Optimal Damping Research Articles

Air‐Sea Turbulent Heat Flux Affects Oceanic Lateral Eddy Heat Transport

AbstractSea surface temperature anomaly (SSTA) of ocean eddies induces an anomalous air‐sea turbulent heat flux that acts to dampen SSTA. A two‐dimensional SSTA model explores the effect of air‐sea turbulent heat flux, parameterized as SSTA damping, in shaping eddy SSTA patterns. Increased SSTA damping transitions the SSTA pattern from a monopole to dipole, indicating the balance between eddy stirring of the background SST gradient and SSTA damping. The SSTA dipole pattern increases the correlation of eddy velocity and SSTA, but SSTA damping weakens the SSTA, resulting in an optimal damping rate maximizing lateral eddy surface heat transport. Globally, the SSTA damping rate increases toward the equator. In mid‐latitude and high‐latitude regions (e.g., the Kuroshio, the Gulf Stream, and the Southern Ocean), eddy SSTAs are monopoles, while the tropics and subtropics exhibit dipole SSTA patterns due to higher damping rates, facilitating greater lateral eddy heat transport when the SSTA is large.

Torsional damper design for diesel engine: theory and application

Abstract Torsional vibration is the primary cause of engine crankshaft failure. Consequently, the reduction of engine vibration is of paramount importance for the enhancement of automotive safety and comfort. However, the lack of comprehensive insight into the damping mechanism of the torsional damper has impeded the effective control of engine torsional vibration. In order to gain insight into the vibration characteristics of the shaft system in an inline six-cylinder diesel engine, an analysis of the system’s behaviour during both free and forced vibration was conducted. A mathematical relationship was deduced between the dimensions, material, operational temperature and damping properties of the silicone oil damper. The objective was to determine the optimal damping and moment of inertia of the damper, with the aim of minimizing the torsional amplitude of the sixth harmonic. The results demonstrate a reduction in the six-harmonic torsional amplitude from 0.32° to 0.14° following the installation of the damper. The mean and relative deviations between the calculated and experimental results are 0.0018° and 0.83%, respectively. To facilitate the design of the silicone oil damper, a software program, Vibsim, was developed based on Visual Studio for the design and torsional vibration analysis of the silicone oil damper. This software is reliable in calculating results and is user-friendly.

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.

Study on the Application of Determinant-MTMD(TMDD) Vibration Reduction in Cable-Supported Pedestrian Suspension Bridge

In this study, multiple tuned mass dampers (MTMDs) were studied to understand their impact on the human-induced vibration response and comfort level of a pedestrian cable-supported suspension bridge. A spatial finite element model based on a specific engineering case was established. The dynamic characteristics of the bridge under human-induced loads were investigated, and its comfort level under human-induced vibrations was analyzed using the time-history method. Then, this study adjusted the design parameters of the dampers based on various optimal damper parameter expressions. Furthermore, the damping effectiveness of MTMD under different mass ratios (μ) was evaluated, and it was found that increasing the mass ratio significantly impacts damping performance. Finally, determinant-TMD (TMDD) was introduced, and a comparison between the damping effect, robustness, and performance of TMDD and MTMD was conducted. The results indicate that while increasing the mass ratio does not linearly affect maximum vibration acceleration, the damping effect increases initially and then stabilizes, with a damping rate converging at approximately 55%. However, with the TMDD approach, the maximum damping rate can reach approximately 70%, enhancing comfort levels from the “minimum CL3” achieved with MTMD to the “medium CL2” level. Additionally, while TMDD’s robustness is slightly inferior to MTMD at lower mass ratios, it demonstrates superior robustness at higher mass ratios.

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.

