Optimal Damping Research Articles

Hardware-In-the-Loop test for the optimal damping identification of oscillating buoy wave energy converters

The Power-Take-Off (PTO) damping is a significant factor on energy harvesting capacity of Wave Energy Converters (WEC), which cannot be determined through the traditional laboratory test. In order to consider the complexity of the PTO damping mechanism, the Hardware-In-the-Loop (HIL) methodology is employed to focus on the PTO performance and the energy harvesting capacity in this paper. The dynamic numerical model, servo drives, and data transmission system are integrated in the HIL system, and the established system is then applied to the optimal damping identification of the WEC device which is assembled with the PTO containing a Mechanical Motion Rectifier (MMR). The experimental results indicate that the maximum power appears at the different damping values since the multi-stage energy capture characteristics are affected by the damping mechanism within the mechanical PTO, and the wave height has little effect on the damping values corresponding to the maximum power. This phenomenon is worth noting during the process of the PTO test, and could provide intuitive guidance for the reasonable design and control strategy optimization of the PTO.

Degrees of Freedom Effects on a Laboratory Scale WEC Point Absorber

The number of rigid bodies and operational degrees of freedom of a wave energy converter (WEC) have significant impacts on power production magnitude and efficiency across wave periods, but this concept is not well studied. Investigating the effect of the number of bodies and degrees of freedom will help WEC developers design devices that most efficiently meet power and cost needs. This paper presents experimental and numerical results for a point absorber WEC across three modes of operation in regular waves. The three modes of operation are ‘one body heave only’, ‘two body heave only’, and ‘two body six degrees of freedom’. The Laboratory Upgrade Point Absorber (LUPA) was used as the test article. This work builds on the 2021 EWTEC paper [1] by completing fabrication and undergoing wave testing. The LUPA experiment took place in the Large Wave Flume at the O.H. Hinsdale Wave Research Laboratory at Oregon State University in Corvallis, Oregon, USA; the installation and a wave test are shown in Figure 1. LUPA is constructed as a 1:20 scale two body point absorber with a buoyancy driven float, and a spar with a heave plate to act as a reactionary body. The spar is 3.7 meters tall and the float has a 1-meter diameter. Figure 1. (Left) Mooring line installation. (Right) Wave tests in the Large Wave Flume. The ‘one body heave only’ mode locks the LUPA spar so only the float is moving, and only in heave (vertical). The ‘two body heave only’ mode allows both the float and spar to move but both bodies are restricted to heaving. The ‘six degrees of freedom’ mode has taut mooring lines connected to the spar and LUPA can translate and rotate in all directions. A damping optimization of the power take off was performed experimentally and numerically by sweeping damping values across a wide range of regular wave periods. The optimal damping value is used to compare the power generation of the three modes of operation. The LUPA project is an open-source, lab-scale wave energy converter that acts as a testing platform for students and researchers. The data from this testing along with numerical models and engineering design files will be publicly available here: https://github.com/PMEC-OSU/LUPA. This paper presents how increasing complexity of WECs through the number of bodies and degrees of freedom affects power production. It also provides a baseline case for LUPA which other researchers can compare against when applying their research to the LUPA project.

Singularity avoidance method for dual-arm closed-chain system based on damped least squares

When two manipulators cooperate to clamp a rigid object, a closed chain with both ends fixed is formed. The singularity of a single manipulator causes the closed chain to be at a singularity, which results in uncertainty in the velocity mapping between the terminal and joint space. This study proposes a closed-chain singularity processing method for dual-arm collaboration, adopting the Jacobian pseudoinverse method based on damped least squares to obtain an approximate solution. During the solution process, the adaptive damping factor is improved by cubic polynomials, and the optimal damping factor is determined by quadratic sequence programming. Furthermore, this study analyzes the kinematic constraints of the closed-chain system and constructs a closed-chain Jacobian to judge whether the system is in a singular region. Finally, the effectiveness of the proposed method is verified through simulations.

