Equivalent Damping Coefficients Research Articles

Equal-displacement principle-based direct seismic-design method for single-yielding precast-concrete frame

This study aims to improve the seismic performance and reduce damage of a structure using energy-dissipation connectors, while avoiding the design difficulties of existing methods. In this study, a single-yielding–precast-concrete (SYPC) frame was proposed to realize the design of a controllable bending moment at the beam end. An equal-displacement principle-based direct seismic-design method was proposed for the SYPC frame. First, using a dynamic time–history analysis, the key parameters affecting the stiffness of the frame and the adjustment strategy were explored. Subsequently, based on the equal-displacement principle, the seismic intensity control and target interstory drift were directly determined. Finally, a direct seismic-design method for the SYPC frame based on the equal-displacement principle was proposed. A six-story SYPC frame was designed according to the proposed design method. An elastic–plastic dynamic time–history analysis was performed for the designed frame to verify the effectiveness and accuracy of the proposed design method. The results show that the equal-displacement principle can rapidly and accurately determine the target elastic–plastic displacement of the underground motions of the structure and effectively avoid the iterative solution of structural plastic characteristic parameters, such as equivalent damping and ductility coefficient, encountered in traditional design methods. The proposed design method not only effectively controls the deformation pattern of the structure but also realizes an ideal beam-hinge mechanism. Additionally, by controlling the length and section area of the replaceable energy-dissipating connectors (REDCS) to satisfy the ductility requirement, the stiffness was verified to satisfy the requirements of the frame deformation mechanism.

Study on the vibration reduction characteristics of shock absorber throttle orifice in tractor suspension

The hydraulic shock absorber of a certain tractor suspension system is analyzed to determine the influence of the cross-sectional area ratio of the throttling holes of the restoration valve and the compression valve on the vibration damping performance of the whole vehicle, using a new method of machine-hydraulic co-simulation. First, the AMESim model of the hydraulic shock absorber is established, and the Kriging model is used to approximate the parameters of the AMESim hydraulic shock absorber model; the multi-island genetic algorithm and the gradient descent algorithm are used to obtain the three scenarios in which the cross-sectional area ratios of the throttle orifices of the same equivalent damping coefficients are greater than, equal to, or less than one. Then, a co-simulation model of 1/4 vehicle Recurdyn/AMESim and a co-simulation model of the whole vehicle with 162 degrees of freedom were established. The result show that, compared with the traditional method, this machine-hydraulic co-simulation method improves the calculation accuracy, calculation speed, and co-simulation model parameter accuracy. For low-speed conditions, when the throttle orifice area ratio equals 0.32, the minimum vehicle body center acceleration (root mean square value equal to 1.78 m/s2) is achieved. For high-speed driving conditions, when the throttle orifice area ratio is approximately 3.1, the minimum vehicle body center acceleration (root mean square value equal to 3.52 m/s2) is achieved.

Dynamic behavior analysis of systems with friction and hysteretic effects

This paper investigates the steady-state response of a nonlinear system that incorporates both a hysteretic element and frictional contact under harmonic excitation. While previous studies have separately explored hysteretic oscillators and frictional systems, the simultaneous consideration of both elements has received limited attention. In this study, an analytical solution for the steady-state response is proposed, employing the equivalent linearization approach. This method enables the determination of equivalent stiffness and equivalent damping coefficients for the linearized system, which are directly linked to the amplitude of the steady-state response. To validate the derived analytical solution, a numerical model is utilized, demonstrating the agreement between the analytical and numerical results. Moreover, this paper identifies noteworthy dynamic characteristics of the designed system, notably the occurrence of peak amplitude at excitation frequencies lower than the pre-yield natural frequency. Furthermore, the apex point can be adjusted by manipulating the nonlinear parameters. Building upon these observations, a new mounting system is examined, revealing distinctive behavior.

