Radiation Damping Research Articles

Sound attenuation in high mach number oscillating bubble media

We study theoretically and numerically sound attenuation in bubble-containing media when the bubbles are freely oscillating at high Mach numbers. This paper expands one of the main forms of bubble-related acoustic damping factors by extending the previous theories to higher Mach numbers, further improves the theories of nonlinear sound propagation in bubble-containing media. A nonlinear sound propagation model incorporating second-order liquid compression terms is developed, expressing the sound velocity and density in the medium as a function of the driving pressure, and taking into account the higher-order liquid compression effects on sound propagation. The correctness of the proposed model is verified by comparing with a linear model and a nonlinear model containing only low-order Mach number terms. When the bubble oscillates at a high Mach number, radiation damping, which is directly related to Mach number, becomes the main damping component affecting sound attenuation. The higher the driving amplitude, the stronger the nonlinear effect, and the greater the impact of high-order liquid compression effects on the sound attenuation, the more necessary it is to use the proposed model to calculate the sound attenuation. For high Mach numbers, varying the bubble radius and bubble number density, respectively, the difference between the proposed model and the model containing only low-order Mach number terms in capturing the pressure-dependent attenuation is calculated. Due to stronger radiation damping in smaller bubbles, the effect of compressibility becomes more important. The smaller the bubble radius, the greater the half-quality factor of the curve related to the difference in attenuation calculated by the two models, the more necessary it is to calculate the pressure-dependent attenuation using the proposed model. Here, the half-quality factor is defined as the corresponding frequency bandwidth when the curve falls from the maximum value to 22 times. Without considering the coupling effect between bubbles, the half-quality factor of the curve is not affected by the bubble number density.

Comparative study on the capture performance of two wave energy converters integrated into the jacket-frame foundation

The global pursuit of clean energy resources to cope with escalating energy demands has underscored the pivotal roles of wind and wave power as two prominent renewable energy sources for the power industry. In order to promote the comprehensive harnessing of ocean energy, research efforts have increasingly focused on hybrid approaches, aiming to concurrently capture wind and wave energies. This paper proposes two types of wind-wave hybrid device, which combines wind turbine with a wave energy converter (WEC), based on jacket-frame foundation. The numerical models of the WECs were created using SOLIDWORKS, and the subsequent simulations were conducted using ANSYS Workbench. The comparative analysis revealed that the heave-type WEC had less added mass and radiation damping, coupled with larger response amplitude operator (RAO) and shorter natural period compared to the swinging counterpart. Meanwhile, the swing-type WEC exhibited higher motion speed and greater support reaction force and connecting force, thereby exerting more pronounced influence on the foundation. However, the average hourly power generation of the swinging WEC was significantly better in terms of power capture. In practice, the choice between these WEC configurations should consider aligning the power matrix with the probability distribution of prevailing sea state conditions.

Estimation of Radiation Damping Rates Using 133Cs, 7Li and 31P Solution NMR Spectroscopy and a Theoretical NMR RASER Model

Radio amplification using stimulated emission of radiation (RASER) effects in the NMR can increase NMR signals over time due to a feedback loop between the sample magnetization and the probe coil coupled with radiation damping (RD). Previously, RD rates had been directly observed only for the 1H, 3He, 17O and 129Xe nuclei. We report that experimental direct measurements of an NMR RASER to determine RD time constants for the three heteronuclei (133Cs (I = 7/2), 7Li (I = 3/2) and 31P (I = 1/2)) in a highly concentrated solution from the NMR RASER emissions using a conventional NMR probe. Under conditions where the RD rate exceeds the transverse relaxation rate (i.e., the NMR RASER condition is fulfilled), we recorded both the transverse NMR RASER response to imperfect inversion and the recovery of longitudinal magnetization. The data were directly evaluated based on the well-known Bloom model as estimated RD rate constants of 8.0, 1.8 and 25 Hz for 133Cs, 7Li and 31P, respectively. The proposed method can be applied to observe RD rate constants for the other nuclei as well.

