Influences of Floater Motion on Gap Resonance Triggered by Focused Wave Groups

The current study investigates the hydrodynamic characteristics of gap resonance within a narrow gap formed by two adjacent boxes subjected to incident focused transient wave groups.A two-dimensional(2D)numerical wave tank based on the OpenFOAM package is utilized for this purpose.The weather-side box is fixed while the lee-side box is allowed to heave freely under wave actions.The effects of the focused wave amplitude and spectral peak period on the wave amplification within the gap,motion of the lee-side box,and wave forces(including horizontal and vertical wave forces)acting on each box are systematically examined.For comparison,another structural layout consisting of two fixed boxes is also considered.The results reveal that the release of the heave degree of freedom(DoF)of the lee-side box results in remarkably distinct resonance features.In the heave-box system,both its fluid resonant period and the period corresponding to the maximum heave displacement of the lee-side box are significantly larger(i.e.,1.6-1.7 times)than the fluid resonant period of the fixed-box system.However,the wave amplification factor inside the gap in the heave-box system is significantly lower than that in the fixed-box one.Both the variations of the maximum horizontal and vertical wave forces with the spectral peak period and their magnitudes are also significantly different between the two structural systems.

Study on Transient Gap Resonance with Consideration of the Motion of Floating Body

In this paper, the transient fluid resonance phenomenon inside a narrow gap between two adjacent boxes excited by the incident focused waves with various spectral peak periods and focused wave amplitudes is simulated by utilizing the open-sourced computational fluid dynamics software, Open FOAM. The weather-side box is allowed to heave freely under the action of waves, and the lee-side box keeps fixed. This paper mainly focuses on how both the spectral peak period and the focused wave amplitude affect the free-surface amplification inside the gap, the motion of the weather-side box, and the wave loads(including the vertical and the horizontal wave forces) acting on both boxes.For comparison, another two-box system with both boxes fixed is also considered as a control group. It is found that the motion of the weather-side box significantly changes the characteristics of the transient gap resonance, and it would cause that the fluid resonant period becomes 1.4-1.6 times that of the two-box system with both boxes fixed.All the concerned physical quantities(i.e., the free-surface amplification in the gap, the motion of the weather-side box, the wave loads) are found to closely depend on both the spectral peak period and the focused wave amplitude.

Harmonic Analyses of Hydrodynamic Characteristics for Gap Resonance Between Fixed Box and Vertical Wall

Two marine structures arranged side by side with a narrow gap may suffer from violent free-surface resonance,which would cause green water on deck,dramatically raise hydrodynamic loads on structures and seriously threaten the operation safety.The CFD-based open-sourced software,OpenFOAM?,is employed to simulate the twodimensional fluid resonance inside a narrow gap between a fixed box and a vertical wall induced by regular waves with different wave heights.The topographies with various plane slopes are placed in front of the wall.The focus of this article is on the influences of the incident wave height and the topographic slope on the nonlinear characteristics of various hydrodynamic parameters(including the wave height in the gap,the vertical wave force,and the horizontal wave force on the box)during gap resonance.The ratios of their high-order to the corresponding 1 st-order components under different sets of the incident wave height and the topographic slope are analyzed.It is found that the relative importance of all the high-order components increases gradually with the incident wave height for all the three parameters.The topographic influence on them closely depends on the type of the parameters and the incident wave height.In addition,the occurrence of the 2 nd-order gap resonance phenomenon can cause the 2 nd-order wave height and horizontal force to be significantly larger than the corresponding 1 st-order components.

Investigation on Effects of Vertical Degree of Freedom on Gap Resonance Between Two Side-by-Side Boxes Under Wave Actions

The possible wave resonance in the narrow gap formed by the parallel arrangement of ships will lead to the sharp increase of wave loads and the rapid growth of motion response.The fluid resonance inside a narrow gap between two side-by-side boxes is investigated numerically based on an open-source CFD package,OpenFOAM.The upstream box remains fixed,while the downstream box is allowed to heave freely under wave actions.This work aims to examine the influence of the motion of the downstream box on the fluid resonant behaviors inside the gap.The hydrodynamic behaviors considered include the wave height inside the gap,the heave displacement,and the reflection,transmission,and energy loss coefficients.Gao et al.(2021)reported the influence of the motion of the upstream box on gap resonant behaviors.For comparative study,some results of Gao et al.(2021)are also presented in this work.It is found that the heave motion of any box in the two-box system leads to a smaller resonant wave height amplification and a larger fluid resonance frequency.The frequency at which the maximum heave displacement of the downstream box occurs is less than the fluid resonant frequency.The heave motion of any box in the two-box system results in a larger reflection coefficient and a smaller energy loss coefficient.

