Optimal Damping Ratio Research Articles

Industrial pipeline vibration attenuation with magnetorheological tuned mass damper

In order to solve the high-frequency vibration problem of industrial pipeline in petrochemical enterprises, a tuned mass damper (TMD) based on magnetorheological (MR) technology was proposed. The magnetorheological-tuned mass damper (MR-TMD) can reduce the vibration response of the structure by tuning resonance with the pipeline system, it can also have the semi-active control characteristics of MR devices. By analyzing the vibration signals collected on the pipeline site, the relevant design requirements and parameters of the damper were determined. The optimal frequency ratio, passive damping, and mass ratio of the damper were determined using the optimal design theory. Meanwhile, the high-performance MR composite was prepared for the working conditions of MR-TMD and a modified Herschle-Bulkley model was derived to characterize the behavior of the material. Furthermore, the mechanical performance of the proposed MR-TMD was tested, the output damping force is about 890.5 N when the applied current is 2 A, which can meet the working requirements of pipeline vibration attenuation. Then, according to the established vibration control model of pipeline system, the vibration system was simulated and analyzed combined with LQR algorithm, and the vibration attenuation performance in different conditions were predicted and compared. The research shows that the TMD combined with MR technology can effectively reduce the vibration of industrial pipeline system.

Theoretical analysis, simulation, and field experiment for vibration mitigation of suspender cables/hangers using the four‐wire pendulum tuned mass damper

AbstractSuspender cables/hangers occupy a crucial role during the whole service life of suspension bridges/arch bridges/space structures, and their long‐term repeated vibration under corrosion and high‐stress service state will cause fatigue damage and even induce fatigue failure. To mitigate the vibration of the vertical suspender cables/hangers, a four‐wire pendulum tuned mass damper (FWPTMD) is proposed. It mainly consists of the cross bracket, four pendulum ropes, the moving mass, and four universal rotating ball hinges that can rotate in any direction and provide damping. A suspender cable in a real suspension bridge is selected as the research object. First, the design procedure and effect of the modal mass ratio are provided; the optimization design method for parameters of optimal frequency ratio and optimal damping ratio is investigated in detail. Second, simulations are conducted to illustrate its feasibility, and results show excellent vibration mitigation effect. Third, the optimal FWPTMD is designed and fabricated; its performance is further validated by field experiments, and the results are very close to those in simulation. The FWPTMD has the advantages of simple structural form, convenient installation, low cost, easy tuning, easy maintenance, and so forth. Therefore, it can play an obvious vibration mitigation role in the life‐cycle of the suspender cable/hanger, and it has a positive meaning to retard fatigue damage, extend the service life, and assure traffic safety under extreme weather.

Wind-Induced Vibration Control of High-Rise Buildings with Double-Skin Façades Using Distributed Multiple Tuned Façade-Dampers-Inerters

To address the shortcomings of tuned mass dampers (TMD), such as excessive internal space occupation and overlarge physical mass, this paper proposes a tuned façade damper inerter (TFDI) that utilizes parts of the outer façades of double-skin façades (DSF) as damping mass, capitalizing on the lightweight and efficient characteristics of inerters. The TFDI effectively resolves the challenge of multi-layer connections of inerters in high-rise buildings by utilizing corridor space. By vertically distributing TFDIs, a distributed multiple TFDI (d-MTFDI) system is formed. The configuration and motion of equations of this system are presented, and the control effectiveness is validated using wind tunnel test data. Two tuning modes are further proposed: unified tuning mode and distributed tuning mode. For the unified tuning mode, analytical expressions for optimal tuning frequency and damping ratio are derived; for the distributed tuning mode, numerical optimization methods are employed to determine the optimal tuning frequency range and damping ratio. Comparative results indicate that the distributed tuning mode achieves higher control efficiency than the unified tuning mode, with a significant reduction in the required optimal damping ratio. Furthermore, comparisons with d-MTMD demonstrate that d-MTFDI significantly enhances wind-induced vibration control performance.