Toroidal Alfvén eigenmodes observed in low power JET deuterium–tritium plasmas

The Joint European Torus recently carried out an experimental campaign using a plasma consisting of both deuterium (D) and tritium (T). We observed a high-frequency mode using a reflectometer and an interferometer in a D-T plasma heated with low power neutral beam injection, . This mode was observed at a frequency and was located at major radii . The observed mode was identified as a toroidal Alfvén eigenmode (TAE) using the linear MHD code, MISHKA. Beam ions and fusion-born alpha particles were modelled using the full orbit particle tracking code LOCUST, which produces smooth distribution functions suitable for stability calculations without analytical fits or the use of moments. We calculated the stability of the 21 candidate modes using the HALO code. These calculations revealed that beam ions can drive TAEs with toroidal mode numbers with linear growth rates , while TAEs with n < 8 are damped by the beam ion population. Alpha particles drive modes with significantly smaller linear growth rates, due to the low alpha power generated almost exclusively by beam-thermal fusion reactions. Non-ideal effects were calculated using complex resistivity in the CASTOR code, leading to an assessment of radiative, collisional, and continuum damping for all 21 candidate modes. Ion Landau damping was modelled using Maxwellian distribution functions for bulk D and T ions in HALO. Radiative damping, the dominant bulk damping mechanism, suppresses modes with high toroidal mode numbers. Comparing the drive from energetic particles with damping from thermal particles, we find all but one of the candidate modes are damped. The single net-driven n = 9 TAE with a net growth rate matches experimental observations with a lab frequency and location . The TAE was driven by co-passing particles through the resonance. Both co- and counter-passing alpha particles drive the TAE through the resonance. Additional sideband resonances contribute significant drive for both beam and alpha particles.

A new radiation reaction approximation for particle dynamics in the strong field regime

Context. Following particle trajectories in the intense electromagnetic field of a neutron star is prohibited by the large ratio between the cyclotron frequency ωB and the stellar rotation frequency Ω. No fully kinetic simulations on a macroscopic scale and with realistic field strengths have been performed so far due to the huge computational cost implied by this enormous scale of separation. Aims. In this paper, we derive new expressions for the particle velocity subject to strong radiation reaction that are intended to be more accurate than the current state-of-the-art expression in the radiation reaction limit regime, the so-called Aristotelian regime. Methods. We shortened the timescale hierarchy by solving the particle equation of motion in the radiation reaction regime, where the Lorentz force is always and immediately balanced by the radiative drag, and including a friction not necessarily opposite to the velocity vector, as derived in the Landau-Lifshitz approximation. Results. Starting from the reduced Landau-Lifshitz equation (i.e., neglecting the field time derivatives), we found expressions for the velocity depending only on the local electromagnetic field configuration and on a new parameter related to the field strength that controls the strength of the radiative damping. As an example, we imposed a constant Lorentz factor γ during the particle motion. We found that for ultra-relativistic velocities satisfying γ ≳ 10, the difference between strong radiation reaction and the radiation reaction limit becomes negligible. Conclusions. The new velocity expressions produce results similar in accuracy to the radiation reaction limit approximation. We therefore do not expect this new method to improve the accuracy of neutron star magnetosphere simulations. The radiation reaction limit is a simple but accurate, robust, and efficient way to follow ultra-relativistic particles in a strong electromagnetic field.

A random non-uniform wave input method based on complex incident site waves

To improve the deficiency of the wave input method (WIM) in expressing complex incident site waves, in this paper, a random non-uniform wave input method (RNUWIM) is derived from the use of the random incident waves and the visco-elastic boundary condition. The random incident waves are generated and adjusted by the comparison of the horizontal ground motion’s response spectrum and the target spectrum, so that they are representative of the actual wavefield in project sites. Furthermore, the RNUWIM is implemented and verified by the finite element method. The result shows that the RNUWIM inherits the advantages of the WIM in simulating the wave propagation effect and the radiation damping effect. In the new method, the spatial variation of ground motions such as time delays, peak variation, and time-history shape differences can be simulated synthetically. The errors of RNUWIM in ground acceleration, velocity, and displacement at the reference point are respectively 3.23%, 0.66%, and 0.07% in one case, which proves the efficiency of the RNUWIM in seismic response analyses.

