Magnetoelectroelastic shear body waves in periodically layered metalized ferrite–piezoelectric media

A method of deriving the dispersion equations for magnetoelectroelastic shear waves in periodically layered media is proposed. The media are formed by uniting identical metalized laminates, each consisting of two dissimilar piezoelectric layers separated by a layer with the properties of ferrite. A numerical analysis is carried out and the propagation of body waves in different structures consisting of ZnO and GaYtC layers is described within wide ranges of frequencies and wave numbers. The influence of the physical, mechanical, and geometrical parameters of the layers on the structure of the transmission and suppression zones and the effect of the piezoelectric effect of the position of transmission edges are examined     

Acoustoelectric shear body waves in periodically layered metallized piezodielectric media

The paper proposes a technique to derive the dispersion relations for acoustoelastic shear body waves propagating in periodically layered media formed of identical metallized sandwiches, each consisting of two different piezoelectric layers and a dielectric layer between them. A numerical analysis is carried out and the propagation of body waves in different structures is described for a wide range of frequencies and wave numbers. The effect of the physical, mechanical, and geometrical parameters of the layers on the transmission and suppression bands is examined. The influence of the piezoeffect on the arrangement of the transmission edges upon change in the relative thickness of the layers is studied __________ Translated from Prikladnaya Mekhanika, Vol. 44, No. 7, pp. 61–67, July 2008.     

TWO-DIMENSIONAL NUMERICAL ANALYSIS OF STRESS-WAVE-AMPLIFIER

Using dynamic finite element method,the propagation of stress waves in two-dimensional conically shaped stress-wave-amplifiers is analysed.The effects of gometricalfactors,input-pulse shape and pulse rising time on amplifying multiplication and waveshape of transmission waves are discussed.The consistency between numerical results andexperimental results based on Hopkinson bar is satisfactory.The numerical accuracy isinploved comparing with the characteristic method.     

Interaction of rarefaction waves with wet foam

The interaction of rarefaction waves of different shapes with wet water foams is studied experimentally. It is found that the observed values of the pressure are greater, while the surface velocity is lower than the corresponding values predicted by the pseudogas model. The foam breakdown starts as the pressure decreases by 0.3 atm relative to the initial pressure. During downstream propagation of the rarefaction-wave leading edge the propagation velocity decreases.Using of water-based foams as effective screens for damping blast waves in different technological processes has caused considerable interest in studying wave propagation in such systems. The pressure wave dynamics in a foam have been investigated in much detail, both experimentally and theoretically [1–3]. However, the interaction of rarefaction waves with foam has practically never been studied, although it was mentioned in [4] that the unloading phase following the compression wave phase is one of the factors defining the damaging action of blast waves. Besides blast-wave damping, rarefaction wave propagation takes place if such waves are used to breakup foam in oil-producing wells [5].Below, the interaction of rarefaction waves of different shapes with wet water foams is studied. The vertical shock tube described in detail in [3] was used in these experiments.Brest. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 2, pp. 76–82, March–April, 1995.     

Experimental and numerical study of an aquaculture net cage with floater in waves and current

The mooring loads on an aquaculture net cage in current and waves are investigated by dedicated model tests and numerical simulations. The main purpose is to investigate which physical effects are dominant for mooring loads, and in this respect, to investigate the validity of different rational hydrodynamic load models. Also structural and numerical aspects are investigated. The model tests are performed to provide benchmark data, while the numerical model is used to study the effect and sensitivity of different load models and parameters.Compared to a realistic aquaculture plant, the total system is simplified to reduce the complexity. The system does, however, include all the four main components of an aquaculture plant: net cage, floater, sinker weights and moorings. The net cage is bottomless, flexible and circular. It is attached to a circular, elastic floater at the top and has 16 sinker weights at the bottom. The system is nearly linearly moored with four crow feet mooring lines.The loads are measured in the four mooring lines. A systematic variation of current only, wave only as well as combined current and wave conditions is carried out. The numerical simulation results are first benchmarked towards the experimental data. The mean loads in general dominate over the dynamic part of the loads in combined current and waves, and they significantly increase in long and steep waves, relative to current only. Next, a sensitivity study is carried out. A rigid floater significantly alters the loads in the mooring lines compared to a realistic, elastic floater. The theoretical model for the wave matters. The mooring loads are rather insensitive to a majority of the parameters and models, in particular: frequency dependent added mass of the floater and nonlinear restoring loads. It seems not to be necessary to represent the net cage with a very fine numerical mesh.     