Application of pole allocation to optimize passive viscous dampers represented by the Maxwell model

The Maxwell model is used to understand the realistic effectiveness of vibration reduction in the building structures. The model consists of a dashpot and spring in series. The dashpot and spring represent a viscous damper and joint between the damper and the structural frame, respectively. However, few studies have investigated the optimal damper capacity and the corresponding spring stiffness in the practical parameter ranges. Additionally, the optimal damper derived using the fixed-point theory has no relationships with that derived via pole allocation. Therefore, in this study, to examine the effects of the joint spring, the pole allocation method was used to design a structural system wherein the Maxwell model was incorporated into a single-degree-of-freedom damped model. We introduced a closed-form expression, which explicitly described the relationships between the target structural damping ratio, damper capacity, and joint spring. The Maxwell model constrained the control effectiveness using damper parameters and simultaneously suggested an optimal and realistic joint spring for the damper. Pole allocation was also applied to a multi-degree-of-freedom (M-DOF) damped structural system employing multiple Maxwell models. The newly proposed optimized joint spring could easily control the additional damping effect on the M-DOF system. The Maxwell model can be optimized almost manually. The scheme is more useful in the preliminary design stage than the previous numerical optimizations. This study extended the mathematical equation governing the building vibrations to the Maxwell model. The extended equation served as a unified description for considering structural passive control.

Влияние демпфирования по Рэлею на устойчивость земляного полотна железной дороги в условиях сейсмического воздействия

Purpose: to consider the problem of railway subgrade stability under seismic conditions. Show the need to increase stability during an earthquake. Determine the possibility of increasing seismic resistance by introducing a damping layer into the structure. Determine the optimal damping parameters, taking into account the rational use of subgrade materials. Methods: calculations of embankment stability are carried out using the method of G. M. Shakhunyants. An earthquake is taken into account through an increase in shear forces acting on the cells of the sliding massif. The maximum accelerations of the compartments are determined based on the results of finite element method dynamic calculation of a stress-strain state of the embankment during an earthquake, which is specified through an accelerogram. Results: the effectiveness of using a damping layer in the embankment structure, introduced to increase seismic resistance, has been shown. The dependence of the stability coefficient of the embankment on the Rayleigh parameters of the material composing the body of the entire embankment has been determined. For the best material parameters, the optimal thickness and position of the damping layer in the structure are determined, at which the stability coefficient takes on a standard value and the volume of the damping layer is minimal. Practical importance: as an alternative to the normative approach, the possibility of increasing the stability of a railway embankment under earthquake conditions by introducing a damping layer into the structure is presented. An algorithm for selecting optimal damping parameters has been determined in order to increase seismic resistance.

A new contact force model for revolute joints considering elastic layer characteristics effects

The contact forces generated during the motion of revolute joints with clearances significantly impact the dynamic performance of mechanisms, making it essential to develop an accurate contact force model. Traditional contact models often neglect the influence of elastic layers or assume that the bushing thickness is equal to its radius, which limits their applicability. To address the dynamic contact problem in revolute joints with small clearances, this study employs an improved Winkler elastic foundation model and introduces an elastic layer correction coefficient to refine the static contact model. The model's validity is verified using the finite element method. Building on this, a new contact force model is proposed, incorporating the optimal damping term from multiple continuous contact models. Finally, experimental validation is conducted using the crank-slider mechanism and typical applications in the Variable Stator Vane (VSV) mechanism. The results demonstrate that the proposed contact force model effectively predicts the dynamic characteristics of mechanisms with clearances.

Closed‐form optimal solution of two‐degree‐of‐freedom system with Inerter based on equal modal damping with potential application in non‐structural elevator for seismic control

AbstractTargeting the great demand for adding non‐structural elevators to old residential buildings, this article proposes an updated configuration of tuned mass damper inerter (U‐TMDI) applied in external non‐structural elevators. An analog 2‐DOF system is established to describe the residential building controlled by an inerter elevator. Then, three closed‐form optimal solutions for designing the U‐TMDI are derived via the fixed‐point method, equal modal damping criterion, and the infinity damping assumption. Subsequently, these optimal solutions are compared and discussed involving the expressions of tuning frequency ratio and the optimal damping parameters, root locus diagram and supplemental damping ratios, transfer function, and robustness to frequency variation, respectively. Finally, a residential building example is adopted to validate the feasibility of the proposed retrofitting strategy and the closed‐form optimal design solutions. It is demonstrated that the optimal tuning frequency ratios derived by the fixed‐point method and equal modal damping criterion are different for U‐TMDI due to the influence of elevator stiffness ratio , while its degradation forms for tuned mass damper (TMD) are identical, recognizing the importance of the elevator stiffness. Moreover, the proposed retrofitting strategy of using an inerter elevator can significantly mitigate the main structure displacement by about 18%∼23% for both far‐field and near‐fault earthquakes.