Enhanced circular dichroism in twisted double layer nanoparticle arrays with the excitation of hybridized surface lattice resonances

The realization of enhanced circular dichroism using chiral nanostructures is crucial for the development of functional nanophotonic devices. This study proposes to construct chiral structures by adjusting the relative orientation between two vertically shifted rectangular nanodisk arrays. In comparison to localized plasmon modes, the twisted array allows selective excitation of hybridized surface lattice resonances by left- or right-handed circularly polarized incidence, and the strong interactions among individual nanoparticles result in enhanced circular dichroism. The calculation results demonstrate a significant differential transmittance of up to 0.61, which is more than one order of magnitude stronger than that of localized modes. Moreover, the chiral responses can be effectively controlled by manipulating geometry parameters such as inter-layer separation, twisted angle, and lattice spacing, as these factors govern the coupling efficiency with the external field and the radiative damping of the hybridized modes. The proposed twisted array structure offers a versatile platform for manipulating chiral light fields.

Estimation of the dissipation due to radiation damping for the pile embedded in soil: A closed-form solution

In the present work, the overall energy dissipation of a pile embedded in the soil, modeled as visco-elastic springs, is thoroughly investigated. The term dissipation is used to measure the rate of decay of amplitude of displacement response in the time domain. The estimation of dissipation in piles is necessary to understand how quickly a pile reaches its steady state or equilibrium under dynamic loads or in cases of free vibration, respectively. A higher level of dissipation indicates a shorter duration of transient vibration, which is a deserving trait for vibration mitigation in extreme events, such as earthquakes, storms, blasts, shocks, etc. The dispersion relation which is a function of wavenumber and free wave frequency is obtained for the pile embedded in the soil medium by implementing the generalized form of Bloch’s theorem. The dispersion relationship is solved in the free-wave approach, in which a real wave number yields a set of complex frequencies. For predicting the overall dissipation of the system from the complex frequency values, an analytical closed-form expression is proposed in this paper. Further, the predicted dissipation is validated with a finite element-based numerical model of the soil–pile system.

Global method for nonlinear seismic analysis of embedded base-isolated nuclear island buildings in layered sites

Owing to the increasing scarcity of high-quality sites, the seismic analysis of base-isolated nuclear power plants (NPPs) under complex non-lithology sites has gained important engineering significance. In this study, a global method for nonlinear numerical analysis was developed for the seismic evaluation of base-isolated NPPs in complex layered sites. The seismic analysis of layered sites is realised using the equivalent linear method and one-dimensional wave propagation theory, the radiation damping of the infinite domain is modelled with a visco-elastic artificial boundary, and the nonlinear behaviour of the isolators is fully considered using a bilinear hysteretic model. Using this method, the influence of soil–structure interaction (SSI) and soil nonlinearity on the behaviour of base-isolated NPPs under the design basis earthquake and beyond design basis earthquake was analysed and compared, in terms of the floor response spectra (FRS) and inter-story displacement angle. In addition, the influence of embedment is also studied. The results show that in layered sites, the SSI significantly amplifies the response values for base-isolated NPPs, and as the ground motion input increases, the soil nonlinearity more effectively inhibits the response of base-isolated NPPs. In addition, embedding can significantly reduce the response, but it increases the FRS at some frequency domains. The isolation effect of base-isolated NPPs decreases significantly when SSI effects are considered, and the soil nonlinearity and embedment have little impact on the base isolation capacity. The method proposed in this study can be easily applied to study base-isolated NPPs in layered sites.

