Wide Range Of Wave Frequencies Research Articles

Wave scattering and radiation by a surface-piercing vertical truncated metamaterial cylinder

In this paper, we study wave scattering and radiation by a surface-piercing vertical truncated metamaterial cylinder composed of a closely spaced array of thin vertical barriers, between which fluid can flow. A theoretical model is developed under full depth-dependent linearised water wave theory, where an effective medium equation and effective boundary conditions are employed, respectively, to describe the fluid motion inside the cylinder and match the flow between the fluid regions in and outside the metamaterial cylinder. A damping mechanism is introduced at the surface of the fluid occupied by the metamaterial cylinder to consider the wave power dissipation in narrow gaps between the thin vertical plates. The wave excitation forces acting on the cylinder and the hydrodynamic coefficients can be calculated straightforwardly in terms of the velocity potential inside the cylinder. An alternative way is by using the velocity potential outside the cylinder, the expression of which has the reduction of the integral and an infinite accumulation that are included in the straightforward expression. The results highlight the patterns of the radiated waves induced by the oscillation of the cylinder and the characteristics of the hydrodynamic coefficients. The metamaterial cylinder when fixed in place and with a damping mechanism included is found to capture more wave power than that of a traditional axisymmetric heaving wave energy converter over a wide range of wave frequencies.

Energy transmission pathways of equatorial waves within the Maritime Continent: a view with the wave energy flux

Detailed pathway of wave energy exchange between the Pacific and Indian Oceans through the Indonesian archipelago for a wide range of wave frequency is investigated using a reduced gravity model with realistic coastline. The wave energy flux analysis that can be applicable for all latitudes in a linear shallow water system is adopted. The energy fluxes diagnosed from the model outputs for the incoming Rossby waves from the Pacific clearly indicate two major energy pathways to the Indian Ocean: one turning southward in the Halmahera Sea and reaches the Indian Ocean via the Banda Sea and the Timor Passage, and the other passing through the Makassar and Lombok Straits. The former route, however, is shifted to the western side of the island chain within the Banda Sea due to energy trapping around the island chain. It is also found that strong energy dissipation occurs along the northern coast of New Guinea when the incoming wave period is shorter than 1.5 years. In the case of the Kelvin waves from the Indian Ocean, it is found that the major energy pathway is through the Lombok and Makassar Straits to the Pacific Ocean. However, there appears another pathway along the eastern side of the Sulawesi Island in the Banda Sea to exit through the Molucca Sea only when the wave period is shorter than about one month. This secondary pathway makes it easier for the wave energy from the Indian Ocean to reach the western Pacific Ocean for the short-period waves.

New Strategy on Power Absorption of a Concentric Two-Body Wave Energy Converter

The wave energy converter (WEC) system, which extracts electricity through the relative heave motion of two concentric cylinders, comprises an inner cylinder and a torus-type outer cylinder sliding along the inner cylinder. To maximize the relative heave motion between two cylinders, the natural frequencies of the two cylinders must be precisely tuned to resonate and be situated on each side of the peak frequency of the wave spectrum. However, the demerit of this strategy is that it demands a deep draft of each cylinder for tuning, and a large-scale PTO damping device is necessary for mechanical power amplified by resonance. As an alternative to efficient and stable WECs, we adopt a new strategy in which the outer cylinder follows the incoming waves and the motion of the inner one is restricted to be minimal using a heave disk. The viscous damping due to formation of vortices at the disk edge is realized by the drag force in the Morison equation. The developed hydrodynamic model of two-body WEC based on a matched eigenfunction expansion method (MEEM) is applied to irregular waves characterized by significant wave height and peak period. It is found that the present two-body WEC with heave disk produces wave energy stably across a wide range of wave frequencies compared to the previous two-body WECs using resonance.

