Layered metastructure containing freely-designed local resonators for wave attenuation

Combining periodic layered structure with three-dimensional cylindrical local resonators,a hybrid metastructure with improved wave isolation ability was designed and investigated through theoretical and numerical approaches.The metastructure is composed of periodic rubber layers and concrete layers embedded with three-dimensional resonators,which can be freely designed with multi local resonant frequencies to attenuate vibrations at required frequencies and widen the attenuation bandgap.The metastructure can also effectively attenuate seismic responses.Compared with layered rubber-based structures,the metastructure has more excellent wave attenuation effects with greater attenuation and wider bandgap.

Frequency-dependent attenuation of P and S waves in Yunnan region

We analyzed digital seismogram data of 5668 earthquakes that occurred in Yunnan region between July of 1999 and December of 2003. Among the 22 seismic stations, six ones, namely Baoshan, Yongsheng, Lijiang, Heqing, Yimen, and Luquan, were selected and their attenuations of P and S waves were measured by using the extended coda-normalization method. The six stations were classified into three regions according to their location, that is, Baoshan area, Yongsheng-Lijiang-Heqing (YLH) area and Luquan-Yimen (LY) area. The values of QS-1 and QP-1 are expressed as QS-1=0.00867 f-0.86, QP-1=0.01155 f-0.93, QS-1=0.01824 f-0.92, QP-1=0.02288 f-0.92, and QS-1=0.01647 f-0.91, QP-1=0.02826 f-0.97 in Baoshan, YLH, LY areas respectively. The attenuation of YLH, LY are closer to each other, however, Baoshan area is apparently lower. Comparing attenuation in the three areas with other areas of the world using the same method, it is suggested that the attenuations of P and S waves in YLH and LY areas are close to Kanto of Japan, but much higher than southeast of South Korea. The QS-1 and QP-1 in Baoshan area are slightly higher than southeastern South Korea. Furthermore, the results indicate that our QS-1 in Yunnan area is close to others by analyzing the coda attenuation.

The attenuation of stress waves in fluid saturated porous rock

The dynamic mechanical frequency spectrum and temperature spectrum measurements of dry and saturated sandstone with three different porosity are conducted by use of the viscoelastic spectrum instrument in the 0.01～100 Hz frequency region. The frequency responses of the attenuation and modulus at different temperature peaks are obtained. With increase of the porosity and the loss of the complex modulus, the attenuation in the saturated sandstones is increased, and the frequency dispersion is enhanced. The relation between the frequency spectrum and the temperature spectrum are also discussed.

Modeling wave attenuation by vegetation with accompanying currents in SWAN

Coastal wetlands such as salt marshes and mangroves provide important protection against stormy waves.Accurate assessments of wetlands’capacity in wave attenuation are required to safely utilize their protection services.Recent studies have shown that tidal currents have a significant impact on wetlands’wave attenuation capacity,but such impact has been rarely considered in numerical models,which may lead to overestimation of wave attenuation in wetlands.This study modified the SWAN(Simulating Waves Nearshore)model to account for the effect of accompanying currents on vegetation-induced wave dissipation.Furthermore,this model was extended to include automatically derived vegetation drag coefficients,spatially varying vegetation height,and Doppler Effect in combined current-wave flows.Model evaluation against an analytical model and flume data shows that the modified model can accurately simulate wave height change in combined current-wave flows.Subsequently,we applied the new model to a mangrove wetland on Hailing Island in China with a special focus on the effect of currents on wave dissipation.It is found that the currents can either increase or decrease wave attenuation depending on the ratio of current velocity to the amplitude of the horizontal wave orbital velocity,which is in good agreement with field observations.Lastly,we used Hailing Island site as an example to simulate wave attenuation by vegetation under hypothetical storm surge conditions.Model results indicate that when currents are 0.08–0.15 m/s and the incident wave height is 0.75–0.90 m,wetlands’wave attenuation capacity can be reduced by nearly 10%compared with pure wave conditions,which provides implications for critical design conditions for coastal safety.The obtained results and the developed model are valuable for the design and implementation of wetland-based coastal defense.The code of the developed model has been made open source,in the hope to assist further research and coastal management.