Mechanical properties and damping ratio of gradient polymer concrete for damping beam structure

AbstractDue to its higher overall performance than ordinary concrete, polymer concrete (PC) beam has been widely used in the field of structural engineering. However, it is widely recognized that PC cannot simultaneously achieve the highest mechanical strength and optimal damping performance to reduce vibration during its long‐term service lifetime. To address this contradiction, the effect of various diluents contents on the overall performance of PC was investigated first in this investigation. Experimental findings revealed that the bending strength of PC exhibits an initial increase followed by a decrease with an increment of diluents, while its damping ratio displays an inverse trend. To obtain excellent overall performance (higher flexural strength and damping ratio) of PC, gradient PC has been manufactured by horizontal partition casting process (HPCP) and stereoscopic layered casting process (SLCP). Experimental results demonstrated that the gradient PC manufactured by HPCP exhibited better overall performance compared to SLCP. Furthermore, the graphite and carbon fiber were incorporated into the above gradient PC, and experimental results revealed that the incorporated graphite and carbon fiber can further increase the overall performance of the above gradient PC. Similarly, the incorporation of glass fiber cloth and carbon fiber cloth, along with surface treatment, significantly enhanced the overall performance of PC. The significance of this study lies in enhancing the comprehensive performance of PC beam structures, thus broadening its utilization scope within structural engineering.

A novel optimal design method for tuned mass dampers with elastic motion‐limiting stoppers

AbstractTuned Mass Dampers (TMDs) are commonly used passive control devices in practical engineering applications. However, motion‐limiting stoppers are usually installed to control the excessive TMD displacement due to the building space limitation, resulting in piecewise nonlinearity and detuning of TMD. This paper studies the influence of elastic motion‐limiting stoppers on the optimal design of TMDs through a piecewise stiffness TMD (PSTMD) model. Performance of a PSTMD with classical design is first investigated and proven to be ineffective. To optimize the PSTMD parameters, the motion of PSTMD is decoupled from the controlled structure, and the frequency response equation of PSTMD is obtained analytically through the averaging method. Subsequently, the solution of the optimal design frequency for PSTMD is transformed into the solution of the jump frequency in the frequency response equation. With the optimal frequency of PSTMDs, the optimal damping and control performance of PSTMDs are discussed and analyzed compared with classical linear design, which fully showcases the effectiveness of the novel design method. Finally, the effectiveness of the novel design method is verified using a nine‐story benchmark frame structure, and the results demonstrate that the control performance of the optimal PSTMD can be improved by nearly under specific seismic excitation, compared to the PSTMD with classical linear method. In summary, the novel design method can effectively take into account the influence of piecewise nonlinearity caused by elastic motion‐limiting stoppers and improve the optimal control performance of TMD in a more realistic engineering environment.

Mechanism and improvement for tail vehicle swaying of power-centralized EMUs

The swing phenomenon of the tail vehicle will reduce the stability of the train operation, and even seriously deteriorate the ride comfort of passengers. In response to the relevant railway department, this paper reported the different dynamics performances in tail vehicle swaying when power-concentrated EMUs passed through a tunnel under push/pull operation. To analyze the characteristics and mechanism of the EMU tail swaying, field tests and numerical simulations were conducted. Firstly, through the on-track test, it was found that under push operation, the EMU tail continued to sway at a frequency of 1.3 Hz inside the tunnel, while under pull operation, only a swing of 1.7 Hz appeared at the tunnel entrance. Subsequently, through a simulation analysis, it was found that under push operation, the vortex-induced vibration of the tail carbody occurred inside the tunnel, leading to the sustained swing with a carbody hunting frequency of 1.3 Hz; under pull operation, due to the aerodynamic effect of the tunnel entrance, the secondary lateral stop had an abnormal elastic collision with the bogie frame, and the lateral impact on the bottom of the tail carbody caused a swing of 1.7 Hz, which was verified by the field test. Finally, for the motor vehicle of the EMU tail, two improvement measures of yaw damper optimization were proposed to alleviate the EMU tail swaying inside the tunnel. Furthermore, the research results can provide a reference for the aerodynamic swing problem of other trains, which has certain engineering significance.