Mitigation of seismic waves using graded broadband metamaterial

In recent years, researchers have shown interest in blocking low-frequency vibrations with the aid of metamaterials due to their inherent wave-filtering properties. However, proposing a practical metamaterial layout remains a challenge, taking into consideration the size, shape, and availability of metamaterial components. This study proposes a new configuration that can increase the range of the attenuation frequency. The configuration focuses on the capability of graded metamaterials in filtering a wide range of wave frequencies that can be generated by low-amplitude waves. To find the best configuration with the widest bandgap, square periodic sections using different materials including steel, rubber, concrete, tungsten, and carbon fiber-reinforced polymer were considered. Unit cells with two layers of materials were examined numerically to determine the attenuation zones and the effect of material properties and core size on the bandgap width and frequency range. Furthermore, the performance of the unit cells in a soil medium under the low-amplitude low-frequency surface and bulk waves is evaluated in the frequency domain using finite element analysis, in which the metamaterial is embedded periodically in a soil medium with different configurations, including a graded distribution. The results show that having an array of unit cells spaced periodically can decrease the transmission of the wave to the protected zone located after the array, and the application of grading can increase the attenuation zones to filter frequencies as low as 4.5 Hz and up to 29 Hz.

Hydroelastic analysis of interaction between water waves and a floating laminated disk

This paper studies the interaction between water waves and a very large floating laminated disk in water of finite depth. The disk is a composite structure consisting of two surface sheets and a middle low-density elastic core layer. Based on the linear potential flow theory, an analytical solution of the hydroelastic problem is developed using the eigenfunction expansion method for the velocity potential of fluid motion. In the solution procedure, the laminated disk is regarded as double circular Euler sheets connected by a series of closely spaced and mutually independent vertical springs, and then an eighth-order differential equation of motion of the laminated disk is derived as the elastic boundary condition of the hydroelastic problem. An approximated model is then developed for the hydroelastic problem in shallow water. The deflection and bending moment of the disk and the free surface elevation near the disk are calculated, and it is found that the series solution for the velocity potential converges rapidly. Typical examples are presented to show the effects of different parameters, including wave frequency, the edge conditions of the disk, and the elastic coefficient of the core layer, on wave force, structural hydroelastic response, and wave field. Moreover, viscoelastic damping is introduced in the core layer, and its effect on the hydroelastic response is evaluated by adopting the complex stiffness method. The results indicate that the wave force on the laminated disk is larger than that on a corresponding rigid one over a very wide range of wave frequencies, and the local deformation of the lower sheet can be suppressed by designing a core layer with viscoelastic damping.

Design of Phononic Bandgap Metamaterials Based on Gaussian Mixture Beta Variational Autoencoder and Iterative Model Updating

AbstractPhononic bandgap metamaterials, which consist of periodic cellular structures, are capable of absorbing energy within a certain frequency range. Designing metamaterials that trap waves across a wide wave frequency range is still a challenging task. In this paper, we present a deep feature learning-based design framework for both unsupervised generative design and supervised learning-based exploitative optimization. The Gaussian mixture beta variational autoencoder (GM-βVAE) is used to extract latent features as design variables. Gaussian process (GP) regression models are trained to predict the relationship between latent features and properties for property-driven optimization. The optimal structural designs are reconstructed by mapping the optimized latent feature values to the original image space. Compared with the regular variational autoencoder (VAE), we demonstrate that GM-βVAE has a better learning capability and is able to generate a more diversified design set in unsupervised generative design. Furthermore, we propose an iterative GM-βVAE model updating-based design framework. In each iteration, the optimal designs found property-driven optimization is used to update the training dataset. The GM-βVAE model is re-trained with the updated dataset for the optimization search in the next iteration. The effectiveness of the iterative design framework is demonstrated by comparing the proposed designs with the designs found by the traditional single-loop design method and the topologically optimized designs reported in literatures. The caveats to designing phonic bandgap metamaterials are summarized.

Gyrotropic superlattice as a transformer of light polarization

We suggest a novel approach to predict and clarify the transformation of an arbitrarily polarized wave into two circularly polarized ones, based on the peculiar features of their transmission and reflection from a stack with regularly arranged gyrotropic layers. In spite of the fact that in the Faraday geometry gyrotropic media possess four electromagnetic eigenmodes, we have managed to modify the problem to be analytically resolved within the conventional transfer-matrix method. As a result, we have obtained and analyzed the dispersion relation, as well as the transmission and reflection coefficients, which are applicable for any elliptic polarization of a wave irradiating a gyrotropic superlattice with finite number of unit cells. It is shown that there exists a wide range of wave frequency and magneto-optical parameter (proportional to external dc magnetic field) inside of which the wave of given circular polarization is perfectly transmitted, while the wave with the opposite circular polarization is completely reflected. Thus, under certain conditions, the incident plane wave (taken as an appropriate example) splits up into the transmitted and reflected circular waves with mutually inverse rotations. We indicate conditions when a relatively small variation of the magnetization can reverse the polarizations mentioned above.