Small-Signal Synchronous Stability of a New-Generation Power System With 100% Renewable Energy

The traditional power system dominated by synchronous generators (SGs) is now evolving into a new-generation power system dominated by voltage source converter (VSC)-based renewable energy, causing substantial changes in the dynamical behavior. This paper investigates the small-signal synchronous stability of a new-generation power system composed solely of grid-following and/or grid-forming power electronics devices in the absence of an infinitely strong bus. The phase-lock-loop (PLL)-based VSC is taken as a representative of grid-following devices and treated as a controlled-current source whose phase is driven by the power factor angle. In sharp contrast, the virtual synchronous generator (VSG)-based VSC is taken as a representative of grid-forming devices and treated as a controlled-voltage source whose phase is driven by the active power. Small-signal synchronization stability models are established for multiconverter power systems within the framework of the classical Phillips–Heffron model for traditional power systems. Explicit expressions for equivalent inertia, damping, and synchronization coefficients are obtained. We find that both PLL-based and VSG-based VSCs show similar synchronization principles and contribute to the inertia and damping of the system. All these findings are well supported and verified by our modal analysis and time-domain simulations.

The negative stiffness electromagnetic tuned inerter damper for damping enhancement of stay cables

Long stay cables may be subject to vortex-and rain-wind-induced vibrations. To suppress the two types of vibrations simultaneously, integrating the advantages of negative stiffness and inerter-based damper, a new negative stiffness electromagnetic tuned inerter damper (NSETID) is proposed in this study. The equivalent mechanical model of the NSETID is presented according to its working principle. On this basis, non-dimensional analytical equations of the cable with NSETID are developed. Subsequently, the optimum parameters of the NSETID are identified by optimizing the damping ratio of the tuned cable mode. The effects of the cable sag and flexural stiffness on the control performance and optimum parameters of the NSETID are also taken into consideration. In addition, the benefits and damping enhancement of the NSETID for mitigating single-mode and multi-mode cable vibrations are illustrated by comparing with tuned inerter damper (TID), negative stiffness damper (NSD), and negative stiffness inerter damper (NSID). Finally, the damping enhancement mechanism of the NSETID for cable multi-mode is explored through its stiffness and damping properties. The results highlight the superior damping enhancement capabilities of the NSETID in mitigating single-mode and multi-mode cable vibrations. The better control performance of the NSETID can be attributed not only to its negative stiffness behavior but also to the adaptability of its equivalent damping and negative stiffness coefficients to the cable mode order.

Experimental Study on Magnetorheological Damper Prototype and Obtaining Its Equivalent Damping Coefficients

In this work, a magnetorheological (MR) damper prototype that provides controllable damping force was designed, manufactured and tested. The design and dimensions of the MR damper piston were determined according to the static magnetic analysis results made in ANSYS/Emag (Electromagnetics) software. The MR damper’s damping performance was tested in laboratory by utilizing a damper testing device. The tests were carried out under different currents applied to coil of the MR damper. According to the test results, the equivalent damping coefficients of the MR damper were calculated for different currents. The test results show that the highest damping force is 169.4 N with frequency of 3.18 Hz and applied current of 2 A. In this case, the equivalent damping coefficient is 302 Ns/m. The equivalent damping coefficient is 181 Ns/m when no current is supplied to the coil. The area of the dynamic force range also becomes larger with increasing the applied current. In addition, according to the quarter car model based simulation results in MATLAB/Simulink, it was seen that the semi-active suspension system using MR damper was more effective and successful in vibration mitigation.

Cyclic plasticity and ULCF behavior of steel butt-joints considering different welding methods