Data-driven multi-step solar photovoltaic predictions with limited and uncertain information: Insights from a collaboratively-optimized nonlinear grey Bernoulli model

As solar energy grows as a crucial substitute for fossil energy worldwide, it is worth investigating solar photovoltaic predictions characterized by complex patterns and a lack of prior knowledge. Accordingly, an optimized nonlinear grey Bernoulli model is proposed, encompassing three essential advancements. Firstly, the damping accumulated generating operation is initially integrated with the grey Bernoulli model to reduce random disturbances and improve the smoothness of the original collections, extracting more valuable information via preprocessing the raw data. Secondly, the background value is modified to remove the jumping errors arise from converting differential to difference functions based on the Simpson rule. Thirdly, the heuristic intelligent algorithm is employed to collaboratively explore the optimal damping coefficient and power index in the proposed model. For illustration purposes, experiments on predicting the global photovoltaic installed capacity (case one) and solar electricity net generation (case two) are carried out to examine the effectiveness and generality of this new approach. Experimental results indicate that the proposed model achieves significant improvements over the prevalent models in one-to-three-step ahead forecasting, obtaining the average 323.94% and 211.86% improvement rates over the seven benchmarks measured by MAPE and RMSE. Furthermore, robustness tests in terms of Monte-Carlo simulation, algorithm comparison, and hyper-parameter sensitivity analysis are performed to explore the proposed model’s forecasting stability against the intelligent algorithm randomness, choices, and hyper-parameters. Generally, the proposed model is proven to be a reliable method and is deployed for future global solar photovoltaic predictions.

Optimization of tuned mass dampers – minimization of potential energy of elastic deformation

A tuned mass damper (TMD) optimization can be performed under various assumptions and objectives. All the variables of the optimization, such as structural model, performance index and load type affect the optimal parameters of the TMD. This paper presents a new optimization method that implements straightforward performance index and allows taking load spectral characteristics into account. Thanks to the usage of modal coordinates, the method allows fast numerical optimization of TMD attached to large or complicated structures with numerous degrees of freedom. One of the complicated tasks while optimizing TMD is the choice of a performance index. In this paper, the mean value of potential energy stored in the elastic deformation of a structure under periodic load serves as a performance index, which leads to a low numerical complexity task if the optimization is performed in the frequency domain. The new method also allows a simple inclusion of load spectral characteristics and permits TMD optimization for any loading spectral range. When applied to a structure with a single degree of freedom, this method leads to H2 optimization in the case of white noise excitation. However, it is applicable to multiple degrees of freedom structures with single or multiple TMDs and any given load. The paper also presents several examples of numerical optimization of the TMD attached to both single and multiple degrees of freedom structures under various loads, including white noise excitation, pedestrian load, and earthquake strong motion.

Effect of bottom bumpiness of vibrated closed container on granular dissipation behavior.

The dissipation behavior of granular balls inside quasi-two-dimensional closed containers with different levels of bottom bumpiness under vibration is examined in this article using the discrete element method. The quasi-two-dimensional closed granular system used in this paper has dimensions of , and the diameters of the 279 filled granular balls are 4mm. First, the dynamic behavior and damping effects of granular balls within a flat-bottomed closed container are explored across the range of relevant excitation parameters, identifying four high damping granular phases. Second, this study investigated the impact of the container's bottom surface bumpiness, convex height, and number of bumps on the dissipative behavior of internal granular balls. The findings reveal that a single 2mm bump on the container's bottom surface maximally enhances the damping effect on the granular balls. Finally, by comparing the optimal damping behavior of granular balls inside a flat-bottomed container with that of a container featuring a single 2mm bump at the bottom, this study revealed how the protruding bottom surface enhances the damping effect on the granular balls inside the container. This provides theoretical support for optimizing the performance of granular dampers in engineering practice by controlling the morphology of the cavity bottom surface.