Interaction between shed vorticity, free surface waves and forced roll motion of a two-dimensional floating body

A vortex tracking method is used to study forced harmonic roll motion of a two-dimensional floating body with sharp corners. The effect of free surface waves is incorporated. Errors due to numerical and physical problems are discussed. The presented test cases show that free surface waves have an effect on the vortex generation, whereas the free shear layers do not have a noticeable influence on the free surface waves. The results show that roll damping due to eddymaking and wave generation cannot be separated.     

Dynamics of dual pontoon floating structure for cage aquaculture in a two-dimensional numerical wave tank

The trend of using floating structures with cage aquaculture is becoming more popular in the open sea. The purpose of this paper is to investigate the dynamic properties of a dual pontoon floating structure (DPFS) when attached to a fish net by using physical and numerical models. A two-dimensional (2-D) fully nonlinear numerical wave tank (NWT), based on the boundary element method (BEM), is developed to calculate the wave forces on the DPFS. The wave forces on a fish net system are then evaluated using a modified Morison equation. The comparisons of dynamic behaviors between numerical simulations and experimental measurements on the DPFS show good agreement. Results also display that a fish net system causes the resonant response of body motions and mooring forces to be slightly lower due to the net's damping effect. Finally, for designing the rearing space of cage aquaculture, the influences which net depth and net width have on the DPFS dynamic responses are also presented in this paper.     

Nonreflecting boundary conditions based on nonlinear multidimensional characteristics

Nonlinear characteristic boundary conditions based on nonlinear multidimensional characteristics are proposed for 2‐ and 3‐D compressible Navier–Stokes equations with/without scalar transport equations. This approach is consistent with the flow physics and transport properties. Based on the theory of characteristics, which is a rigorous mathematical technique, multidimensional flows can be decomposed into acoustic, entropy, and vorticity waves. Nonreflecting boundary conditions are derived by setting corresponding characteristic variables of incoming waves to zero and by partially damping the source terms of the incoming acoustic waves. In order to obtain the resulting optimal damping coefficient, analysis is performed for problems of pure acoustic plane wave propagation and arbitrary flows. The proposed boundary conditions are tested on two benchmark problems: cylindrical acoustic wave propagation and the wake flow behind a cylinder with strong periodic vortex convected out of the computational domain. This new approach substantially minimizes the spurious wave reflections of pressure, density, temperature, and velocity as well as vorticity from the artificial boundaries, where strong multidimensional flow effects exist. The numerical simulations yield accurate results, confirm the optimal damping coefficient obtained from analysis, and verify that the method substantially improves the 1‐D characteristics‐based nonreflecting boundary conditions for complex multidimensional flows. Copyright © 2009 John Wiley & Sons, Ltd.     

On the group velocity of symmetric and upwind numerical schemes

Dissipative numerical approximations to the linear advection equation are considered with respect to their behaviour in the limit of weak dissipation. The context is wave propagation under typical far-field conditions where grids are highly stretched and waves are underresolved. Three classes of schemes are analysed: explicit two-level (i) symmetric and (ii) upwind schemes of optimal accuracy are considered as well as (iii) (symmetric) Runge-Kutta schemes. In the far-field the dissipation of all schemes diminishes. Group speeds of high-frequency modes assume the incorrect sign and may admit ‘backward’ wave propagation if waves are not damped. A fundamental difference arises between the symmetric and upwind cases owing to the different rates at which the dissipation diminishes. In the upwind case, while the amount of damping per time step diminishes, the accumulative damping remains exponential in time. In the symmetric case the accumulative damping tends to unity, yielding in practice non-dissipative schemes. In this light, parasitic modes constitute much less of a problem in the upwind case than in the symmetric case. Numerical tests confirm these findings.     