Attenuation of ground vibrations due to different technical sources

The attenuation of technically induced surface waves is studied theoretically and experimentally. In this paper, nineteen measurements of ground vibrations induced by eight different technical sources including road and rail traffic, vibratory and impulsive construction work or pile driving, explosions, hammer impulses and mass drops are described, and it is shown that the technically induced ground vibrations exhibit a power-law attenuation v - r ~ where the exponents q are in the range of 0.5 to 2.0 and depend on the source types. Comparisons performed demonstrate that the measured exponents are considerably higher than theoretically expected. Some potential effects on ground vibration attenuation are theoretically analyzed. The most important effect is due to the material or scattering damping. Each frequency component is attenuated exponentially as exp（-kr）, but for a broad-band excitation, the sum of the exponential laws also yields a power law but with a high exponent. Additional effects are discussed, for example the dispersion of the Rayleigh wave due to soil layering, which yields an additional exponent of 0.5 in cases of impulsive loading.

Wave Attenuation Performance and the Influencing Factors of A Lower Arc-Plate Breakwater

Comprehensive experimental and numerical studies have been undertaken to investigate wave energy dissipation performance and main influencing factors of a lower arc-plate breakwater. The numerical model, which considers nonlinear interactions between waves and the arc-plate breakwater, has been constructed by using the velocity wave- generating method, the volume of fluid (VOF) method and the finite volume method. The results show that the relative width, relative height and relative submergence of the breakwater are three main influencing factors and have significant influence on wave energy dissipation of the lower arc-plate open breakwater. The transmission coefficient is found to decrease with the increasing relative width, and the minimum transmission coefficient is 0.15 when the relative width is 0.45. The reflection coefficient is found to vary slightly with the relative width, and the maximum reflection coefficient is 0.53 when the relative width is 0.45. The transmission and reflection coefficients are shown to increase with the relative wave height for approximately 85% of the experimental tests when the relative width is 0.19 0.45. The transmission coefficients at relative submergences of 0.04, 0.02 and 0 are clearly shown to be greater than those at relative submergences of 0.02 and 0.04, while the reflection coefficient exhibits the opposite relationship. After the wave interacts with the lower arc-plate breakwater, the wave energy is mainly converted into transmission, reflection and dissipation energies. The wave attenuation performance is clearly weakened for waves with greater heights and longer periods.

ON THE INTERACTION OF WATER WAVES AND SEABED BY THE POROUS MEDIUM MODEL

The interaction of water waves and seabed is studied by using Yamamoto's model, which takes into account the deformation of soil skeletal frame, compressibility of pore fluid flow as well as the Coulumb friction. When analyzing the propagation of three kinds of stress waves in seabed, a simplified dispersion relation and a specific damping formula are derived. The problem of seabed stability is further treated analytically based on the Mohr-Coulomb theory. The theory is finally applied to the coastal problems in the Lian-Yun Harbour and compared with observations and measurements in soil-wave tank with satisfactory results.

Hydrodynamic Performance of Vertical Porous Structures Under Regular Waves

The hydrodynamic efficiency of the vertical porous structures is investigated under regular waves by use of physical models. The hydrodynamic efficiency of the breakwater is presented in terms of the wave transmission （kt）, reflection （kr） and energy dissipation （ka） coefficients. Different wave and structural parameters affecting the breakwater efficiency are tested. It is found that, the transmission coefficient （kt） decreases with the increase of the relative water depth （h/L）, the wave steepness （Hi^L）, the relative breakwater widths （B/L, B/h）, the relative breakwater height （D/h）, and the breakwater porosity （n）. The reflection coefficient （kr） takes the opposite trend of kt when D/h=l.25 and it decreases with the increasing h/L, HJL and B/L when D/h〈1.0. The dissipation coefficient （kd） increases with the increasing h/L, HilL and B/L when D/h〈_l.O and it decreases when D/h=l.25. In which, it is possible to achieve values ofkt smaller than 0.3, k~ larger than 0.5, and kd larger than 0.6 when D/h=1.25, B/h=0.6, h/L〉0.22, B/L〉O. 13, and H/L 〉0.04. Empirical equations are developed for the estimation of the transmission and reflection coefficients. The results of these equations are compared with other experimental and theoretical results and a reasonable agreement is obtained.