Design of Battery Energy Storage System Torsional Damper for a Microgrid with Wind Generators Using Artificial Neural Network

Ancillary frequency controllers such as droop controllers are beneficial for frequency regulation of a microgrid with high penetration of wind generators. However, the use of such ancillary frequency controllers may cause torsional oscillation in the doubly fed induction generator (DFIG). In this paper, a supplementary torsional damper in a battery energy storage system (BESS) is designed to improve the damping ratio for the DFIG torsional mode. Since the optimal damper gain depends on system variables such as the number of diesel generators, the number of wind generators, and BESS droop gain, an artificial neural network (ANN) is trained using these system variables as inputs and the desired BESS damper gain as the output. After the ANN has been trained with the training patterns, it can provide the desired BESS damper gain in an accurate and efficient manner. The effectiveness of the proposed ANN approach for BESS damper design is demonstrated by MATLAB/SIMULINK R2022b simulations.

Vibration Suppression of Two Adjacent Cables Using an Interconnected Tuned Mass Damper/Nonlinear Energy Sink

Due to their high flexibility, low damping, and small mass, stay cables are prone to large-amplitude vibrations. Various mechanical measures, typically installed near the cable anchorage to the deck, have been developed to suppress cable vibration. These dampers, however, may not be effective for ultralong cables since the damper is close to the cable anchorage, the cable node. In this paper, a tuned mass damper (TMD)/nonlinear energy sink (NES) are considered for installation between two adjacent stay cables for vibration mitigation. Firstly, the static equilibrium equation of the stay cable–damper system is established, and the influence of the self-weight of the damper on cable shape is investigated. The governing equations describing the motion of the two adjacent cables with a damper are then established using the Hamilton principle, which are then solved by the method of separation of variables. For cases of swept-sine excitation and harmonic excitation, the optimal designs of TMD and NES are achieved with the purpose of suppressing the first- and third-mode-dominated vibrations, respectively. Both optimal TMD and NES may substantially suppress cable vibrations, with each having advantages under certain situations. Finally, the dynamic response characteristics of two adjacent cables with an optimal damper are analyzed. Interesting dynamic behaviors, such as energy input suppression, phase shift, cable frequency shift, and phase diagram boundary rotation, are identified, and their mechanisms are explained.

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.

Design and application of composite lanchester damper for milling thin-walled part

Thin-walled parts often produce chatter during mechanical processing due to their poor stiffness. Increasing damping can effectively improve the equivalent stiffness of thin-walled parts and weaken the vibration generated during the machining process. Based on the principles of fluid viscous damping and eddy current damping, this article proposes a design scheme for a composite viscous damper. It optimizes the structural parameters of the composite Lanchester damper according to the optimal damping coefficient. Finally, a composite viscous damper was manufactured, and modal tests showed that the amplitude of the first three vibration modes decreased by 83%, 90%, and 85% after installing the damper. In the milling test, the vibration amplitude of the thin-walled part decreased by the highest of 77%.

Research on Damping Hole Optimization of Hydro-Pneumatic Suspension for Mining Trucks under Variable Load Conditions

The hydro-pneumatic suspension, known for enhancing vehicle ride comfort and stability, finds widespread use in engineering vehicles. Presently, the majority of mining trucks employ hydro-pneumatic suspension with a fixed damping hole, underscoring the critical importance of selecting appropriate damping hole parameters. Initially, an equilibrium mathematical model of the ¼ hydro-pneumatic suspension is established, and the influencing factors of the damping characteristics are analyzed. Subsequently, the simulation model and experimental bench for the hydro-pneumatic suspension are constructed. Sinusoidal signals with different frequencies and amplitudes serve as the excitation signals to analyze the variation trend of the force on the rod with displacement changes. The simulation and experimental results demonstrate a high degree of consistency, validating the rationality and validity of the simulation model. Building upon this foundation, various damping apertures are then selected to study the damping characteristics of the hydro-pneumatic suspension. The research indicates that as the damping aperture increases, the setting time of the hydro-pneumatic suspension system after excitation extends, accompanied by a decrease in the acceleration overshoot. As a result, a comprehensive evaluation index is developed, considering various factors, such as different weight setting times and peak longitudinal accelerations to assess the ride comfort of the suspension. This approach is then employed to determine the optimal damping aperture under both full-load and no-load conditions. The findings of this research offer valuable insights for the development of adaptive variable damping hydraulic suspensions, especially under variable load conditions.