Experimental hydrodynamic assessment of a cylindrical-type floating solar system exposed to waves

In this paper, an experimental investigation on the wave loads and structural motions of two semi-fixed semi-immersed horizontal cylinders type rafts in the free surface zone is conducted. The physical models are tested at the 1:4.5 scale and exposed to a range of regular and irregular waves in a wave flume at Queen's University Belfast. The physical models and experimental setup are discussed alongside an investigation of the hydrodynamic phenomena, surge forces, and dynamic responses that each structure exhibits in the coastal wave climates. Furthermore, an investigation into the wave attenuation by both models is carried out. The results show that the surge forces have a positive correlation with wave steepness for both models. Hydrodynamic phenomena such as wave runup and overtopping, radiative damping and reflected waves, constructive interference, diffraction and flow separation were identified during the experiments. A negative mean heave displacement is observed during the monochromatic sea states which could result in impact loading and submergence of the superstructure components and photovoltaic panels at full-scale. The results presented in this paper may be used to calibrate and verify numerical models that calculate the global responses and hydrodynamic forces. It may also benefit the design processes of geometrically similar floating solar technologies by providing data on surge loads, motion responses and hydrodynamic observations.

Implementation of a coupled FEM-SBFEM for soil-structure interaction analysis of large-scale 3D base-isolated nuclear structures

Accurately simulating the radiation damping of an infinite domain is a crucial issue for reasonably and effectively evaluating the isolation effect of three-dimensional (3D) base-isolated nuclear structures considering soil-structure interaction (SSI). The scaled boundary finite element method (SBFEM) has excellent advantages that enable it to precisely fulfil the radiation conditions. In this study, the finite element method (FEM) and SBFEM were combined to develop a coupled FEM-SBFEM technology. The structure and finite domain were discretized using FEM, and the infinite soil was realised using SBFEM. A complete and efficient calculation procedure for SSI analysis was developed based on the coupled FEM-SBFEM, improving the calculation efficiency through parallel programming. The accuracy of the developed procedure was verified using a numerical example. Furthermore, the dynamic response of a large-scale refined 3D base-isolated reactor building considering SSI was analysed using the proposed method. The results demonstrate that the 3D base isolation technology has excellent isolation performance. Additionally, we compared the response results of the proposed coupled FEM-SBFEM and direct method. The proposed procedure has broad engineering applicability and can be used for seismic SSI analysis of large-scale nuclear structures while maintaining high computational accuracy and stability.

Efficient hydrodynamic analysis for preliminary design of Floating Offshore Wind substructures

The cost of Floating Offshore Wind (FOW) is driven by the foundation, thus it can be reduced by optimising the floater design from the early stage. Most of the numerical tools for the platform design integrate radiation–diffraction theory-based software, but it can make the whole process very time-consuming since the preliminary design phases usually imply the analysis of a large number of designs. In order to accelerate the first stages of design, and consequently, achieve the foundation cost reduction, this study proposes an efficient methodology for the hydrodynamic added mass, radiation damping, and excitation loads calculation. The method is implemented for a semi-submersible platform, and it is verified against the radiation–diffraction commercial software AQWA. The methodology is validated through a comparative analysis of the response of ten different platforms, and it has shown that the hydrodynamic coefficients derived from either radiation–diffraction analysis or from the proposed method lead to equivalent conclusions. The maximum values of the platform’s pitch angle and the nacelle acceleration are assessed, achieving a maximum deviation among the most critical designs of 3% and 17%, respectively. This methodology has demonstrated to provide with reasonable accuracy the dynamic behaviour of the offshore wind substructures achieving a significant computational cost reduction compared to the state-of-the-art methods, which enables to accelerate the optimisation process and thus, resulting in a more accurate floater preliminary design.

Beam shifts controlled by orbital angular momentum in a guided-surface plasmon resonance structure with a four-level atomic medium.

We proposed a scheme to realize tunable giant Goos-Hänchen (GH) and Imbert Fedorov (IF) shifts of the Laguerre-Gauss (LG) beam on a guided-wave surface plasmon resonance (GWSPR) structure backed by a coherent atomic medium with the spontaneously generated coherence (SGC) effect. The orbital angular momentum carried by the incident LG beam can be applied to enhance and control IF shifts but is not beneficial to GH shifts. However, in the presence of SGC effect in the atomic medium, both GH and IF shifts can be simultaneously enhanced and well controlled. With the SGC effect, the linear absorption of the atomic medium vanishes, while the nonlinear absorption of that can be significantly enhanced and controlled by the trigger field, which contributes to controlling of the beam shifts. In particular, the direction of GH shifts can be switched by the Rabi frequency of the trigger field, which can be interpreted as the result of a competition between the inherent damping and the radiative damping corresponding to the nontrivial change in the loci of the reflection coefficients. This scheme provides an effective method to flexibly control and enhance the beam shifts, so it has potential applications in integrated optics, optical sensors, etc.