Damping of large-amplitude solitary waves

We consider the damping of large-amplitude solitary waves in the framework of the extended Korteweg-de Vries equation (that is, the usual Korteweg-de Vries equation supplemented with a cubic nonlinear term) modified by the inclusion of a small damping term. The damping of a solitary wave is studied for several different forms of friction, using both the analytical adiabatic asymptotic theory and numerical simulations. When the coefficient of the cubic nonlinear term has the opposite sign to the coefficient of the linear dispersive term, the extended Kortweg-de Vries equation can support large-amplitude “thick” solitary waves. Under the influence of friction, these “thick” solitary waves decay and may produce one or more secondary solitary waves in this process. On the other hand, when the coefficient of the cubic nonlinear term has the same sign as the coefficient of the linear dispersive term, but the opposite sign to the coefficient of the quadratic nonlinear term, the action of friction may cause a solitary wave to decay into a wave packet.     

考虑阻尼的无限长小垂度缆索弹性波的传播

缆索结构被广泛应用于电气、土木、海洋和航空工程等领域,随着缆索在工程中的应用长度越来越长,高阶振动越来越明显,研究时应该考虑扰动沿着缆索的传播.现有对缆索弹性波传播的研究中,通常不考虑阻尼项,然而阻尼对于波的传播有着重要影响.文章考虑阻尼的影响,发展了包含阻尼项的三维弹性缆索运动方程.通过求解上述含阻尼项的运动方程,分别考察了面内面外弹性波的频率关系、相速度和群速度等自由传播特性,进而通过计算无限长弹性缆索在初始余弦型脉冲作用下的位移响应,分析扰动沿着该缆索的传播规律,考察波的色散现象以及阻尼对于缆索弹性波传播的影响.结果表明,考虑阻尼后,面内波和面外波均为色散波,面内波在曲率的作用下,为高度色散波.此外,在阻尼的影响下,波的峰值在传播过程不断减小,且波的后缘端点响应总是高于前缘端点响应.     

Analysis of hydrodynamic behaviors of multiple net cages in combined wave–current flow

Numerical simulation is performed to analyze the hydrodynamic response of a net cage and submerged mooring grid system exposed to waves and current. A series of experiments are conducted to validate the numerical model of net cage and grid mooring system. The numerical results of this model correspond with those obtained from experimental observations. Then, the numerical simulation of a multi-cage and mooring system under the action of waves combined with current is conducted. The influence of waves and current directions and the length of grid lines on the cage responses are discussed. The twin mooring system and the orthogonal mooring system are compared. Results show that for the orthogonal mooring system, the maximum tension force on the anchor line of the four-cage system is less than four times of that of the single-cage system, when both waves and current travel along the x-axis. The minimum net cage volume holding coefficient of the single-cage system is smaller than that of the four-cage system. The amplitude of the mooring line tension force for the twin mooring system is larger than the orthogonal mooring system.     

Structural response of high solidity net cage models in uniform flow

Hydrodynamic loads acting on a fish farm may be affected by the growth of different biofouling organisms, mainly due to increased solidity of the nets. In this paper, the hydrodynamic loads acting on high solidity net cage models subjected to high uniform flow velocities and the corresponding deformation of the net cages are studied. Model tests of net cylinders with various solidities were performed in a flume tank with a simulated current. Standard Morison-type numerical analyses were performed based on the model tests, and their capability of simulating the occurring loads and the observed net cage deformations for different flow velocities was evaluated.Large deformations of the net cage models were observed, and at high velocities the deformations were close to what is physically possible. Net cage deformation appeared to be less dependent on solidity than on flow velocity and weights. Drag forces increased with increasing flow velocity and were dependent on both bottom weights and netting solidity. For the lowest solidity net, drag forces were close to proportional to flow velocity. For the three high solidity nets, the measured drag forces were of similar magnitude, and drag increased less with increasing flow velocity above approximately 0.5 m/s than at lower velocities.This study shows that a basic reduced velocity model is not sufficient to model the interaction between the fluid flow and net (hydroelasticity) for high solidity net cages subjected to high flow velocities.The standard numerical analysis was in general able to make good predictions of the net shape, and was capable of making an acceptable estimate of hydrodynamic loads acting on the lowest solidity net model (Sn=0.19). For high solidities and large deformations, numerical tools should account for changes in water flow and the global drag coefficient of the net.     