In order to reveal the influence of welding method on the cyclic plasticity and ultra-low cycle fatigue (ULCF) behavior of low-alloy butt-joints, three different welding methods, namely, shielded metal arc welding (SMAW), gas metal arc welding (GMAW), and submerged arc welding (SAW), were considered. Dog-bone flat-plate specimens with the welds were cut off from the plates for cyclic tests. The load-carrying capacity, energy dissipation property, and ULCF performance of the specimens were discussed. According to the experimental results, GMAW and SAW lead to the highest and lowest peak loads, respectively. The various welding methods have a slight influence on the equivalent viscos damping (EVD) coefficient of the specimens. Compared with those of the base metal (BM) specimen, ductility of the welded specimens is degraded by 34.62–61.54%, yield strength is deteriorated by 2.86–13.20%, ULCF life is decreased by 71.33%-92.31%. Metallurgical and scanning electron microscope (SEM) analysis were further conducted to reveal the mechanism behind the significantly compromised ULCF behavior of the welded specimens. In-depth numerical analysis was also conducted to reproduce the experimental processes. In the finite element (FE) analysis, inverse calibration technique was applied to determine the Voce-Chaboche (VC) combined hardening constitutive model parameters, and then cyclic void growth model (CVGM) was adopted for fracture simulation.

Influence of Real Lubricant Density–Pressure Behavior on the Dynamic Response of Elastohydrodynamic Lubricated Conjunctions

Abstract The current work investigates the influence of real lubricant density–pressure behavior on the dynamic response of elastohydrodynamic lubricated conjunctions. Such a response is often based on a nonrealistic universal equation of state, despite longstanding evidence of its lack of support by measurements. A finite element framework is employed to investigate the damping and stiffness characteristics of line contact elastohydrodynamic (EHD) lubricating films, subject to a harmonic loading. Both the equivalent stiffness and damping coefficients of lubricating films are found to increase with the base applied external load and its amplitude of oscillation. They decrease however with increasing mean entrainment speed and load oscillation frequency. That is, they both increase as lubricant films get thinner. By comparison with the real density–pressure response of a highly compressible silicon oil, the universal equation of state is shown to underestimate the lubricant film’s stiffness and damping characteristics. The relative deviations in equivalent damping and stiffness coefficients can reach up to about 12% and 25%, respectively. Therefore, realistic lubricant characteristics should always be considered. In particular, the use of the universal equation of state should not be taken for granted, as is customary in the elastohydrodynamic lubrication (EHL) literature. Lubricant density–pressure response is not of a secondary nature when it comes to predicting the dynamic performance characteristics of EHL conjunctions.

MAXIMUM SEISMIC RESPONSE PREDICTION BASED ON CAPACITY SPECTRUM METHOD FOR VIBRATION-CONTROLLED CEILING STRUCTURE EMPLOYED PULLEY MECHANISM

This paper proposes a new procedure for predicting the maximum seismic response based on the capacity spectrum method (CSM) for the passively controlled suspended ceiling structures named “Pulley Damper Ceiling System (PDCS)”. The structural system has a supplemental nonlinear viscous damper and a bilinear hysteretic damper in parallel with displacement amplification mechanisms of block and tackle pulley system. The single degree-of-freedom model of the PDCS is initially discussed. The accuracy of a simplified calculation method for obtaining the structural equivalent damping coefficient, determined by the sum of the inherent damping and the square root of sum of squares (SRSS) of each damping provided by the nonlinear viscous damper and the bilinear hysteretic damper, is verified by comparing with the full-scale shake table test results of the PDCS. Then, the pseudo capacity curve of the structure is generated by continuously plotting the transition of maximum force and displacement values under different amplitudes of sinusoidal waves. Finally, the availability of the response prediction based on proposed CSM procedure considering floor response spectrum (FRS) is examined by the comparison of time history analysis results, and the sufficient accuracy to evaluate the seismic response is confirmed.

Experimental evaluation on seismic performance of multi-celled corrugated-plate CFST walls

In modern engineering applications, composite walls have drawn much attention owing to their good mechanical properties and standardized production. In this study, the multi-celled corrugated-plate CFST wall (MCCW) was studied experimentally and numerically as an innovative type of composite wall in engineering structures. Seven full-scaled MCCW specimens were tested, in which axial force ratios and sectional dimensions were considered as the main research variables. The typical deformation modes were classified and discussed, and the global buckling mode was observed after the load-carrying capacity dropped to 85% of the ultimate load for the specimens with axial force ratios of 0.55 and 0.65. In addition, the load-bearing capacity, ductility, stiffness and energy dissipation capacity of these specimens were evaluated in detail. The ductility factors of almost all specimens were greater than 3.0, and the final equivalent damping coefficients of all specimens exceeded 0.3. The key design parameters including axial force ratio and width of end steel tube were recommended for practical application of MCCWs. Furthermore, a finite element (FE) model was established and validated by test results. In general, this study can provide valuable references for practical designs of MCCW members under seismic effects.