Optimal decay estimates for the Vlasov–Poisson system with radiation damping

Optimal decay estimates for the Vlasov–Poisson system with radiation damping

Vibration and sound radiation of an acoustic black hole plate immersed in heavy fluid

Vibrational acoustic black holes (ABHs) have shown great promise for reducing structural vibrations and sound radiation in light fluids. However, it is still unknown whether the acoustic black hole (ABH) effect can be materialized in heavy fluids. This paper discusses this issue by developing a semi-analytical model on a simply supported ABH plate that vibrates and radiates sound into water. The proposed model is validated by finite element models and used to investigate the vibration and sound radiation properties of the ABH plate in different frequency ranges. The results show that the ABH effect can be systematically manifested in heavy fluids, as reflected by a significant increase in structural damping and a decrease in vibration and sound radiation. Numerical analysis of the radiation damping and mass loading effects shows that the radiation damping has little effect on the vibration reduction of the water-loaded plate. However, the mass loading effect mitigates the low-frequency drawback of conventional ABH structures in air, resulting in a broadband reduction in structural vibration and sound radiation from the water-loaded ABH plate.

Seismic damage characteristics of high arch dams under oblique incidence of SV waves

This study investigates the seismic damage characteristics of high arch dams considering the oblique incidence of seismic waves. Based on the dynamic implicit finite element method, a viscous-spring artificial boundary is applied to consider radiation damping of the infinite foundation, the seismic wave input is converted into an equivalent nodal force of the artificial boundary, and the equivalent nodal loads of the wave input under oblique incidence of the SV wave is deduced. Taking JP Ⅰ arch dam as an example, combined with the concrete damaged plasticity (CDP) model, the nonlinear dynamic response of the dam under 25° oblique incidence of the SV wave is conducted considering the geometrical nonlinearity of contraction joints and the dynamic mechanical properties of concrete materials. Based on the incremental dynamic analysis (IDA) method, the relative displacement and transverse joint opening are selected as the damage measures for fragility analysis of the arch dam. According to the damage distribution from the analysis of a large number of seismic time-history responses, the damage levels of the arch dam are classified. Three limit states of slight damage, moderate damage and severe damage are proposed for the arch dam. The average responses of the 10 earthquakes are considered as the limit values to quantitatively describe the damage of the arch dam. By fitting the results of incremental dynamic analysis, the seismic probabilistic demand model and seismic fragility curves for the two damage measures to predict the probability of the arch dam reaching damage levels under different seismic actions have been established. The fragility curve shows that the probability of severe damage is almost zero under the maximum design earthquake (PGA = 0.1971 g) and less than 5% under the maximum credible earthquake (PGA = 0.2299 g). It is concluded that JP Ⅰ arch dam has a high degree of safety redundancy and fully satisfies the “two levels” design requirements.

Evaluation of Geometrical Influence on the Hydrodynamic Characteristics and Power Absorption of Vertical Axisymmetric Wave Energy Converters in Irregular Waves