Parameter optimization of tuned inerter damper for vibration suppression in structures with damping

This study investigates the parameter optimization of tuned inerter damper (TID) in a single degree of freedom (SDOF) system, with a focus on vibration mitigation. As a type of inerter based dynamic vibration absorber (IDVA), TID achieves vibration suppression of the primary structure by replacing the mass block in traditional dynamic vibration absorber (DVA) with an inerter, thereby minimizing the increase in physical mass. With the displacement response of the primary structure as the objective function, this study first employs the classical fixed point theory (FPT) to derive the analytical formulations for the optimal parameters of TID following the H∞ optimization approach and neglecting the inherent damping of primary structure. The influence of optimal parameter deviations on the vibration mitigation effect of TID is also analyzed, revealing that the deviation of the optimal natural frequency ratio has a significant impact on the vibration mitigation performance. By flattening the amplitude curve of the displacement transfer function of primary structure between the fixed points, this study derives the analytical solution for the optimal damping ratio of TID using the extended fixed point theory (EFPT). When the inherent damping of primary structure is considered, this study employs the approximate extended fixed point theory (AEFPT) to derive the approximate optimal parameters of TID. A comparative study of the optimal natural frequency ratios obtained using FPT, AEFPT and numerical searches reveals that the discrepancies among the three methods are minimal for structures with low inherent damping. However, as the inherent damping ratio of the primary structure increases, the optimal natural frequency ratio obtained using FPT deviates significantly from the exact value, whereas the approximate optimal natural frequency ratio derived using AEFPT can significantly reduce this deviation. Combining the conclusion that the vibration mitigation effect of TID is significantly influenced by the natural frequency ratio, this study suggests that for highly damped primary structures, the use of AEFPT can yield more optimal TID parameters, thereby enhancing the robustness of vibration mitigation performance.

Closed-form solutions for the optimal parameters of three inerter-enhanced dampers (IEDs) equipped on a ground acceleration-excited structure

Replacing the viscous damper of tuned mass damper (TMD) with the proposed inerter-enhanced dampers (IEDs), novel vibration mitigation methods, namely the IED-TMDs, are proposed. Unlike the TMD, which brings only one additional freedom into the system, the proposed IED-TMDs introduce more freedoms into the considered dynamic system. As a result, the traditional fixed-point theory cannot be used. To address this issue, this paper develops an extended fixed-point theory. Firstly, the inerter and the springs of the IED-TMDs are optimized considering that all four fixed points are of the same height. The closed-form solutions for the optimal inerter and springs of the IED-TMDs are obtained. Secondly, to obtain the optimal damping ratio for the IED-TMDs with multi-fixed points, a new optimization criterion is introduced. Different from the traditional fixed-point theory which controls the slope of the transfer function at the fixed points, the new optimization criterion assumes that the local peaks of the transfer function in between the four fixed points have the same height as the fixed points. And, a flat plateau is achieved in the transfer function. Further, the closed-form solutions for the optimal damping ratio are simplified in consideration of actual applications. Finally, the vibration mitigation performance of the IED-TMDs is evaluated. Results show that the vibration mitigation performance of IED-TMDs is superior to that of the conventional TMD. This superior vibration mitigation performance is more significant for the IED-TMDs with a smaller mass ratio.

Analytical optimization of an inerter‐based dynamic vibration absorber for suppressing plate vibration

AbstractAn inerter‐based dynamic vibration absorber (IDVA) is proposed and applied to suppress the vibration of a plate. The dynamic model of a thin rectangular plate attached with an IDVA is established and the frequency response function of the transverse displacement of the plate is derived through the classical vibration theory and the analysis in the domain. In addition, the equation for frequency ratios of fixed points is obtained, and the condition for the existence of four fixed points is found by investigating the problem of solving quartic equations. Moreover, the extended fixed‐point method is employed to analytically obtain the optimal parameters of the IDVA attached to a plate, the expressions of the optimal damping ratio and other dimensionless qualities are presented.