Numerical investigation of scaling effect in two-dimensional oscillating water column wave energy devices for harvesting wave energy

Oscillating water column (OWC) devices utilise wave-induced oscillation of water column in partially submerged chambers to extract energy of waves in ocean. The principal aim of this paper is to investigate scaling effects of two-dimensional OWC through numerical simulations. The fluid motion under waves is simulated by solving the two-dimensional incompressible Reynolds-Averaged Navier-Stokes equations using finite element method under Arbitrary Lagrangian-Eulerian scheme. To investigate scaling effects, the waves and the OWC are scaled up or down according to Froude number similarity. The turbine is scaled up or down using three different scaling methods: (1) Turbine coefficient remains unchanged, i.e. not scaling the turbine at all; (2) Equivalent pneumatic damping coefficient of the turbine is constant and (3) the two-dimensional turbine coefficient is constant. The numerical results show that method (2) has the smallest effects on the best hydraulic efficiency and method (3) has the smallest effects on the best performance wave number, i.e. the wave number where the OWC receives the largest percentage of the wave energy. The worst scaling method is not scaling the turbine. Because the best performance wave number varies with the model scale in method (1) and (2), it is very likely the scaling effects of the model scale on the hydrodynamic performance at different wave numbers are different from each other. In addition, the effects of the wave height and the chamber volume are studied. Increasing chamber volume causes a reduction of the best performance, however it may improve general performance of OWC because it increases the frequency band of waves with high hydraulic efficiency. Increasing wave height causes a reduction of the hydraulic efficiency.

Stability Analysis of Articulated Bus in Straight-ahead Running Manoeuvre

A comprehensive study on the stability of a planar linearized single-track model of a two-section pusher articulated bus is presented with the aid of a complete set of stability maps. The two sections of the vehicle model are connected at the hitch point by a revolute joint; an equivalent visco-elastic characteristic function describes its rotational visco-elastic properties, playing a major role in stability control and therefore in passive safety. The equations of motion are derived in analytical form, allowing easy implementation of the non-linear model (eventually including a non-linear viscoelastic characteristic functions of the joint). Stability of the linearized model is then studied in equilibrium configurations by means of sensitivity analysis with respect to the model’s governing parameters. Stability maps are drawn on the basis of sets of parameter values related to straight-ahead running, steady-state manoeuvres. The most important parameters controlling the onset of unstable motions are identified, paying attention to the role played by the equivalent rotational damping coefficient and the equivalent torsional stiffness characterizing the connection joint, with the aim of finding criteria for its design.

Identification of dynamic contact parameters between contact roller and filament package

During the high-speed winding of polyester filament, a contact roller must be applied to press on the filament package’s surface to ensure the filament is placed stably and precisely on the package surface. Thus, a twin-rotor system with contact coupling characteristics between the contact roller and the filament package is formed. Identifying the contact parameters between the contact roller and the package are prerequisite to precisely analyze the dynamic behavior of the winding system, as well as to determine the technical parameters. In this paper, an approach was proposed to identify the equivalent contact stiffness and contact damping coefficients by means of coordination through experiment and simulation. First, based on the forced non-resonance method of a single-degree-of-freedom system, the testing scheme was drawn up in consideration of the winding process parameters. Then, an experimental device for the twin-rotor system was developed, and the dynamic contact parameters just in the working frequency band corresponding to low linear speed of winding were obtained by the experiment, due to the requirement of the forced non-resonance theory and economic limitations of the experimental device. Third, the basic parameters including equivalent radial Young’s modulus and damping ratio of the package were obtained through experimental test. Furthermore, the contact parameters in the working frequency band corresponding to high linear speed of winding were obtained through simulation. Finally, the curve fitting of contact parameters was finished; in addition, the comparative results between the simulation and the experiment are in good agreement. The dynamic contact parameters present nonlinear frequency variation characteristics.