A rapid assessment method for calculating the drag coefficient in wave attenuation by vegetation

Vegetation in wetlands is a large-scale nature-based resource that can provide multiple benefits to human beings and the environment,such as wave attenuation in coastal zones.Traditionally,there are two main calibration approaches to calculate the attenuation of wave driven by vegetation.The first method is a straightforward one based on the exponential attenuation of wave height in the direction of wave transmission,which,however,overlooks the crucial drag coefficient(CD).The other method is in accordance with more complicate equations for predicting the damping factor,which is regarded as a function of CD.In this study,a new relation,combining these above two conventional approaches,is proposed to predict the CD in an operative approach.Results show that values yielded by the new assessment method perform a strong linear relationship with a collection of historical observations,with a promising R2 value of 0.90.Besides,the linear regression derives a new predictive equation for the bulk drag coefficient.Additionally,a calibrated value of 4 for the empirical plant drag coefficient(CP)is revealed.Overall,this new equation,with the superiority of the convenient exponential regression,is expected to be a rapid assessment method for calculating wave attenuation by vegetation and predicting the drag coefficient.

Wave Extraction and Attenuation Performance of An Edinburgh Duck Wave Energy Converter

Edinburgh Duck wave energy converter(ED WEC)has excellent energy extraction performance and shows a great potential to integrate with other marine structures.This paper aims to investigate its wave energy extraction performance as a WEC and wave attenuation performance as a protection method for shoreline or marine structures.The wave and ED WEC interactions in regular waves are modeled using the Star-CCM+software and verified by comparisons with published experimental results.The motion response,energy conversion efficiency,and transmission coefficient of the ED WEC with different attack angles,rotation center,and incident wave heights are investigated.Results indicate that the ED WEC with an attack angle of 42°and a rotation center of 0.55 m below the mean water line can achieve both good wave energy extraction and wave attenuation performances.The wave energy extraction and wave attenuation performance of the ED WEC decrease significantly with the increase of wave nonlinearity characterized by the wave steepness.This paper can guide the practical application of the ED WEC at the early stage of design.

Dispersion of Axisymmetric Longitudinal Waves in A Bi-Material Compound Solid Cylinder Made of Viscoelastic Materials

The paper studies the dispersion of axisymmetric longitudinal waves in the bi-material compound circular cylinder made of linear viscoelastic materials.The investigations are carried out within the scope of the piecewise homogeneous body model by utilizing the exact equations of linear viscoelasto-dynamics.The corresponding dispersion equation is derived for an arbitrary type of hereditary operator and the algorithm is developed for its numerical solution.Concrete numerical results are obtained for the case where the relations of the constituents of the cylinder are described through fractional exponential operators.The influence of the viscosity of the materials of the compound cylinder on the wave dispersion is studied through the rheological parameters which indicate the characteristic creep time and long-term values of the elastic constants of these materials.Dispersion curves are presented for certain selected dispersive and non-dispersive attenuation cases under various values of the problem parameters and the influence of the aforementioned rheological parameters on these curves is discussed.As a result of the numerical investigations,in particular,it is established that in the case where the rheological parameters of the components of the compound cylinder are the same,the viscosity of the layers’materials causes the axisymmetric wave propagation velocity to decrease.