Linear wave-induced dynamic structural stress analysis of a 2D semi-flexible closed fish cage

Closed fish cages in the sea are proposed as a new concept in marine aquaculture, replacing the conventional net cages in order to meet ecological challenges related to fish lice and escapes. A closed fish cage can be compared to a floating tank structure with an internal free surface. Several types of closed cages have been suggested, and they are categorised according to structural properties as flexible membrane structures (fabric), semi-flexible structures (glass fibre) and rigid structures (steel or concrete). To be able to develop safe and reliable structures, more knowledge is required on the seakeeping behaviour of closed cages in waves and the structural response to the wave loads. This paper builds on a theory presented in Strand and Faltinsen (2019) on the linear wave loads on a 2D closed flexible fish cage. A modelling error has been found in Strand and Faltinsen (2019), however, all the main conclusions are in hold. The error has been corrected in the model in the present paper. The present paper extends the model to include bending in the structural model to be able to handle semi-flexible structures where bending stiffness is significant. In this paper, the linear theory of a 2D semi-flexible closed fish cage in waves is developed and analysed to investigate the structural response of the semi-flexible closed cage in waves. We have compared a quasi-static analysis with a fully coupled hydroelastic analysis to investigate if it is a valid and conservative assumption to assume that the stresses in the structure can be assumed quasi-static. If a hydroelastic analysis is necessary or not, is dependent on the stiffness of the structure. We have investigated what happens with the stress in the curved beam part of the closed fish cage for increasing and decreasing stiffness relative to a reference composite structure. One stiffer and two softer cases have been analysed. One major concern for the structural stresses in a closed cage is the effect of sloshing. Sloshing is internal wave motion inside the cage and have multiple resonance periods. The results indicate that to use the quasi-static assumption in structural stress calculation is conservative within the given frequency range for all examined stiffnesses and frequencies, except the frequencies very close to the second sloshing frequency. Close to the second sloshing frequency for all the examined stiffnesses, a localised peak can be observed in the coupled hydroelastic results. The second sloshing frequency is a frequency connected to a symmetric sloshing mode. Rigid body motion is not affected at the symmetric sloshing frequency for an assumed rigid structure, and are therefore also not visible in the stress results from the quasi-static analysis. The structural stress in irregular sea was calculated. These results show no indication of increased stress close to the second sloshing frequency. However, this is not a surprising result since the stress peak is very localised in frequency, and the accumulated effect on the stress standard deviation is therefore small.     

波浪作用下网帘的水动力载荷和变形计算

 离岸水产养殖中的网箱养殖逐渐成为全球水产养殖业的主导．海洋环境中网箱的水动力荷载对网箱结构的整体设计提出了更高的要求．本文建立了一种计算波浪荷载下网帘结构水动力和变形的数值计算方法,利用质点杆单元模型模拟网帘结构,通过Morison 公式求解网帘结构在波浪荷载下的受力,得到网帘结构的空间分布,同时运用迭代法对网帘结构结点受力及运动变形时的位移进行数值迭代计算,通过双目测距系统对网帘结构变形测量的结果,获得等效弹性系数,并对数值结果进行了验证．     