Analyzing quarter car model with Magneto-Rheological (MR) damper using equivalent damping and Magic formula models

Mathematical modelling of Magneto-Rheological (MR) damper has been an intriguing field of research ever since the invention of the device itself. An accurate model of MR damper results in development of an efficient controller for a semi-active system with MR damper. Hence, a number of models have been put forward to accurately predict the MR damper behavior. One of these models is Magic formula model. Based on the famous Magic formula used in tire force calculation, this model can be used for representing the peak damper force vs damper piston velocity amplitude graph. This model was later modified to capture the force displacement diagram of MR damper. The former model is denoted as Magic Formula Model-1 (MFM-1) and the latter one is denoted as Magic Formula Model-2 (MFM-2) here onwards. In the current study a commercial MR damper has been tested for various piston velocities and currents. The equivalent damping coefficient is then calculated for the tested conditions. The equivalent damping coefficients are used for analyzing a quarter car model. Two quarter car models with MR damper are simulated, one uses MFM-1 for MR damper and the other uses MFM-2. All the quarter car models are subjected to single pulse input and the sprung mass response is measured in terms of displacement. The RMS error between the response of quarter car model with equivalent damping and quarter car models with MR damper is used to determine the performance of each mathematical model. The study revealed that MFM-1 represents the MR damper behavior more accurate than that of MFM-2.

Numerical investigations of bistable piezoelectric cantilever for enhanced energy harvesting

Piezoelectric energy harvesting applications have been highly impacted research area recently. Numerical investigations for bistable piezoelectric cantilevers have great importance to understand its dynamic performance. This paper aims to develop comprehensive numerical models to simulate the dynamic response of aunimorph piezoelectric bender under bistability effect for enhanced energy harvesting. To this end, the equivalent stiffness, damping, electromagnetic coupling and capacitance coefficients of a bistable piezoelectric cantilever have been numerically developed. Besides, finite element models are developed to determine the bistability repulsion force between magnets. The resulting simulations are then implemented in an electromechanical model to predict the output voltage and power over a range of load resistance.

Numerical investigation on hydrodynamic performance of an innovative aeration device with an array of wave-driven heaving buoys

In the recent decades, the occurrence of hypoxia in coastal bottom waters has had adverse influences on the ecological system and fishery production. Therefore, to address this, an innovative aeration device with an array of four wave-driven heaving buoys was proposed in this study to produce bubbles and supply oxygen into the bottom seawater. A series of laboratory experiments were conducted to investigate the hydrodynamic performance of the device in regular waves, and a relatively simple 3-D computational fluid dynamics (CFD) numerical model was used to simulate the motion response of the array of four heaving buoys. The results indicate that the average heaving amplitude (AHA) and the capture width ratio (CWR) of the seaside buoy are higher than those of the lee-side buoy. Specifically, with increasing incident wave height, AHA increases but CWR decreases. Both AHA and CWR decrease with the increments in incident wave steepness, relative height and density of buoy and relative equivalent damping coefficient. Furthermore, the prediction formulas were calculated to assess the AHA of the seaside and lee-side buoys with a relatively high accuracy. The results obtained are significant for the optimal design and operation of the proposed innovative aeration device.