Wave Attenuation and Friction Coefficient on the Coral-Reef Flat

Several sets of S4 direction-wave-current-tide meters have been deployed on the coral-reef flat of Yongshu Reef in the sea area of Nansha Islands.Based on the observational sea wave data, the attenuation characteristics of the waves propagating on the coral reef flat, the bottom friction coefficients and the transfer of wave energy are discussed in the paper. The results show that, in the relative depths of 0.0613～0.0867, the wave height attenuation per unit distance of wave propagation is 22.09%～46.56%, with an average of 31.35%; the wave energy attenuation coefficient, 33.74%～53.22%, with an average of 43.61%. The average of the bottom friction coefficients on the coral-reef flat is 0.1346, which is about 10 times that on the sand or silt bottom. In the course of propagation on the reef flat, the waves sustain more loss in high frequency than in low frequency and the spectral energy transfers to the low frequency. These results may be used for reference in island and reef engineering.

Characteristics of Vibrational Wave Propagation and Attenuation in Submarine Fluid-Filled Pipelines

As an important part of lifeline engineering in the development and utilization of marine resources, the submarine fluid-filled pipeline is a complex coupling system which is subjected to both internal and external flow fields. By utilizing Kennard＇s shell equations and combining with Helmholtz equations of flow field, the coupling equations of submarine fluid-filled pipeline for n=0 axisymmetrical wave motion are set up. Analytical expressions of wave speed are obtained for both s=1 and s=2 waves, which correspond to a fluid-dominated wave and an axial shell wave, respectively. The numerical results for wave speed and wave attenuation are obtained and discussed subsequently. It shows that the frequency depends on phase velocity, and the attenuation of this mode depends strongly on material parameters of the pipe and the internal and the external fluid fields. The characteristics of PVC pipe are studied for a comparison. The effects of shell thickness/radius ratio and density of the contained fluid on the model are also discussed. The study provides a theoretical basis and helps to accurately predict the situation of submarine pipelines, which also has practical application prospect in the field of pipeline leakage detection.

Research on propagation properties of elastic waves in two-phase anisotropic media

With the development of seismic engineering and seismic exploration of energy, the underground media that westudy are more and more complicated. Conventional anisotropy theory or two-phase isotropy theory is difficult todescribe anisotropic media containing fluid, such as fractures containing gas, shales containing water Based onBlot theory about two-phase anisotropy, with the use of elastic plane wave equations, we get Christoffel equations.We calculate and analyze the effects of frequency on phase velocity, attenuation, amplitude ratio and polarizationdirection of elastic waves of two-phase, transversely isotropic media. Results show that frequency affects slow Pwave the greatest among the four kinds of waves, i.e., fast P wave, slow P wave, fast S wave and slow S wave.Fluid phase amplitude to solid phase amplitude ratio of fast P wave, fast S wave and slow S wave approaches unitfor large dissipation coefficients. Polarization analysis shows that polarization direction of fluid phase displacement is different from, not parallel to or reverse to, that of solid phase displacement in two-phase anisotropic media.

Hydroelastic Investigation on A Pile Breakwater Integrated with A Flexible Tail for Long-Wave Attenuation

A novel concept of wave attenuator is proposed for the defense of long waves,through integrating a flexible tail to the lee-side surface of a pile breakwater.The flexible tail works as a floating blanket made up of hinged blocks,whose scale and stiffness can be easily adjusted.A two-phase-flow numerical model is established based on the open-source computational fluid dynamics(CFD)code OpenFOAM to investigate its wave attenuation performance.Incompressible Navier−Stokes equations are solved in the fluid domain,where an additional computational solid mechanics(CSM)solver is embedded to describe the elastic deformation of the floating tail.The coupling of fluid dynamics and structural mechanics is solved in a full manner to allow assess of wave variation along the deforming body.The accuracy of the numerical model is validated through comparison with experimental data.Effects of the flexible tail on performance of the pile breakwater are investigated systematically.Dynamic behaviours of the tail are examined,and characteristics of its natural frequency are identified.For safety reasons,the wave loads impacting on the main body of the pile breakwater and the stress distribution over the tail are specially examined.It is found that both the length and stiffness of the tail can affect the wave-attenuation performance of the breakwater.A proper choice of the length and stiffness of the tail can greatly improve the long-wave defending capability of the pile breakwater.The maximum stress over the flexible tail can be restrained through optimising the deformation and stiffness of the tail.