Investigations on Fluid Resonance Within A Narrow Gap Formed by Two Fixed Bodies with Varying Breadth Ratios

The resonant motion of the fluid inside a narrow gap between two fixed boxes induced by incident regular waves with various wave heights is investigated by adopting a two-dimensional numerical wave flume based on an opensourced CFD package,OpenFOAM.The two boxes have identical draft and height,but the upstream box has a variable breadth.This article focuses on the influences of the breadth ratio,defined as the ratio of the breadth of the upstream box to that of the downstream box,on the following three aspects of hydrodynamic characteristics of gap resonance:(1)the wave height amplifications inside the gap,and in front and at the rear of the structure system,(2)the reflection,transmission,and energy loss coefficients of the structure system,and(3)the response and damping time of the fluid resonance.It is found that the fluid resonant frequency,the amplification factor of the resonant wave height inside the gap and the maximum energy loss coefficient of the structure system are shown to gradually decrease with the increase of the breadth ratio.The response time of gap resonance is shown to first increase and then decrease with the breadth ratio overall,regardless of the incident wave height,and the configuration that the two boxes have the same breadth would bring the largest response time of gap resonance.

A Semi-Analytical Potential Solution for Wave Resonance in Gap Between Floating Box and Vertical Wall

Based on potential flow theory, a dissipative semi-analytical solution is developed for the wave resonance in the narrow gap between a fixed floating box and a vertical wall by using velocity potential decompositions and matched eigenfunction expansions. The energy dissipation near the box is modelled in the potential flow solution by introducing a quadratic pressure loss condition on the gap entrance. Such a treatment is inspired by the classical local head loss formula for the sudden change of cross section in channel flow, where the energy dissipation is assumed to be proportional to the square of local velocity for high Reynolds number flows. The dimensionless energy loss coefficient is calibrated based on experimental data. And it is found to be insensitive to the incident wave height and wave frequency. With the calibrated energy loss coefficient, the resonant wave height in gap and the reflection coefficient are calculated by the present dissipative semi-analytical solution. The predictions are in good agreement with experimental data. Case studies suggest that the maximum relative energy dissipation occurs near the resonant frequency, which leads to the minimum reflection coefficient. The horizontal wave forces on the box and the vertical wall attain also maximum values near the resonant frequency, while the vertical wave force on the box decreases abruptly there to a small value.

Conditions and Phase Shift of Fluid Resonance in Narrow Gaps of Bottom Mounted Caissons

This paper studies the viscid and inviscid fluid resonance in gaps of bottom mounted caissons onthe basis of the plane wave hypothesis and full wave model, The theoretical analysis and the numerical results demonstrate that the condition for the appearance of fluid resonance in narrow gaps is kh=（2n＋1）π （n=0, 1, 2, 3 ）, rather than kh=nn （n=0, 1, 2, 3, ...）; the transmission peaks in viscid fluid are related to the resonance peaks in the gaps. k and h stand for the wave number and the gap length. The combination of the plane wave hypothesis or the full wave model with the local viscosity model can accurately determine the heights and the locations of the resonance peaks. The upper bound for the appearance of fluid resonance in gaps is 2b/L〈l （2b, grating constant; L, wave length） and the lower bound is h/b〈~ l. The main reason for the phase shift of the resonance peaks is the inductive factors. The number of resonance peaks in the spectrum curve is dependent on the ratio of the gap length to the grating constant. The heights and the positions of the resonance peaks predicted by the present models agree well with the experimental data.