Seismic Reduction Analysis of Super-Long Span Suspension Bridge with Lattice Composite Tower and Damping System: A Case of Study for Qiongzhou Strait Bridge

In this paper, we proposed a lattice composite tower damping system to reduce the seismic response of super-long-span suspension bridges. Taking the QiongZhou strait bridge as a case study, we evaluated seismic performances through a finite element analysis (FEA) and shaking-table tests. First, the seismic responses of a super-long-span suspension bridge with or without a lattice composite tower to far-fault and near-fault earthquakes were analyzed and compared. The influence of the lattice composite tower on the dynamic characteristics and seismic performance was then investigated using shaking-table tests. Finally, the influences of different damping systems on the seismic response were evaluated, considering factors such as the damper type, damper arrangement scheme and design parameters. The results indicated that lattice composite tower could significantly increase the seismic performance of super-long span suspension bridge, while the optimal damping system could markedly improve the energy dissipation ability of whole system. Subsequently, this could provide references to enhance the seismic safety of the super-long span suspension bridge under strong earthquakes.

Analysis of Sharp Eagle Oscillating Surge Wave Energy Converter Based on a Two-Dimensional Numerical Wave Flume Model

To investigate the overtopping and slamming phenomena that occur in the interactions between waves and oscillating surge wave energy converters (OSWECs), a two-dimensional numerical wave flume was established using computational fluid dynamics (CFD) software Fluent by adding the momentum source terms into the original Navier–Stokes equation. Numerical convergence studies of the mesh sizes and time steps were firstly performed to ensure the sufficient accuracy of the numerical model. The variations in the wave heights along the wave propagation direction in the wave-generating area, working area, and wave-absorbing area were analyzed. The dynamics of the flap-type OSWEC were simulated using the overset mesh function embedded in Fluent. In addition, the numerical results were compared with the experimental data, and good agreements were achieved. External torque was applied to the hinge joint of the OSWEC to simulate the forces due to the power take-off (PTO) system, and the identified optimal PTO damping was compared with the numerical results based on the potential flow theory, which verified the correctness of the numerical PTO system. On this basis, nonlinear wave slamming by the sharp-eagle OSWEC was analyzed. The results show that under certain incident wave conditions, the sharp-eagle OSWEC can effectively reduce the maximum rotation angle and angular velocity compared with those of the flap-type OSWEC, and there is no overtopping that occurring for the sharp-eagle OSWEC. Furthermore, the sharp-eagle OSWEC performs better than the flap-type OSWEC.

Effect of excitation frequency on dissipation behavior of vibrated granular balls.

The dissipation behavior of granular balls in a quasi-2D vertically oscillating closed container is studied by the discrete element method with varying excitation frequencies in this work. Combining the dynamic behavior with dissipation effect of vibrated granular balls, the optimal damping effect of the phase transition critical stage between granular density inversion and granular Leidenfrost effect that involves four high damping granular phases (HDGPs) is revealed. Moreover, the high damping granular phases near and away from this phase transition critical stage are compared and analyzed further, which indicates the universal dynamic behavior of dense granular clusters playing the optimal damping effect. Finally, the optimal damping mechanism of granular balls in the quasi-2D closed container is clarified. Damping properties and motion states of partic.

Design Considerations and Optimum Parameters of a Friction Damper in SDOF Systems for Seismic Response Reduction

ABSTRACT Friction damper is characterized by two parameters, its stiffness and slip load. The present study provides the optimum values of these parameters providing the maximum efficiency of the damper. Various performance indices are evaluated at the optimum damper parameters and a new performance index is defined having a more consistent performance. This new performance index can be minimized to find out the optimum system performance. Fragility analysis is also carried out to identify the probability of slip and effectiveness of damper action as a function of natural period of the system and design spectral acceleration.

Human-Induced Vibration Analysis and Reduction Design for Super Long Span Pedestrian Arch Bridges with Tuned Mass Dampers

With the increasing demands on span length, aesthetics, and urban landscapes of pedestrian bridges, the fundamental frequency of pedestrian bridges is continuing to decrease, and their vibration and walking comfort issues are becoming increasingly prominent. The pedestrian load model of the pedestrian bridge was introduced here referencing current design specifications, and a spatial finite element model was established to study the dynamic characteristics of the case of a long-span pedestrian arch bridge. The comfort of the bridge under human-induced vibration was analyzed using the time history analysis method. According to the optimal damper parameter expression, the design parameters of the damper were obtained. In addition, the vibration reduction effects of different generalized mass ratios were analyzed, and the damping effects of setting the tuned mass damper (TMD) at different positions were compared. The results indicated that setting the TMD on the bridge can enhance the damping effect, and the transverse vibration can be suppressed by setting TMDs on both the arch ribs and the bridge deck. The research content could provide recommended parameters for the vibration reduction design of long-span pedestrian arch bridges.