Experimental Study on Wave Attenuation Performance of A New Type of Floating Breakwater with Twin Pontoons and Multi Porous Vertical Plates

A floating breakwater(FB)has extensive potential applications in the fields of coastal,offshore,and ocean engineering owing to its advantages such as eco-friendliness,low cost,easy and rapid construction,and quick dismantling and reinstallation.An FB composed of twin pontoons and multi-porous vertical plates is proposed to improve the wave attenuation performance.The wave attenuation performance is investigated for different FB structures and vertical plate types under different incident wave heights and periods using 2D wave physical model tests in a wave flume.The results demonstrate that the proposed FB has a better performance than that of the conventional single pontoon-type FB.It reduces the wave transmission due to its enhanced wave reflection and energy loss.The wave transmission coefficient of the proposed FB decreases with an increase in the number of layers and relative draft depth of the vertical plates.However,a further decrease in the wave transmission coefficient is not observed when the number of porous vertical plates is increased from 4 to 5 layers.An equation has been derived to predict the wave transmission of the proposed FB based on the experimental results.

Wave Extraction and Attenuation Performance of A Hybrid System of An Edinburgh Duck WEC and A Floating Breakwater

Installing the Edinburgh Duck Wave Energy Converter(ED WEC)on a floating breakwater provides a potential solution to reduce costs and improve the reliability of the ED WEC.To investigate the interactions between the ED WEC and the breakwater,a two-dimensional numerical model of a hybrid WEC-breakwater system is established based on Star-CCM+Computational Fluid Dynamics(CFD)software.The wave energy extraction performance,wave attenuation performance,and wave forces on the breakwater of the hybrid system are compared with those of the corresponding single device.The effects of the initial attack angle,the distance between the WEC and the breakwater,and the incident wave height on the pitch motion,energy conversion efficiency,transmission coefficient,and wave forces on the breakwater of the hybrid system are analyzed.The results indicate that combing the ED WEC with a breakwater can improve the energy extraction performance of the ED WEC and reduce the wave forces on the breakwater in shorter-period waves.The conversion efficiency of the hybrid system with the initial attack angle of 42°is the largest in shorter-period waves,but is reduced with the increase of initial attack angle in longer-period waves.The wave attenuation performance of the hybrid system is determined by the draft of the breakwater.The distance between the WEC and the breakwater has little effect on the hybrid system.Wave energy extraction of the ED WEC of the hybrid system decreases significantly with the increase of the incident wave height.

An electromagnetic wave attenuation superposition structure for thin-layer plasma

This work proposes a new plasma super-phase gradient metasurfaces(PS-PGMs)structure,owing to the limitations of the thin-layer plasma for electromagnetic wave attenuation.Based on the cross-shaped surface unit configuration,we have designed the X-band absorbing structure through the dispersion control method.By setting up the Drude dispersion model in the computer simulation technology,the designed phase gradient metasurfaces structure is superposed over the plasma,and the PS-PGMs structure is constructed.The electromagnetic scattering characteristics of the new structure have been simulated,and the reflectance measurement has been carried out to verify the absorbing effect.The results demonstrate that the attenuation effect of the new structure is superior to that of the pure plasma structure,which invokes an improved attenuation effect from the thin layer plasma,thus enhancing the feasibility of applying the plasma stealth technology to the local stealth of the strong scattering part of a combat aircraft.

Multi-transmitting formula for attenuating waves

The MTF is extended to case of attenuating incident wave by introducing an attenuation coefficient. The reflection coefficients of this modified MTF and MTF are evaluated and compared when an attenuating wave impinges on the boundary, and the results demonstrate that MTF can be used to absorb slightly attenuating waves and the modified MTF is more capable of absorbing heavily attenuating waves than MTF. The accuracy of modified MTF is also tested by numerical examples of fluid saturated porous media.

Attenuation of stress wave in sandstone

This article has processed the experimental study of stress wave propagation using Hopkinson Pressure Bar, andmeasured with groups of PVDF stress sensors, obtained the waveform characteristics and the attenuation constant, and got the dynamic constitutive relations using Lagrangian analysis method.