Experimental investigation on the hydrodynamic performance of a new type floating Oscillating Water Column device with dual-chambers

A comprehensive experimental study is carried out to investigate the efficiency of a novel floating dual-chamber Oscillating Water Column Wave Energy Converter device in terms of converting the energy of the waves to pneumatic power. The influence of the power take-off damping as well as the wave characteristics on the hydrodynamic performance is investigated. The significant hydrodynamic performance of the introduced novel concept has been proven in the wide range of wave frequencies for both regular and random wave conditions. It is found that the fore and rear chambers of the device have the dominant role in absorbing energy of the waves in a specific range of wave periods. Their mutual interactions have a significant effect on the enhancement of the overall hydrodynamic performance.

Modelling and design of a perfectly-absorbing wave energy converter

This paper concerns the absorption of energy from two-dimensional water waves propagating over fluid of constant depth by a wave energy converter consisting of small buoyant floating rafts constrained to move in heave motion and attached to the bed with springs and dampers. Under a shallow water approximation to the fluid motion, it is shown that spatially-varying spring and damper settings allow all of the wave energy to be absorbed from all wave frequencies. The basis of the design is a formulation of a novel type of ‘Perfectly Matched Layer’ equation which can be mapped onto a shallow water model of the wave energy converter. The theoretical predictions are tested with computations based on a full description of linearised water waves and show that near-perfect absorption persists over a wide range of wave frequencies.

Hydroelastic analysis of a ship with forward speed using orthogonal polynomials as mode functions of timoshenko beam

Legendre polynomials and Chebyshev polynomials are adopted as simpler mode functions to replace the dry eigen-modes of the Timoshenko beam. Then the mode-expansion method is applied to prove that a superposition of orthogonal mathematical functions can represent the flexural deflection of a ship in waves, despite a fact that each of these mathematical functions does not satisfy the required boundary conditions and has no physical meaning. Validation of obtained results with Euler-beam and Timoshenko-beam approximations is performed through comparison with the experimental results of a flexible barge conducted by Malenica et al. (2003) as well as the numerical results of Kim et al. (2009b), Kim et al. (2009a) implemented using the direct coupling method in the experimental wave-frequency range. For the forward-speed case, by means of the Rankine panel method (RPM), validation in a wide range of wave frequency is performed through comparison of computed results for the modified Wigley model between dry eigen-modes and orthogonal polynomials used as the mode function. From this comparison, the rationality of consistency in the proposed method is proven and availability in various engineering fields can be expected. The ratio of flexural and shear rigidities is intentionally increased in a numerical study to see the effect of shearing force on various related quantities using Legendre polynomials. Limitation and convergence of the proposed mode functions are also discussed.

Wave flume testing of an oscillating-body wave energy converter with a tuned inerter

In this study, the effectiveness of an oscillating-body WEC with a tuned inerter (TI) proposed by the authors is shown through wave flume testing. The TI mechanism consisting of a tuning spring, a rotational inertial mass, and a viscous damping component is able to increase energy absorption capability by taking advantage of the resonance effect of the rotational mass. This mechanism has been recently introduced for civil structures subjected to external loadings such as earthquakes and winds to decay vibration response immediately. The authors applied this mechanism to oscillating-body WECs and showed that the proposed WEC increased the power generation performance and broadened the effective frequency range without increasing the mass of the buoy itself through numerical simulation studies. To verify the validity of the proposed WEC experimentally, a small-scale prototype of the proposed device is designed and wave flume testing is carried out with various regular wave inputs of different frequencies. The results show that the WEC with the properly adjusted TI mechanism demonstrates better power generation performance compared to the conventional WEC over a wide range of wave frequencies.