Abstract To obtain the mechanical energy of waves from arbitrary directions, the vibration absorbers of wave energy converters (WEC) are usually vertically axisymmetric. In such case, the wave-body interaction hydrodynamics is an essential research topic to obtain high-efficiency wave energy. In this paper, a semi-analytical method of decomposing the complex axisymmetric boundary into several ring-shaped stepped surfaces based upon the boundary approximation method (BAM) is introduced and examined. The hydrodynamic loads and parameters, such as the wave excitation forces, added mass and radiation damping of the vertical axisymmetric oscillating buoys, can then be achieved by using the new boundary discretisation method. The calculations of the wave forces and hydrodynamic coefficients show good convergence with the number of discretisation increases. Comparison between the constringent results and the results of the conventional method also verifies the feasibility of the method. Then, simulations and comparisons of the hydrodynamic forces, motions and wave power conversions of the buoys with series draught and displacement ratios in regular and irregular waves are conducted. The calculation results show that the geometrical shape has a great effect on the hydrodynamic and wave power conversion performance of the absorber. In regular waves, though the concave buoy has the lowest wave conversion efficiency, it has the largest frequency bandwidth for a given draught ratio, while in irregular waves, for a given draught ratio, the truncated cylindrical buoy has the best wave power conversion, and for a given displacement of the buoy, the concave buoy shows the best wave power conversion ability.

Hydrodynamic Investigation on Floating Offshore Wind Turbine Platform Integrated with Porous Shell

As the siting of wind turbines increasingly transitions from shallow water to offshore deep-water locations, improving the platform stability of floating offshore wind turbines is becoming a growing concern. By coupling a porous shell commonly used in traditional marine structures, with a FOWT (floating wind turbine platform), a new spar-buoy with a porous shell was designed. A numerical model investigating the coupling effect of the aero-hydro-mooring system is developed, and the results of the motion response are compared with the OC3-Hywind spar. The motion response of the two platforms was simulated in the time-domain with the incident wave period varied in the range of 5~22 s. The exciting wave force with added mass and radiation damping of the spar with the porous shell is compared with the OC3-Hywind spar. The results demonstrate that the motion response amplitude of the spar with the porous shell decreases in all three main motion freedoms (i.e., surge, heave and pitch, etc.), among which the heave motions are most significantly attenuated. The study shows that the coupling of porous shells with a floating platform to achieve the reduced motion responses is feasible and can be an innovative structure for the development of deep-sea offshore floating wind turbines.

Influence of Topographic and Geological Features on the Seismic Response of the Reef Site in the South China Sea

Insufficient comprehension of the seismic impact of the reef terrain, geology, and material properties of the reefs in the South China Sea still presents considerable impediments in studying the seismic response of reef engineering sites and assessing their seismic safety. To surmount this challenge, a seismic response analysis model of the reef-seawater system is established. This model takes into account the fluid-solid interaction effect, the wave radiation effect of the infinite seawater layer and the semi-infinite seabed, as well as the seismic wave input process of the reef-seawater system. Through targeted parameter analyses, the impact of various factors, including the shear wave velocity, thickness, and slope of distinct reef layers, the width of the reef flat, and the dynamic coupling effect of seawater on the seismic response of reef sites, is thoroughly examined. It has been determined that the seismic response of the reef site is markedly amplified as the shear wave velocity decreases and the thickness of the uppermost reef layer increases. While the effects of the slope gradient of the topmost reef layer and the width of the reef flat on the seismic response of the reef site are chiefly observed in the edge area and the central area, respectively. The layer of seawater plays a crucial role in radiation damping, serving as a medium for the dissipation of seismic energy and thereby weakening the overall seismic response of the reef site.

Nonlinear nonlocal metasurfaces

Optical metasurfaces have recently emerged as the game changer in light manipulation and opened up new perspectives in many subfields of optics and photonics. Recent developments in nonlocal metasurfaces, in which the nanoscale building blocks respond to the incoming light collectively rather than as individual objects, are especially promising for enhancing and controlling the nonlinear optical phenomena. In this article, we provide a brief overview of the basic principles of nonlocal metasurfaces in the context of their nonlinear optical functionalities. We discuss the origin and the regimes of the nonlocal response, covering the aspects of multiple scattering, radiation damping, quality factor, local-field enhancement, and temporal dynamics. Some important aspects are illustrated by computational examples. We also give our personal viewpoint on the selected ideas and research directions in nonlocal and nonlinear metasurfaces, including the role of spatial symmetry in nonlocal interactions, the effects of phase and momentum matching in frequency conversion, as well as the possibilities offered by new material platforms and novel concepts, such as bound states in the continuum, parity–time symmetry, and time-variant metasurfaces.