Analysis of damped guided waves using the method of multiple scales

We analytically investigate the influence of damping on Lamb waves, which are a specific type of guided wave in two-dimensional plates. Considering material attenuation, we suppose that Lamé constants are complex numbers. This leads to the associated wavenumbers being complex, with the imaginary part of the wavenumber being associated with effect of attenuation of the guided wave. In this paper, we show how dispersion curves and attenuation coefficients can be obtained using the self-adjointness and the method of multiple scales (MMS), which is a type of perturbation method. Using the self-adjointness and the MMS, we can calculate the frequency- and wavenumber-dependent attenuation coefficients from the integral values and boundary values of a corresponding eigenfunction with respect to each propagation mode. This analytical method can yield not only dispersion curves but also mode-by-mode attenuation coefficients regardless of the numerical initial values, unlike numerical approaches using the Newton method. Thus, the proposed method can more easily calculate the attenuation coefficients with respect to a particular mode than conventional methods. Furthermore, the results obtained by proposed method were in good agreement with those obtained by the semi-analytical finite element (SAFE) method, which validates the proposed method.     

In-plane elastic wave propagation and band-gaps in layered functionally graded phononic crystals

In-plane wave propagation in layered phononic crystals composed of functionally graded interlayers arisen from the solid diffusion of homogeneous isotropic materials of the crystal is considered. Wave transmission and band-gaps due to the material gradation and incident wave-field are investigated. A classification of band-gaps in layered phononic crystals is proposed. The classification relies on the analysis of the eigenvalues of the transfer matrix for a unit-cell and the asymptotics derived for the transmission coefficient. Two kinds of band-gaps, where the transmission coefficient decays exponentially with the number of unit-cells are specified. The so-called low transmission pass-bands are introduced in order to identify frequency ranges, in which the transmission is sufficiently low for engineering applications, but it does not tend to zero exponentially as the number of unit-cells tends to infinity. A polyvalent analysis of the geometrical and physical parameters on band-gaps is presented.     

Structural analysis of aquaculture net cages in current

A method for structural analysis of aquaculture net cages has been developed and verified for a netting solidity of 0.23, water current velocities from 0.1 to 0.5 m/s and relatively large deformations (volume reduction up to 70%) by comparing the numerical results to tests in a flume tank. Strength analysis was performed using commercial explicit finite element software to calculate distribution of loads in the net cage due to current, weights and gravity. The net cage was modelled using truss elements that represented several parallel twines. Sub-elements allowed the trusses to buckle in compression, and only negligible compressive forces were seen in the numerical results. Resulting drag loads and cage volume were shown to be dependent on the net cage size and weight system. Drag loads increased almost proportional to the current velocity for velocities in the range of 0.2–0.5 m/s, while the cage volume was reduced proportional to the current velocity. The calculated forces in ropes and netting of full-size net cages were well below the design capacity for current velocities up to 0.5 m/s. However, netting seams in the bottom panel of the net cage were identified as a potential problem area as the forces could reach the design capacity.     

流管声传播与膜结构相互作用的机理研究

以等价分布源方法为基础研究流管声传播与膜结构相互作用的机理. 根据广义格林函数 给出任意截面管道的通用模型. 并在此基础上研究了结构参数、流动马赫数、高阶模态波对 膜结构消声器降噪量及临界频率的影响. 此外,还讨论了流体介质对声波与膜片相互作 用的影响,可以看出膜结构消声器在水下也能得到广泛的应用.     

A meshless numerical wave tank for simulation of nonlinear irregular waves in shallow water

Time domain simulation of the interaction between offshore structures and irregular waves in shallow water becomes a focus due to significant increase of liquefied natural gas (LNG) terminals. To obtain the time series of irregular waves in shallow water, a numerical wave tank is developed by using the meshless method for simulation of 2D nonlinear irregular waves propagating from deep water to shallow water. Using the fundamental solution of Laplace equation as the radial basis function (RBF) and locating the source points outside the computational domain, the problem of water wave propagation is solved by collocation of boundary points. In order to improve the computation stability, both the incident wave elevation and velocity potential are applied to the wave generation. A sponge damping layer combined with the Sommerfeld radiation condition is used on the radiation boundary. The present model is applied to simulate the propagation of regular and irregular waves. The numerical results are validated by analytical solutions and experimental data and good agreements are observed. Copyright © 2008 John Wiley & Sons, Ltd.