Optimal models of outrigger locations and damping parameters for combined energy dissipation outrigger systems subject to seismic and wind loads

This paper investigates the optimal outrigger locations (OOLs) and optimal damping parameters (ODPs) for combined energy-dissipating outrigger systems (CEDOs) in high-rise buildings subject to seismic and wind loads. Using a pseudo excitation method (PEM), the paper first proposes simplified models of the CEDOs subject to either seismic or wind loads. Based on the changing trends with different structural factors, the paper then defines a dimensionless parameter to characterize the CEDOs. The dimensionless parameter captures the structural stiffness and damping characteristics comprehensively. Using the dimensionless parameter analysis, probabilistic models are developed to define two optimal outrigger locations as a function of such a dimensionless parameter. Finally, using the model selection, the paper proposes parsimonious probabilistic models to define the optimal damping parameters as functions of the outrigger location and another dimensionless parameter that captures the structural stiffness characteristic.

Performance Evaluation of Inerter-Based Dampers for Bridge Flutter Control: A Comparative Study

As the number of long-span bridges continues to grow, wind-induced vibration issues have become increasingly intensified. Among them, flutter is a serious wind-induced vibration that can lead to bridge collapse. To address this problem, this paper proposes inerter-based dampers as a solution for flutter control and compares their performance to traditional tuned mass dampers (TMDs). Firstly, eight distinct inerter-based dampers were proposed, based on various combinations of mass-inerter-spring-damper (MISD) components. Secondly, the equations of motion of the bridge-MISD system were derived based on the two-mode coupled flutter theory and the mechanical impedance analysis method. Thirdly, the flutter control performance of the eight proposed MISDs is examined using a simply supported beam, with the six better-performing dampers further evaluated using the Jiangyin Bridge. The results show that inerter-based dampers can effectively improve the critical flutter wind speed of bridges, with performance sensitive to frequency. Additionally, incorporating an inerter decreases the static displacement of the mass block, while increasing the mass of MISD and the distance between the damper and the section center improves flutter control performance. The optimal spring stiffness ratios for the six MISDs are identified, largely dependent on the damper’s inertance and mass. In conclusion, this paper offers a promising solution to addressing flutter in long-span bridges and provides insights into the design and optimization of inerter-based dampers.

Design optimization of sloshing tank using weakly compressible mesh free model

The sloshing effects from baffle and non-baffled water tank was investigated under different external excitation frequencies and amplitudes. It was simulated and analyzed using the Weakly Compressible Moving Particle Explicit (WCMPE) method under condition of high-precision simulation data. The effects from different baffle configuration, external excitation frequency and amplitude, and the behaviour of liquid sloshing were analyzed through the conversion of simulated data and images. The results showed that half-proportional baffles resulted in a highly complex water motion, which resulted in the damping of the liquid slosh. On the other hand, the sloshing of the water in the tank at non-natural frequency resulted in mutual cancellation of the particle velocities. With greater understanding of the sloshing and damping effects, the use of half-scale baffle and liquid depth at different position were further examined. Three case scenarios were simulated and analyzed. First, the length of the baffle was kept constant with gradual lifting of the baffle from the bottom of the tank until it protrudes the water surface. Secondly, the length of the baffle was gradually increased from bottom of tank until it protrudes above the water surface to explore the optimal damping effect. Lastly, the top of the baffle is situated immediately below the water surface. Determination of the optimal ratio of baffle length and liquid depth was completed from the three hypothetical case studies.

Optimal design method of the load-level isolation system for industrial steel racking

This paper focuses on an innovative system for mitigating seismic actions on industrial steel racking, called Load-Level Isolation System (LLIS). It consists of placing isolators directly between the pallet masses and the load level, thus exploiting the pallet masses (much greater than the structural mass) as tuned mass dampers. Specifically, the paper aims to derive a general design procedure for the LLIS, based on the amount of mass isolated, the position of the LLIS within the rack, and the main dynamic characteristics of the structural system. To this end, an analytical optimization method is proposed, based on the minimization of the displacement variance of a reduced structural model, representative of the rack dynamics with the LLIS. This method is applied parametrically to derive the optimal damping and frequency values of the LLIS in various design situations, and a sensitivity analysis is subsequently conducted to propose cost-effective LLIS design solutions. Prediction models of the LLIS parameters are therefore provided, as well as a simple step-by-step procedure for designing the control system. Finally, a case study is presented, with the dual objectives of showing the application of the design procedure and the effectiveness of the LLIS in mitigating seismic effects in a standard pallet rack. The results of the Time-History analysis demonstrate the validity of the proposed design method and the possibility of achieving large reductions in the seismic response of the rack using this control system, and up to 60% for both maximum displacements and axial forces of the uprights.