Extension of the fixed point theory to tuned mass dampers with piezoelectric stack energy harvester

A tuned mass damper with a piezoelectric stack energy harvester (TMD-PSEH) is a passive vibration control device for the dual purpose of absorbing vibration and harvesting energy. This paper develops the fixed point theory for the optimal design of a TMD-PSEH attached to an undamped primary structure under harmonic external excitation. It has been proven that the existence of two fixed points of the amplitude-frequency curve doest not depend on the damping of the primary structure. Based on the requirements for suppressing the vibration of the primary structure and enlarging the harvested power, the analytical expressions for the optimal tuning, damping, and resistance ratios are determined. It is found that the minimum damping ratio occurs in the vicinity of the electrical resistance ratio α=1 for various values of the electromechanical coupling coefficient. Power flow analysis is carried out resulting in closed-form expressions of instantaneous and average powers. Numerical examinations of the system with the obtained optimal parameters are performed demonstrating a very good compatibility between theory and computation. In addition, the effect of damping in the primary structure is also investigated. It is shown that not only the vibration of the primary structure effectively reduces, but also a large amount of the harvested energy can be captured in the main resonance region.

Subsynchronous oscillation suppression strategy of wind turbine’s phase-locked loop based on optimal damping ratio

The dynamic characteristics of the phase-locked loop (PLL) of the wind turbine are the key to the synchronous operation of these renewable energy sources with the power grid. In this paper, the coupled dynamic model of PLL of the permanent magnet synchronous generator (PMSG)-base wind turbine and power grid is established firstly. The complex torque method is used to calculate the synchronous and damping torque coefficients in the PLL oscillation mode. Secondly, the influence of the PLL parameter, voltage at the point of common coupling (PCC), wind turbine’s output power and electrical distance on the oscillation damping behavior of the PLL is analyzed. Further, a novel control strategy based on optimal damping ratio is proposed to suppress the subsynchronous oscillation of the system caused by wind turbine’s PLL in weak interconnected grids. Finally, a simulation model of regional power network with high penetration of wind power generation is built to demonstrate the effectiveness of the proposed control scheme in suppressing the system’s subsynchronous oscillation caused by the wind turbine’s PLL.

A Method to Improve Both Frequency Stability and Transient Stability of Virtual Synchronous Generators during Grid Faults

Transient stability and frequency stability of virtual synchronous generator (VSG)-controlled converters during grid faults are critical for the stable operation of high-share renewable energy power systems. However, the existing transient stability methods often overlook the consideration of frequency stability. This paper presents a method to improve both frequency stability and transient stability of VSGs during grid faults. The influence mechanism of inertia and damping on transient stability and frequency stability is comprehensively analyzed under two types of faults, with or without stable equilibrium points. To address the conflict between frequency stability and transient stability of VSGs with large inertia under the first type of fault, an improved VSG control with angular frequency deviation feedback is proposed. The transient response of this control method is analyzed using small-signal and large-signal models. Furthermore, to achieve optimal dynamic performance, this improved VSG control introduces the optimal damping ratio and presents a parameter design method. Finally, the correctness of the proposed method and its theoretical analysis is verified through experimental results.

Closed-form optimal design of the tuned inerter damper (TID) connecting adjacent flexible buildings

The tuned inerter damper (TID) is a viable solution for addressing the vibration issue of the adjacent-building system. However, the conventional optimal calibration of the TID is conducted based on the classic 3-degree-of-freedom (3-DOF) model with one resonant DOF for each structure, which ignored the background flexibility contribution that comes from non-resonant modes of each one, and thus leads to non-optimal control performance. This paper developed a novel analogue 3-DOF model, in which the background flexibility contribution of each flexible building at the damper attachment location is represented by an equivalent stiffness element. An enhanced formula for the TID optimal frequency is developed accordingly (targeting the fundamental mode of the taller building) using the ‘root-locus’ method, where the background flexibility as well as the resonant mode contributions that come from both buildings are accounted for. For completeness, the optimal frequency formula that ignores the background flexibility contribution is derived based on the classic 3-DOF model. A robust approach is adopted to determine the optimal damping ratio based on the classic model. Numerical analysis is conducted based on a 25-15 floors adjacent-building system. Results demonstrate that when the enhanced frequency-tuning formula is used, a much more balanced frequency response curve of the taller building is achieved. Further, time-domain seismic analysis indicates that the TID performance is consistently improved when background flexibility is accounted for in the design formulas.