Bubbly Water as a Natural Metamaterial of Negative Bulk-Modulus

In this study, an oscillator model of bubble-in-water is proposed to analyze the effective modulus of low-concentration bubbly water. We show that in a wide range of wave frequency the bubbly water acquires a negative effective modulus, while the effective density of the medium is still positive. These two properties imply the existence of a wide acoustic gap in which the propagation of acoustic waves in this medium is prohibited. The dispersion relation for the acoustic modes in this medium follows Lorentz type dispersion, which is of the same form as that of the phonon-polariton in an ionic crystal. Numerical results of the gap edge frequencies and the dispersion relation in the long-wavelength regime based on this effective theory are consistent with the sonic band results calculated with the plane-wave expansion method (PWEM). Our theory provides a simple mechanism for explaining the long-wavelength behavior of the bubbly water medium. Therefore, phenomena such as the high attenuation rate of sound or acoustic Anderson localization in bubbly water can be understood more intuitively. The effects of damping are also briefly discussed. This effective modulus theory may be generalized and applied to other bubble-in-soft-medium type sonic systems.

Wave coupling simulation of ICRF antenna in EAST relying on the perfectly matched layer technique

A coupling model for the waves in ion cyclotron resonance frequency (ICRF) in tokamak plasmas is described. The simulation is performed based on the finite element method. A cold plasma dielectric tensor is used. A perfectly matched layer (PML) is applied to describe the ICRF wave single-pass absorption in the core plasma. The selection of PML characteristic parameters is optimized in a wide wave frequency range and validated for plane waves and ICRF waves. The dependencies of the coupling resistance on the plasma-antenna gap, average plasma density, and plasma profiles are given. The simulation results are in good agreement with the experimental results.

Hydrodynamic performance of a T-shaped floating breakwater

The comprehensive utilization of floating breakwaters, specially acting as a supporting structure for offshore marine renewable energy explorations, has received more and more attention recently. Based on linear water-wave theory, the hydrodynamic performance of a T-shaped floating breakwater is semi-analytically investigated through the matched eigenfunction expansion method (MEEM). Auxiliary functions, to speed up the convergence and improve the accuracy in the numerical computations, are introduced to represent the singular behavior of fluid field near the lower salient corners of the structure. The effects of the height and installation position of the vertical screen on the reflection and transmission coefficients, dynamic response and wave forces are examined. It is found that the presence of the screen shifts the resonance frequency of RAO for both surge and pitch modes to the low-frequency area, while has no effect on heave mode. The identical added masses, damping and transmission coefficients can be obtained in the cases where the screen holds the same distance away from the longitudinal central axis of the upper box-type structure. Moreover, a relatively small pitch response can be achieved in a wide wave–frequency range, when the breakwater is Γ-shaped.

Surface-Wave Based Model for Estimation of Discontinuity Depth in Concrete

In this paper, we propose an accurate and practical model for the estimation of surface-breaking discontinuity (i.e., crack) depth in concrete through quantitative characterization of surface-wave transmission across the discontinuity. The effects of three different mixture types (mortar, normal strength concrete, and high strength concrete) and four different simulated crack depths on surface-wave transmission were examined through experiments carried out on lab-scale concrete specimens. The crack depth estimation model is based on a surface-wave spectral energy approach that is capable of taking into account a wide range of wave frequencies. The accuracy of the proposed crack depth estimation model is validated by root mean square error analysis of data from repeated spectral energy transmission ratio measurements for each specimen.

Hydrodynamic Performance of an Array of Wave Energy Converters Integrated with a Pontoon-Type Breakwater

The cost of wave energy converters (WECs) can be reduced significantly by integrating WECs into other marine facilities, especially in sea areas with a mild wave climate. To reduce the cost and increase the efficiency, a hybrid WEC system, comprising a linear array (medium farm) of oscillating buoy-type WECs attached to the weather side of a fixed-type floating pontoon as the base structure is proposed. The performance of the WEC array is investigated numerically using a boundary element method (BEM) based on the linear potential flow theory. The linear power take-off (PTO) damping model is used to calculate the output power of the WEC array. The performance of the WEC array and each individual WEC device is balanced by using the mean interaction factor and the individual interaction factor. To quantify the effect of the pontoon, the hydrodynamic results of the WEC arrays with and without a pontoon are compared with each other. Detailed investigations on the influence of the structural and PTO parameters are performed in a wide wave frequency range. Results show that the energy conversion efficiency of a WEC array with a properly designed pontoon is much higher than that without a pontoon. This integration scheme can achieve the efficiency improvement and construction-cost reduction of the wave energy converters.