Application of viscoelastic dampers for reducing dynamic response of high-speed railway bridges

AbstractDue to the extensive development of high-speed railway lines which are operating at increasing velocities, the dynamic performance of railway bridges has become an important issue of scientific research. The aim of this study is to investigate the possibility of reducing the vertical acceleration and displacement of pre-stressed reinforced concrete bridges beams by using passive nonlinear viscoelastic dampers to retrofit them. The proposed solution is based on connecting the dampers directly to the abutments and the bottom surface of the bridge deck with an eccentricity between the neutral axis of the bridge and the contact point of the viscoelastic dampers. First, the dampers are modeled through the concept of linearized fractional derivatives to obtain energetic equivalent linear viscoelastic dampers. Optimization of the configuration of these dampers was performed then as function of the orientation angle and the eccentricity. Considering two bridges having different length that were studied in the literature with other systems of damping, it was found that the best orientation angle of dampers is close to 60°. It was found also that, in order to satisfy Eurocode 1 requirements, the total equivalent damping coefficient for the actual damping system is less than half of that required for systems using auxiliary beam to fix dampers, which indicates higher efficiency of the proposed solution.

Stochastic Response of SDOF Self-Centering System

As a new type of seismic resisting device, the self-centering system is attractive due to its excellent re-centering capability, but research on such a system under random seismic loadings is quite limited. In this paper, the stochastic response of a single-degree-of-freedom (SDOF) self-centering system driven by a white noise process is investigated. For this purpose, the original self-centering system is first approximated by an auxiliary nonlinear system, in which the equivalent damping and stiffness coefficients related to the amplitude envelope of the response are determined by a harmonic balance procedure. Subsequently, by the method of stochastic averaging, the amplitude envelope of the response of the equivalent nonlinear stochastic system is approximated by a Markovian process. The associated Fokker–Plank–Kolmogorov (FPK) equation is used to derive the stationary probability density function (PDF) of the amplitude envelope in a closed form. The effects of energy dissipation coefficient and yield displacement on the response of system are examined using the stationary PDF solution. Moreover, Monte Carlo simulations (MCS) are used for ascertaining the accuracy of the analytical solutions.

Sparse learning of network-reduced models for locating low frequency oscillations in power systems

With increasing penetration intermittent renewable energy and the interactions between different power sources in an interconnected system, low frequency oscillations may occur and potentially threaten the security of power systems if the grid cannot support adequate damping. Locating sources of low frequency oscillations is of great importance, which needs finding the mechanism of the damping of low frequency oscillations for interpretation. The difficulty of this problem lies in the fact that the parameters associated with the power system model can range from slightly uncertain to entirely unknown. Therefore, we firstly focus on identifying the network-reduced model to characterize low frequency oscillation, and then utilizing Hamilton analysis to reveal mechanism of oscillation. Accordingly, the problem of locating low frequency oscillation is equivalent to identify equivalent negative damping coefficient. In this paper, we propose a novel data-driven method that estimates equivalent damping coefficients and topological parameters of the network-reduced model simultaneously. More specifically, the proposed method utilizes the sparse representation to select the most dominant nonlinear terms from a set of dictionary functions, which finally balances the data fitness and achieves dynamics learning. We validate and evaluate the proposed method on IEEE 9-bus test system and IEEE 39-bus test system. The results demonstrate the effectiveness of the proposed method in achieving dynamics learning and locating sources of low frequency oscillations from measurement data.

Research on the Vertical Vibration Characteristics of Hydraulic Screw Down System of Rolling Mill under Nonlinear Friction

The rolling mill with hydraulic system is widely used in the production of strip steel. For the problem of vertical vibration of the rolling mill, the effects of different equivalent damping coefficient, leakage coefficient, and proportional coefficient of the controller on the hydraulic screw down system of the rolling mill are studied, respectively. First, a vertical vibration model of a hydraulic screw down system was established, considering the nonlinear friction and parameter uncertainty of the press cylinder. Second, the correlation between different equivalent damping coefficient, internal leakage coefficient, proportional coefficient, vertical vibration was analyzed. The simulation results show that, in the closed-loop state, when Proportional-Integral-Derivative (PID) controller parameters are fixed, due to the change of the equivalent damping coefficient and internal leakage coefficient, the system will have parameter uncertainty, which may lead to the failure of the PID controller and the vertical vibration of the system. This study has theoretical and practical significance for analyzing the mechanism of vertical vibration of the rolling mill.