Shaking Table Test and Parametric Research on Damping Performance of Centralized Damping Structure

The lateral stiffness of the external frame and internal core tube (CT) in super‐tall CT structures exhibits significant differences. This paper presents a novel centralized damping structural system (CDS), which utilizes the differential lateral displacements of the internal and external substructures by centrally installing centralized damping devices between the CT and the external frame to achieve energy dissipation and seismic mitigation objectives. First, a theoretical analysis model for CDS was established, and its dynamic transfer function was derived. Parameter analysis was conducted to investigate the influencing factors. The optimal damping ratio for CDS is determined using the fixed‐point theory. Experimental shake table tests were performed to validate the seismic mitigation effectiveness of CDS, of which the results demonstrate significant reductions in both the top‐level acceleration of the internal frame and the top‐level displacement of the external frame. Finally, comparative numerical analyses are performed between traditional structures and the CDS structures, revealing that the centralized damping structral system can effectively reduce the acceleration of the internal CT and the interstory displacement of the external frame. The CDS structure achieves superior seismic mitigation effects compared to traditional structures with fewer damping devices.

Research on fast matching method of suspension stiffness and damping based on unmanned special vehicle

At present, the domestic research on the matching of stiffness and damping of the suspension system of unmanned special vehicles mainly adopts the empirical method and experimental method. This method is time-consuming and laborious, which prolongs the development cycle of unmanned special vehicles. In order to improve the vehicle ride comfort and reduce the research and development time, based on the single wheel two degree of freedom driving vibration model, this paper analyzes the influence of suspension stiffness and damping on the acceleration response of vehicle body, deduces the general calculation formulas of acceleration, suspension dynamic deflection and root mean square value of wheel dynamic load, and establishes the mathematical model of the optimal damping ratio of suspension system based on driving safety and comfort, The damping ratio design of the suspension system of an unmanned special vehicle is completed. The results show that this method can quickly and accurately complete the stiffness and damping matching design of suspension system, and shorten the time of vehicle design and development.

Analytical Formulae and Applications of Vertical Dynamic Responses for Railway Vehicles

To effectively improve the estimated level of railway vehicles’ vertical dynamic responses and provide a more suitable reference for the selection of its secondary suspension damping parameter, this paper has derived the root mean square values analytical formulae of the car body vertical acceleration, the secondary suspension vertical stroke, and the axle box vertical action force for railway vehicles under the random excitation of the track closer to the actual track characteristics. The correctness of the analytical formulae is verified by testing a real vehicle. Then, according to the analytical formulae derived, an analytical design method of the optimal damping ratio for the secondary suspension system is constructed based on the multi-objective programming and single-objective interval constraint analysis, which can be used to find the best trade-off for conflicting performance indices, such as ride comfort, running smoothness, and running safety, and the influences of the system parameters on the optimal damping ratio are analysed. This research can effectively characterize the vertical vibration response of railway vehicles and provide an effective reference for the initial design of the railway vehicle secondary suspension damping parameter.

Damping Ratio Prediction for Redundant Cartesian Impedance-Controlled Robots Using Machine Learning Techniques

Implementing impedance control in Cartesian task space or directly at the joint level is a popular option for achieving desired compliance behavior for robotic manipulators performing tasks. The damping ratio is an important control criterion for modulating the dynamic response; however, tuning or selecting this parameter is not easy, and can be even more complicated in cases where the system cannot be directly solved at the joint space level. Our study proposes a novel methodology for calculating the local optimal damping ratio value and supports it with results obtained from five different scenarios. We carried out 162 different experiments and obtained the values of the inertia, stiffness, and damping matrices for each experiment. Then, data preprocessing was carried out to select the most significant variables using different criteria, reducing the seventeen initial variables to only three. Finally, the damping ratio values were calculated (predicted) using automatic regression tools. In particular, five-fold cross-validation was used to obtain a more generalized model and to assess the forecasting performance. The results show a promising methodology capable of calculating and predicting control parameters for robotic manipulation tasks.