AdpPL: An adaptive phase linking-based distributed scatterer interferometry with emphasis on interferometric pair selection optimization and adaptive regularization

The distributed scatterer (DS) interferometry (DSI) technology is a powerful geodetic tool for measuring the deformation over abundant land covers. As a state-of-the-art DSI technology, the SqueeSAR approach considered the statistical behavior of the decorrelated DS and proposed the phase triangulation algorithm (PTA) as the pioneering implementation of the phase linking (PL) theory to estimate the equivalent single-reference (ESR) phases from all interferometric combinations. Subsequently, many advanced estimators of the systematic phase series have been introduced. Interestingly, this paper has demonstrated that the utilization of weakly coherent interferometric pairs is not conducive to the theoretical accuracy improvement of the PL theory in case of the fast decorrelation scenario. Moreover, the reduction of the small baseline scales will worsen the positive definite degree of the time series coherence matrix, which makes the ill-posed solution problem more serious. Therefore, this paper proposes a novel adaptive PL (AdpPL) method integrating the following two innovations for mapping surface deformation: 1) in terms of the interferometric pair selection optimization (IPSO), this paper performs the homogeneity measure-based IPSO (HoMeIPSO) method to remove the lowly coherent candidate subset progressively and select the moderate interferometric pairs adaptively; 2) in terms of the robust parameter estimation, an adaptive regularization (AdpReg) approach suggests selecting an optimal damping factor according to the minimum fitting error of all interferogram observables. Experimental results demonstrate that the proposed method can restore the systematic phase series more clearly and detect the deformation area with spatially highly dynamic characteristics successfully.

Application of Parametric Forced Tuned Solid Ball Dampers for Vibration Control of Engineering Structures

In this paper, parametric forced tuned solid ball dampers (TSBD) are considered for vibration control of engineering structures in an untypical way. The special feature of the presented investigation is to evaluate the potential application of parametric forcing of the rolling cylindrical or spherical body in the runway for reducing the vertical vibrations of a vibration-prone main system. Typically, tuned solid ball dampers are applied to structures that are prone to horizontal vibrations only. The coupled nonlinear differential equations of motion are derived and the phenomenon of parametric resonance of the rolling body in the runway is analyzed. A criterion for avoiding parametric resonance is given to achieve the optimal damping effect of the TSBD. In the second part of the article, a method for the targeted use of parametric resonance to reduce the vertical vibrations of engineering structures is presented and verified, considering a biaxially harmonic excited pedestrian bridge. It is shown that, with a suitable choice of damper parameters, a stable vibration of the rolling body in the runway is formed over the course of the vibration despite the occurrence of parametric resonance and that the maximum vertical vibration amplitudes of the main system can be reduced up to 93%. Hence, the here presented untypical application of parametric forced TSBD for reducing the vertical forced vibrations of vibration-prone main systems could be successfully demonstrated.

A Vanka‐based parameter‐robust multigrid relaxation for the Stokes–Darcy Brinkman problems

AbstractWe consider a block‐structured multigrid method based on Braess–Sarazin relaxation for solving the Stokes–Darcy Brinkman equations discretized by the marker and cell scheme. In the relaxation scheme, an element‐based additive Vanka operator is used to approximate the inverse of the corresponding shifted Laplacian operator involved in the discrete Stokes–Darcy Brinkman system. Using local Fourier analysis, we present the stencil for the additive Vanka smoother and derive an optimal smoothing factor for Vanka‐based Braess–Sarazin relaxation for the Stokes–Darcy Brinkman equations. Although the optimal damping parameter is dependent on meshsize and physical parameter, it is very close to one. In practice, we find that using three sweeps of Jacobi relaxation on the Schur complement system is sufficient. Numerical results of two‐grid and V(1,1)‐cycle are presented, which show high efficiency of the proposed relaxation scheme and its robustness to physical parameters and the meshsize. Using a damping parameter equal to one gives almost the same convergence results as these for the optimal damping parameter.

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.