Efficacy of Water Chamber Type Seawall to Dissipate Incident Wave and Its Performance to Extract Wave Power

This study examined performance a water chamber type of seawall to dissipate incident wave and also extract wave power. The model of water chamber is consists of two water chamber type. The low reflection wave resulted by flow separation in lower end of vertical wall and it occurs after wave resonant condition. This structure is appropriate for short and long wave condition. A horizontal plate was setup in the end of vertical wall in order to improve performance of water chamber type seawall. This trial test taken to dissipate much longer waves condition and it’s related to utilize the wave energy inside the water chamber. Additional trial of the cross section, such as an adoption of a bevel edge instead of a right angle edge was also examined. It was seen that the seawall of a water chamber type with a horizontal plate is very effective to reduce reflected waves for both short and long waves. Also it was confirmed that large amplifications of pumping mode wave motions in the two water chambers appear for comparatively wide range of wave frequency

Numerical solutions of mild slope equation by generalized finite difference method

The mild slope equation (MSE) has been widely used to describe combined wave refraction and diffraction in the field of coastal and offshore engineering owing to its applicability for a wide range of wave frequencies. In this paper, a meshless numerical algorithm, based on the generalized finite difference method (GFDM), is firstly proposed to efficiently and accurately solve the MSE. As a newly-developed domain-type meshless method, the GFDM can truly get rid of time-consuming meshing generation and numerical quadrature. The partial differential terms of the MSE for each point in the computational domain can be discretized into linear combinations of nearby function values with the moving-least-squares method of the GFDM, so the numerical implementation is very convenient and efficient. To evaluate the accuracy and capability of the proposed scheme for MSE, a series of numerical tests were conducted, covering a range of complexity that included propagation and transformation of waves due to a parabolic shoal, a circular island mounted on a paraboloidal shoal and elliptic shoal situated on a slope, as well as breakwater gap. The results were compared with experimental data, analytical solutions and other numerical methods, and reasonable agreements have been achieved.

Wave-induced steady forces and yaw moment of a ship advancing in oblique waves

Wave-induced added resistance, steady sway force, and steady yaw moment, which are of second order in the incident-wave amplitude, are studied for the forward-speed case using the far-field method based on the principles of momentum and energy conservation. The Kochin functions representing ship-disturbance waves, important input data in the far-field method, are evaluated by means of both enhanced unified theory (EUT) and new strip method (NSM) to see the difference due to bow wave diffraction, 3D and forward-speed effects in the final results of second-order steady forces and moment. Special attention is paid on the precise integration method to ensure convergence in semi-infinite integrals in the calculation formulae, introducing no artificial decaying factor unlike conventional strip-theory methods. Validation of the present calculation method is made through comparison with the experiment conducted with a bulk-carrier model advancing in regular oblique waves and motion-free condition. Good agreement between computed and measured results and also superiority of EUT to NSM are confirmed for all modes of ship motion and the steady forces and yaw moment in a wide range of wave frequency.

Hydrodynamic interactions of oscillating wave surge converters in an array under random sea state

The oscillating wave surge converter (OWSC) type devices (e.g., an Oyster wave energy converter) generate electric power via rotating motion about the bottom of the device. This type of wave energy converters have a wide power absorption bandwidth which enables the electricity generation at a wide range of wave frequencies. The power produced by the OWSCs could be maximised by configuring individual devices within an array. This paper examines the power production performance of multiple OWSCs in an array under regular, uni-directional irregular wave and multi-directional sea using the industry standard hydrodynamic software WAMIT. The performance of the OWSC array is represented as q-factor, which is a quantity defined as the ratio of the average total power produced in an array to the power produced by an individual OWSC. The results show that the OWSCs arranged in an array would produce both constructive and destructive interferences depending on the wave directions and frequencies. Further, the spreading function, the resonance bandwidth and the optimal spacing between the devices are shown to affect the performance of the OWSC significantly. The results provide an enhanced understanding of the behaviour and performance of the OWSCs when arranged in an array of different configurations.