The influence of up-wave barge motion on the water resonance at a narrow gap between two rectangular barges underwaves in the sea

A three-dimensional time-domain potential flow model is developed and applied to simulate the wave resonance in a gap between two side-by-side rectangular barges. A fourth-order predict-correct method is implemented to update free surface boundary conditions. The response of an up-wave barge is predicted by solving the motion equation with the Newmark-β method. Following the validation of the developed numerical model for wave radiation and diffraction around two side-by-side barges, the influence of up-wave barge motion on the gap surfaceresonance is investigated in two different locations of the up-wave barge relative to the back-wave barge at various frequencies. The results reveal that the freely floating up-wave barge significantly influences the resonance frequency and the resonance wave amplitude. Simultaneously, the up-wave barge located in the middle of the back-wave barge leads to a reduction in the resonance wave amplitude and motion response when compared with other configurations.

Local resonance phononic band gaps in modifiedtwo-dimensional lattice materials

In this paper, modified two-dimensional peri- odic lattice materials with local resonance phononic band gaps are designed and investigated. The design concept is to introduce some auxiliary structures into conventional pe- riodic lattice materials. Elastic wave propagation in this kind of modified two-dimensional lattice materials is studied us- ing a combination of Bloch＇s theorem with finite element method. The calculated frequency band structures of illus- trative modified square lattice materials reveal the existence of frequency band gaps in the low frequency region due to the introduction of the auxiliary structures. The mechanism underlying the occurrence of these frequency band gaps is thoroughly discussed and natural resonances of the auxiliary structures are validated to be the origin. The effect of geo- metric parameters of the auxiliary structures on the width of the local resonance phononic band gaps is explored. Finally, a conceptual broadband vibration-insulating structure based on the modified lattice materials is designed and its capabil- ity is demonstrated. The present work is anticipated to be useful in designing structures which can insulate mechanical vibrations within desired frequency ranges.

Fluid Resonance Between Twin Floating Barges with Roll Motion Under Wave Action

The wave-induced fluid resonance between twin side-by-side rectangular barges coupled with the roll motion of the twin barges is investigated by both numerical simulation and physical model test.A 2D numerical wave flume,based on an open source computational fluid dynamics(CFD)package OpenFOAM,is applied for the numerical simulation.After numerical validations and convergent verifications,the characteristics of the fluid resonance in the gap between the twin rolling side-by-side barges are examined.The resonant frequency of the oscillating fluid in the gap between the twin rolling barges decreases compared with that between the twin fixed barges.Generally,the twin barges roll in the opposite directions,and their equilibrium positions lean oppositely with respect to the initial vertical direction.A physical model test is carried out for a further investigation,in which the twin barges are set oppositely leaning and fixed.From the present experimental results,a linear decrease of the resonant frequency with the increasing leaning angle is found.Combined with the numerical results,the deflection of the equilibrium positions of the twin barges is a relevant factor for the resonant frequency.Besides,the effects of the gap width and incident wave height on the fluid resonance coupled with roll motion are examined.

Numerical study of fluid resonance of a two-dimensional heaving-free moonpool in a wide range of incident waves

The fluid resonance of a moonpool freely heaving in a beam sea is studied by an in-house constrained interpolation profile(CIP)code.Generally,the moonpool behaves as in the piston mode with a narrow opening.The numerical studies are carried out for a wide range of the incident waves,and a new secondary resonant region is identified in the low frequency region of the incident waves,besides the ordinary main resonant region.Numerical results demonstrate that the horizontal wave forces are significant in the secondary resonant region,although the resonant wave elevations are less remarkable than those of the main resonant region.It is concluded that the fluid resonance of the low frequency is excited mainly by the heave motion of the moonpool.Parameter studies of the moonpool draft and the gap width of the moonpool based on the fluid resonance are also performed.

Theoretical and numerical investigations of wave resonance between two floating bodies in close proximity

A simple theoretical dynamic model with a linearized damping coefficient is proposed for the gap resonance problem, as often referred to as the piston mode wave motion in a narrow gap formed by floating bodies. The relationship among the resonant response amplitude and frequency, the reflection and transmission coefficients, the gap width, and the damping coefficient is obtained. A quantitative link between the damping coefficient of the theoretical dynamic model（ε） and that devised for the modified potential flow model（μ_p） is established, namely, μ_p=3πεω_n/8 （where ω_n is the natural frequency）. This link clarifies the physical meaning of the damping term introduced into the modified potential flow model. A new explicit approach to determine the damping coefficient for the modified potential model is proposed, without resorting to numerically tuning the damping coefficient by trial and error tests. The effects of the body breadth ratio on the characteristics of the gap resonance are numerically investigated by using both the modified potential flow model and the viscous RNG turbulent model. It is found that the body breadth ratio has a significant nonlinear influence on the resonant wave amplitude and the resonant frequency. With the modified potential flow model with the explicit damping coefficient, reasonable predictions are made in good agreement with the numerical solutions of the viscous fluid model.

