Towards identification of a general model of damping

Characterization of damping forces in a vibrating structure has long been an active area of research in structural dynamics. In spite of a large amount of research, understanding of damping mechanisms is not well developed. A major reason for this is that unlike inertia and stiffness forces it is not in general clear what are the state variables that govern the damping forces. The most common approach is to use `viscous damping' where the instantaneous generalized velocities are the only relevant state variables. However, viscous damping by no means the only damping model within the scope of linear analysis. Any model which makes the energy dissipation functional non-negative is a possible candidate for a valid damping model. This paper is devoted to develop methodologies for identification of such general damping models responsible for energy dissipation in a vibrating structure. The method uses experimentally identified complex modes and complex natural frequencies and does not a-priori assume any fixed damping model (eg., viscous damping) but seeks to determine parameters of a general damping model described by the so called `relaxation function'. The proposed method and several related issues are discussed by considering a numerical example of a linear array of damped spring-mass oscillators.

Implementation of semi-active damping on a tri-axle heavy-vehicle suspension

A semi-active truck damper was developed in conjunction with a commercial shock absorber manufacturer. A linearized damper model was developed for control system design purposes. Open- and closed-loop damper force tracking control was implemented, with tests showing that an open-loop approach gave the best compromise between response speed and accuracy. A hardware-in-the-loop test facility was used to investigate performance of the damper when combined with a simulated quarter-car model. The input to the vehicle model was a set of randomly generated road profiles, each profile traversed at an appropriate speed. Modified skyhook damping tests showed a simultaneous improvement over the optimum passive case of 13 per cent in vertical body acceleration and 8 per cent in dynamic tyre forces. Full-scale vehicle tests of the damper on a heavy tri-axle trailer were carried out. Implementation of modified skyhook damping yielded a simultaneous improvement over the optimum passive case of 8 per cent in vertical body acceleration and 8 per cent in dynamic tyre forces. © IMechE 2008.

Natural frequency and damping ratio of a vertically vibrated surface foundation

It is possible and common to obtain equivalent natural frequency and damping for a soil-foundation system from results of experimental or numerical analysis assuming the system has a single degree of freedom. Three approaches to extract natural frequency and damping were applied to the vertically vibrated soil-foundation system. The sensitivity of the computed natural frequency and damping to the soil properties was evaluated through parametric studies. About 10-20% of discrepancy in values of natural frequency was observed due to different approaches. The results help to assess the reliability of equivalent soil properties determined from the reported natural frequency of the system. Finally the results obtained using theoretical predictions with linear soil properties measured in situ were compared to those calculated from experimental data. The prediction and experimental results showed good agreements if the embedment of the foundation is neglected with stepped sine test but considered with impulse test. © 2010 Elsevier Ltd.

The role of damping in steel pan manufacture

Results are presented of systematic studies of vibration damping in steel of a type, and processed by a route, rel-evant to Caribbean steel pans. Damping is likely to be a significant factor in the variation of sound quality be-tween different pans. The main stages in pan manufac-ture are simulated in a controlled manner using sheet steel, cold-rolled to a prescribed level of thickness reduc-tion then annealed at a chosen temperature in a laboratory furnace. Small test strips were cut from the resulting material, and tested in free-free beam bending to deduce the Young’s modulus and its associated loss factor. It is shown that the steel type, the degree of cold working and the annealing temperature all have a significant influence on damping. Furthermore, for each individual specimen damping is found to decrease with rising frequency, ap-proximately following a power law. Comparison with samples cut from a real pan show that there are further influences from the pan’s geometrical details.

Shock amplification, curve veering and the role of damping

The circumstances are investigated under which high peak acceleration can occur in the internal parts of a system when subjected to impulsive driving on the outside. Previous work using a coupled beam model has highlighted the importance of veering pairs of modes. Such a veering pair can be approximated by a lumped system with two degrees of freedom. The worst case of acceleration amplification is shown to occur when the two oscillators are tuned to the same frequency, and for this case closed-form expressions are derived to show the parameter dependence of the acceleration ratio on the mass ratio and coupling strength. Sensitivity analysis of the eigenvalues and eigenvectors indicates that mass ratio is the most sensitive parameter for altering the veering behaviour in an undamped system. Non-proportional damping is also shown to have a strong influence on the veering behaviour. The study gives design guidelines to allow permissible acceleration levels to be achieved by the choice of the effective mass and damping of the indirectly driven subsystem relative to the directly driven subsystem. © 2013 Elsevier Ltd.