Tuned Mass Damper Design of Substation Post Switchgear in Gale Area

Post switchgear of substation in a gale area is a typical wind-sensitive structure. In order to reduce the wind-induced response of substation post switchgear in a gale area, in this paper, according to the theoretical formula of the optimal frequency ratio and the optimal damping ratio of TMD given by Den Hartog, a tuned mass damper (TMD) is proposed to reduce the vibration of the first-order vibration mode outside the plane of the structure. The Simulink simulation model of the simplified structure with TMD is established and the fluctuating wind speed of the equipment is simulated by the Kaimal wind speed spectrum. The wind vibration control effect of TMD is checked, and the rationality of the TMD design is verified.

An efficient two-stage hybrid framework to evaluate vortex-induced vibration for bridge deck based on divergent vibration

High-fidelity CFD (computational fluid dynamics) numerical modeling offers an attractive alternative of VIV investigation for bridge deck. Conventional strategy to perform VIV prediction using CFD is to directly characterize the two-way coupled free vibration of structure and flow which could become dramatically expensive in computational cost. To bridge the gap, this study presents an efficient two-stage hybrid approach that combines a divergent vibration simulation for fast aerodynamic damping extraction and a nonlinear model to predict the VIV. A negative structural damping is imposed in the motion equation to intentionally create a divergent vibration which significantly accelerates the growth of motion and takes less than 1/3 of the elapsed time compared with a conventional VIV simulation whereas maintains reasonable accuracy in aerodynamic identification. A Π-shaped bridge deck is employed as a demonstration of the proposed approach. The modeled steady-state VIV performance is well validated against wind tunnel tests. The effect of negative damping on instantaneous flow field, surface pressure and amplitude prediction are discussed and the optimal damping ratio achieving balanced accuracy and efficiency is suggested. The proposed framework shows favorable efficiency while simultaneously retains satisfactory accuracy and is a potential numerical alternative of VIV investigation for bridge deck.

Transverse Third-Damper to Improve Suspension Systems for In-Wheel Motor Driven Electric Vehicles

Abstract The commensurate increase of unsprung mass due to in-wheel motors can have negative effects on either ride comfort or roadholding capability of electric vehicles (EVs). To counteract those effects, semi-active or fully active suspension systems are deployed, which tend to be high-energy consumers. This is undoubtedly problematic for EVs, since battery life and range are already limiting factors in design. Furthermore, when performance is comparable, passive suspension systems are preferred due to their simplicity, higher reliability, lower implementation cost, and zero energy consumption. In this work, using an energy-based approach, we conduct the frequency analysis response of a suspension system containing a transverse third-damper. A transverse half-car model is employed, and the behaviors of both wheels are analyzed based on disturbances on one wheel. Our results show that with an optimal damping ratio for the transverse damper, the amplitude ratio at the second resonance of one wheel could be significantly decreased, especially for high (≈80 kg) and medium (≈60 kg) unsprung masses. The implication is that the decrease in roadholding capability and reliability of the motor bearings associated with in-wheel motors can be mitigated. Additionally, the behavior of the sprung mass with the third-damper suspension system was identical to that of the conventional system (though the analysis was strictly limited to vertical motion). Therefore, due to its passive nature, the third-damper suspension system design is a low-cost solution that may be able to achieve the goals of improving roadholding without affecting rider's comfort. Future experimental work and other types of analysis (e.g., roll dynamics) should be carried out to provide a more complete picture of third-damper suspension system behavior.