Efficient optimal seismic design method of passive energy dissipation systems based on the inelasticity‐separated finite element method

AbstractInstalling passive energy dissipation dampers in the main structure is an effective way to reduce structural seismic response. The traditional optimal design of passive energy dissipation systems requires a massive nonlinear time history analysis, which is an extremely inefficient process and, as a result, limits its application in practice. In this paper, an efficient optimal design method for dampers is proposed based on the inelasticity‐separated finite element method (IS‐FEM) and genetic algorithm. The IS‐FEM is a novel efficient structural nonlinear analysis method that can avoid the real‐time updating and decomposition of the structural global stiffness matrix in a traditional structure analysis and only requires a small‐scale Schur complementary matrix representing local nonlinear behavior being decomposed per iteration. To make the IS‐FEM available for the analysis of structures equipped with an energy dissipation system, the inelasticity‐separated governing equations of displacement‐based dampers are derived first. Then, an improved constrained optimal genetic algorithm based on population feasibility is presented to enhance the searching ability near the feasible domain boundary. Finally, an efficient damper optimization design method is proposed by combining the developed genetic algorithm with the proposed IS‐FEM‐based analysis procedure for passive energy dissipation structures. The accuracy and efficiency of the proposed method are verified by designing a set of metallic yield dampers to retrofit a steel structure.

The prototype, mathematical model, sensitivity analysis and preliminary control strategy for Adaptive Tuned Particle Impact Damper

The paper presents a novel approach for prototyping and modelling of the Adaptive Tuned Particle Impact Damper (ATPID). After introducing the operation and potential disadvantages of the classical Particles Impact Dampers (PIDs) the authors propose the concept of single-grain controllable damper, which can adapt to actual dynamic excitation by a real-time change of the container height. The investigations focus on the methodology of simplified mathematical modelling of the ATPID damper based on grain physical properties, nonlinear soft contact theory, and control function of the absorber height being a novel component used to optimize dynamic response of the system. The proposed ATPID model is positively verified against the experimental results obtained from the developed test stand including a vibrating beam equipped with the proposed innovative attenuator. The conducted analyses clearly reveal the operating principles of the ATPID damper, the types of grain movement, the influence of shock absorber parameters on the vibrating system response and the energy balance of the system. The solution of the formulated optimization problem aimed at minimization of vibration amplitudes allows to find the optimal damper height for various physical parameters of the grain and the external excitation and to achieve a high efficiency of the proposed damper reaching 90%. In addition, a real-time control strategy providing adaptation of the ATPID damper to changing amplitude of kinematic excitation and effective mitigation of steady-state vibrations is proposed and verified experimentally.

Effect of internal damping on locomotion in frictional environments.

The gaits of undulating animals arise from a complex interaction of their central nervous system, muscle, connective tissue, bone, and environment. As a simplifying assumption, many previous studies have often assumed that sufficient internal force is available to produce observed kinematics, thus not focusing on quantifying the interconnection between muscle effort, body shape, and external reaction forces. This interplay, however, is critical to locomotion performance in crawling animals, especially when accompanied by body viscoelasticity. Moreover, in bioinspired robotic applications, the body's internal damping is indeed a parameter that the designer can tune. Still, the effect of internal damping is not well understood. This study explores how internal damping affects the locomotion performance of a crawler with a continuous, viscoelastic, nonlinear beam model. Crawler muscle actuation is modeled as a traveling wave of bending moment propagating posteriorly along the body. Consistent with the friction properties of the scales of snakes and limbless lizards, environmental forces are modeled using anisotropic Coulomb friction. It is found that by varying the crawler body's internal damping, the crawler's performance can be altered, and distinct gaits could be achieved, including changing the net locomotion direction from forward to back. We will discuss this forward and backward control and identify the optimal internal damping for peak crawling speed.

Optimal tuned outrigger-ATMD systems considering seismic and wind loads

This paper formulates the optimal feedback control model for the outrigger-active tuned mass damper (ATMD) system and investigates the influence of some input variables on the control effect while considering seismic and wind loads. The paper first deduces the joint equation of motion of the outrigger-ATMD system. Different control theories are then used to formulate the optimal control force, the optimal frequency tuning, and the optimal damping tuning. Based on such optimal tuned outrigger-ATMD systems, sensitivity analyses for variables from the ATMD and outrigger system are implemented. With many carefully selected schemes, the control effect and efficiency of the control model of the ATMD are verified in the frequency domain and time domain. It is observed that the fixed-points theory is a better choice for the ATMD tuning and the supplement damping in the outrigger system will suppress the control performance of the ATMD.