Gap induced mode evolution under the asymmetric structure in a plasmonic resonator system

The modulation of resonance features in microcavities is important to applications in nanophotonics.Based on the asymmetric whispering-gallery modes(WGMs)in a plasmonic resonator,we theoretically studied the mode evolution in an asymmetric WGM plasmonic system.Exploiting the gap or nano-scatter in the plasmonic ring cavity,the symmetry of the system will be broken and the standing wave in the cavity will be tunable.Based on this asymmetric structure,the output coupling rate between the two cavity modes can also be tuned.Moreover,the proposed method could further be applied for sensing and detecting the position of defects in a WGM system.

Hole arrayed metal-insulator-metal structure for surface enhanced Raman scattering by self-assembling polystyrene spheres

A fabrication process based on the self-assembling polystyrene spheres is proposed to obtain hole arrayed metal-insulator-metal （HA-MIM） structure for surface enhanced Raman scattering （SERS）. The localized field enhancement aroused by the gap resonance in the HA-MIM structure is analyzed by finite-different time domain （FDTD） method. With reference to the theory result, the structure is experimentally fabricated and the Raman scattering spectrum of rhodamine 6G （R6G） is measured by a miniaturized Raman spectrometer. The results shows that the enhancement factor is 3.85 times higher than the control sample with single layered metal hole array. The fabrication process to obtain the HA-MIM SERS substrate is reproducible, fast, large area and low cost.

Numerical and Experimental Investigations on Tunable Low-frequency Locally Resonant Metamaterials

In this paper,a tunable locally resonant metamaterial is proposed for low-frequency band gaps.The local resonator composed of two pairs of folded slender beams and a proof mass is designed based on the theory of compliant mechanism.The design optimization on geometric parameters is carried out to fulfil the quasi-zero-stiffness property.The locally resonant metamaterial is formed by periodically arranged unit cells,and the transmittance of longitudinal wave is studied through three aspects:numerical predictions,finite element simulations and experimental tests.The variation trends revealed by these three methods match well with one another:the band gap moves to lower frequency and both its depth and width get smaller and smaller with the increase of pre-compression(Δ).The band gap overlays the frequency range of 73.10–92.38 Hz and 16.78–19.49 Hz atΔ=0mm andΔ=10mm,respectively,providing a wide range of tunability.Besides,the ultralow-frequency band gap can be achieved asΔapproaches 10 mm.This study may provide an avenue for achieving the tunable ultralow-frequency locally resonant band gap.

Plasmon hybridization engineering in self-organized anisotropic metasurfaces

The engineering of self-organized plasmonic metasurfaces is demonstrated using a maskless technique with defocused ion-beam sputtering and kinetically controlled deposition. The proposed reliable, cost-effective, and controllable approach enables large-area （order of square centimeter） sub-wavelength periodic patterning with close-packed gold nanostrips. A multi-level variant of the method leads to high-resolution manufacturing of vertically stacked nanostrip dimer arrays, without resorting to lithographic approaches. The design of these self-organized metasurfaces is optimized by employing plasmon hybridization methods. In particular, preliminary results on the so-called gap-plasmon configuration of the nanostrip dimers, implementing magnetic dipole resonance in the near-infrared range, are reported. This resonance offers a superior sensitivity and field enhancement, compared with the more conventional electric dipole resonance. The translational invariance of the nanostrip configuration leads to a high filling factor of the hot spots. These advanced features make the large-area metasurface based on gap-plasmon nanostrip dimers very attractive for surface-enhanced linear and nonlinear spectroscopy （e.g., surface-enhanced Raman scattering） and plasmon-enhanced photon harvesting in solar and photovoltaic cells.