The exact closed-form equations for optimal design parameters of enhanced inerter-based isolation systems

This paper introduces the enhanced inerter-based isolation system (EIBI) to improve broadband vibration control. Using the H2 optimization method, the exact closed-form expressions for the optimal design parameters of the EIBI, such as the frequency and viscous damping ratio, have been derived analytically. The optimal frequency and viscous damping ratios of EIBI decrease as the mass ratio of the EIBI increases. For optimal design purposes, the optimal viscous damping ratio of EIBI lies between 0.20 < ζ b < 0.30, which is practically affordable and precise to implement. The exact closed-form expressions for optimal design parameters for traditional base isolators (TBI) have also been derived using the H2 method to make a fair comparison with EIBI. When the base mass ratio of TBI increases, its optimal frequency and viscous damping ratios decrease. The response reduction capacity of each optimized novel isolator was compared to the response reduction capacity of each optimized TBI. Analysis of the frequency domain demonstrates that the response reduction capacity of the proposed EIBI is significantly 2.77% and 17.46% greater than that of the TBI subjected to harmonic and random white-noise base excitations. To verify the accuracy of the optimal closed-form expressions derived for each isolator using near-field earthquake base excitations, a numerical study employing the Newmark-beta method has been conducted. Hence, the time-history analysis reveals that the displacement and acceleration reduction capacities of EIBI are significantly superior to that of the TBI subjected to near-field earthquake base excitations by 12.86% and 24.61%, respectively. The EIBI systems are cost-effective and have greater vibration reduction capacities than TBIs.

Global optimization of locally installed adaptive negative stiffness amplifying damper in steel frames through rocking wall

As a newly-developed damper system, negative stiffness amplifying damper (NSAD) is validated to be of high efficiency. Compared to the strategy of arranging multiple NSADs at multi-stories with much labor cost and sophisticated designing methodologies, this paper proposed a novel but simple strategy of using a single NSAD and a rocking wall (RW), where a global response control effect can be achieved. Seismic responses of typical steel frames with different NSAD and RW arrangement were first demonstrated in this study. Parametric study was conducted to find optimized design parameters of this system. Specifically, the larger the support stiffness the more significant displacement reduction can be achieved at the optimal damping ratios, which are in the range of 1.0–2.0 for all cases. To avoid excessive displacement amplification effect, absolute values of negative stiffness ratios not exceeding 0.3 are recommended. The optimal damping ratio is in the range of 10−0.5 to 10°.1 (i.e., 0.32 to 1.26). On the other hand, the larger the support stiffness and absolute value of negative stiffness, the more significant acceleration reduction can be achieved. Large adaptive NSAD displacement ratio, say larger than 1.5, should be avoided from the perspective of reducing structural displacement responses.

Optimum Parameters of Tuned Inerter Damper for Damped Structures

This study evaluates optimal parameters for a damped system with a tuned inerter damper (TID). TID is a device that works similarly to a tuned mass damper, except that the actual mass is substituted with apparent mass, i.e. the inertance of the inerter. Fixed point theory is used to derive optimal parameters of TID attached to an undamped single degree of freedom (SDOF) structure considering objective responses of relative displacement, relative velocity, absolute acceleration and the force transmitted by the primary structure to the ground. Optimal TID parameters attached to the viscously damped SDOF main system are derived by minimising the four objective responses using a numerical search technique. Based on the results from the numerical search and optimal parameters obtained from the fixed point theory, a curve-fitting technique is utilised to establish explicit formulations for TID parameters for the damped primary system. The closed-form expressions thus obtained are based on the minimum mean square error between optimal parameters obtained by numerical search and corresponding explicit formulae. The expressions proposed have a negligible inaccuracy, making them useful for the design process in the damped systems. The damping of the primary system has a negligible effect on the TID's optimal damping ratio. The damping of the primary system, on the other hand, has a substantial impact on the optimum tuning frequency of TID. Finally, an optimally designed TID is applied to SDOF damped system with a fixed and flexible base as a supplemental damper. It is seen optimal TID is significantly effective in controlling the seismic responses.