whirl vibration.

Design and Analysis of an Aerostatic Pad Controlled by a Diaphragm Valve

Because of their distinctive characteristics, aerostatic bearings are particularly suitable for high-precision applications. However, because of the compressibility of the lubricant, this kind of bearing is characterized by low relative stiffness and poor damping. Compensation methods represent a valuable solution to these limitations. This paper presents a design procedure for passively compensated bearings controlled by diaphragm valves. Given a desired air gap height at which the system should work, the procedure makes it possible to maximize the stiffness of the bearing around this value. The designed bearings exhibit a quasi-static infinite stiffness for load variation ranging from 20% to almost 50% of the maximum load capacity of the bearing. Moreover, the influence of different parameters on the performance of the compensated pad is evaluated through a sensitivity analysis.

Parametric study on seismic response of the knee braced frame with friction damper

The present study deals with a new system based on the combination of knee bracing frame and friction damper (KBFD). The friction damper used in the present study was constructed as a linear friction damper with long slotted holes. Four specimens of these dampers were tested under cyclic loading, and their load-displacement curves were outlined. Then, the numerical model was obtained by modeling the dampers in the finite element software validated with experimental results. By placing this type of damper in the numerical model of KBF frames, the parametric study of KBFD frames was performed under cyclic loads. The number of 42 frames were used in the present research, including six types of dampers in seven types of frames. Reports of analysis results could cover the hysteresis curves, initial and secant stiffness, frame resistance, dissipated energy and equivalent viscous cyclic damping coefficients. The results of analyses demonstrate the excellent seismic performance of the frames with the proposed configuration.

Equivalent Beam Model for Spatial Repetitive Lattice Structures with Hysteretic Nonlinear Joints

This study presented an equivalent modeling method for analysis of the fundamental harmonic response of the spatial repetitive lattice structures with hysteretic nonlinear joints. Firstly, the joint was modelled as a spatial nonlinear spring-damper system with bilinear hysteresis, the equivalent linear stiffness and viscous damping coefficients of the hysteretic joint were derived using the describing function method. Subsequently, high-precision displacement and rotation fields that consider the warping and distortion of the cross section of the lattice structure were presented for the repeating element and the equivalent continuum modeling method based on the principle of energy equivalence was adopted to obtain an 8-DOFs spatial beam element for the repeating element of the lattice structure. Afterwards, the equations of motion of the equivalent beam model for the lattice structure were established in the frequency domain and solved by using the Newton-Raphson method. In the numerical studies, the joints with axial nonlinearity and rotational nonlinearity were considered, and the influences of joint parameters and excitation amplitude on the dynamic response of the lattice structure were investigated. The correctness of the presented modeling method was verified by comparison with the nonlinear finite element model of the original structure.