Magnetic damping of levitated liquid droplets in AC and DC field

The intense AC magnetic field required to produce levitation in terrestrial conditions, along with the buoyancy and thermo-capillary forces, results in turbulent convective flow within the droplet. The use of a homogenous DC magnetic field allows the convective flow to be damped. However the turbulence properties are affected at the same time, leading to a possibility that the effective turbulent damping is considerably reduced. The MHD modified K-Omega turbulence model allows the investigation of the effect of magnetic field on the turbulence. The model incorporates free surface deformation, the temperature dependent surface tension, turbulent momentum transport, electromagnetic and gravity forces. The model is adapted to incorporate a periodic laser heating at the top of the droplet, which have been used to measure the thermal conductivity of the material by calculating the phase lag between the frequency of the laser heating and the temperature response at the bottom. The numerical simulations show that with the gradual increase of the DC field the fluid flow within the droplet is initially increasing in intensity. Only after a certain threshold magnitude of the field the flow intensity starts to decrease. In order to achieve the flow conditions close to the ‘laminar’ a D.C. magnetic field >4 Tesla is required to measure the thermal conductivity accurately. The reduction in the AC field driven flow in the main body of the drop leads to a noticeable thermo-capillary convection at the edge of the droplet. The uniform vertical DC magnetic field does not stop a translational oscillation of the droplet along the field, which is caused by the variation in total levitation force due to the time-dependent surface deformation.

Radiation damping effects on L-shell photoionization cross- sections of O-like Fe xix and N-like recombination rate coefficients for Fe xx

Photoionization cross-sections out of the fine-structure levels (2S(2)2p(4) P-3(2,0,1)) of the O-like Fe ion Fe XIX have been reinvestigated. Data for photoionization out of each of these finestructure levels have been obtained, where the calculations have been performed with and without the inclusion of radiation damping on the resonance structure in order to assess the importance of this process. Recombination rate coefficients are determined using the Milne relation, for the case of an electron recombining with N-like Fe ions (Fe XX) in the ground state to form O-like Fe (Fe XIX) existing in each of the fine- structure ground-state levels. Recombination rates are presented over a temperature range similar to 4.0 less than or equal to log T-e less than or equal to 7.0, of importance to the modelling of X-ray emission plasmas.

Interpolation formula between very low and intermediate-to-high damping Kramers escape rates for single-domain ferromagnetic particles

It is shown that the Mel'nikov-Meshkov formalism for bridging the very low damping (VLD) and intermediate-to-high damping (IHD) Kramers escape rates as a function of the dissipation parameter for mechanical particles may be extended to the rotational Brownian motion of magnetic dipole moments of single-domain ferromagnetic particles in nonaxially symmetric potentials of the magnetocrystalline anisotropy so that both regimes of damping, occur. The procedure is illustrated by considering the particular nonaxially symmetric problem of superparamagnetic particles possessing uniaxial anisotropy subject to an external uniform field applied at an angle to the easy axis of magnetization. Here the Mel'nikov-Meshkov treatment is found to be in good agreement with an exact calculation of the smallest eigenvalue of Brown's Fokker-Planck equation, provided the external field is large enough to ensure significant departure from axial symmetry, so that the VLD and IHD formulas for escape rates of magnetic dipoles for nonaxially symmetric potentials are valid.

Damping torque analysis for DC bus implemented damping control

Damping torque analysis is a well-developed technique for understanding and studying power system oscillations. This paper presents the applications of damping torque analysis for DC bus implemented damping control in power transmission networks in two examples. The first example is the investigation of damping effect of shunt VSC (Voltage Source Converter) based FACTS voltage control, i.e., STATCOM (Static Synchronous Compensator) voltage control. It is shown in the paper that STATCOM voltage control mainly contributes synchronous torque and hence has little effect on the damping of power system oscillations. The second example is the damping control implemented by a Battery Energy Storage System (BESS) installed in a power system. Damping torque analysis reveals that when BESS damping control is realized by regulating exchange of active and reactive power between the BESS and power system respectively, BESS damping control exhibits different properties. It is concluded by damping torque analysis that BESS damping control implemented by regulating active power is better with less interaction with BESS voltage control and more robust to variations of power system operating conditions. In the paper, all analytical conclusions obtained are demonstrated by simulation results of example power systems.

Robustness of Damping Control Implemented by Energy Storage Systems Installed in Power Systems

An energy storage system (ESS) installed in a power system can effectively damp power system oscillations through controlling exchange of either active or reactive power between the ESS and power system. This paper investigates the robustness of damping control implemented by the ESS to the variations of power system operating conditions. It proposes a new analytical method based on the well-known equal-area criterion and small-signal stability analysis. By using the proposed method, it is concluded in the paper that damping control implemented by the ESS through controlling its active power exchange with the power system is robust to the changes of power system operating conditions. While if the ESS damping control is realized by controlling its reactive power exchange with the power system, effectiveness of damping control changes with variations of power system operating condition. In the paper, an example power system installed with a battery ESS (BESS) is presented. Simulation results confirm the analytical conclusions made in the paper about the robustness of ESS damping control. Laboratory experiment of a physical power system installed with a 35kJ/7kW SMES (Superconducting Magnetic Energy Storage) was carried out to evaluate theoretical study. Results are given in the paper, which demonstrate that effectiveness of SMES damping control realized through regulating active power is robust to changes of load conditions of the physical power system.