Fourier analysis of a class of upwind schemes in shallow water systems for gravity and Rossby waves

A Fourier analysis has been performed for a class of upwind finite volume schemes, including the study of phase speed, group velocity, damping and dispersion. In the first part, pure gravity waves are investigated. As expected, most upwind schemes lead to a significant damping, but they exhibit a better phase behavior than most centered schemes. In the second part, the Coriolis parameter is considered and the Rossby modes are studied. In this case, all selected upwind schemes lead to a severe damping. The numerical results are also compared with those obtained by using a slope limiter approach. It is concluded that most upwind schemes with or without slope limiters present poor results for an accurate calculation of the Rossby modes. Copyright © 2008 John Wiley & Sons, Ltd.     

Axisymmetric free vibrations of infinite micropolar thermoelastic plate

The propagation of axisymmetric free vibrations in an infinite homogeneous isotropic micropolar thermoelastic plate without energy dissipation subjected to stress free and rigidly fixed boundary conditions is investigated. The secular equations for homogeneous isotropic micropolar thermoelastic plate without energy dissipation in closed form for symmetric and skew symmetric wave modes of propagation are derived. The different regions of secular equations are obtained. At short wavelength limits, the secular equations for symmetric and skew symmetric modes of wave propagation in a stress free insulated and isothermal plate reduce to Rayleigh surface wave frequency equation. The results for thermoelastic, micropolar elastic and elastic materials are obtained as particular cases from the derived secular equations. The amplitudes of displacement components, microrotation and temperature distribution are also computed during the symmetric and skew symmetric motion of the plate. The dispersion curves for symmetric and skew symmetric modes and amplitudes of displacement components, microrotation and temperature distribution in case of fundamental symmetric and skew symmetric modes are presented graphically. The analytical and numerical results are found to be in close agreement.     

Axisymmetric free vibrations of infinite thermoelastic plate

The propagation of axisymmetric free vibrations in an infinite homogeneous isotropic micropolar thermoelastic plate without energy dissipation subjected to stress free and rigidly fixed boundary conditions is investigated. The secular equations for homogeneous isotropic micropolar thermoelastic plate without energy dissipation in closed form for symmetric and skew symmetric wave modes of propagation are derived. The different regions of secular equations are obtained. At short wavelength limits, the secular equations for symmetric and skew symmetric modes of wave propagation in a stress free insulated and isothermal plate reduce to Rayleigh surface wave frequency equation. The results for thermoelastic, micropolar elastic and elastic materials are obtained as particular cases from the derived secular equations. The amplitudes of displacement components, microrotation and temperature distribution are also computed during the symmetric and skew symmetric motion of the plate. The dispersion curves for symmetric and skew symmetric modes and amplitudes of displacement components, microrotation and temperature distribution in case of fundamental symmetric and skew symmetric modes are presented graphically. The analytical and numerical results are found to be in close agreement.     

Wave dispersion and dissipation performance of locally resonant acoustic metamaterials using an internal variable model

Engineering structures for different dispersion and dissipation levels of wave propagation use internal variable models, which may enhance the performance of acoustic metamaterials (AMMs). In this study, the wave dispersion and dissipation performance of AMMs is studied using an anelastic displacement fields (ADF) model. A symmetric state-space method based on Floquet-Bloch’s theorem for a nonviscously damped unit cell is developed. The study also constructs Bloch’s eigenvalue problems built from the symmetric state-space formulation to obtain the wavevector-dependent damped frequency and damping ratio for wave propagation analysis of periodic structures. The effects of wave dispersion and dissipation on the performance of AMMs are studied by using two numerical examples of mass-in-mass lattice systems containing multiple resonators. It is shown that nonviscous damping increases the wave dispersion performance of AMM. It is also shown that the metadamping phenomenon enhances the wave dissipation performance of AMM. It is demonstrated that the new method in symmetric form is applicable for performance analysis of periodic phononic crystal.     

半平面问题远域辐射阻尼的时域边界元法模拟研究

辐射阻尼在岩石基坑爆破开挖、边坡稳定、结构抗震以及结构-地基动力相互作用等实际工程问题中具有重要意义.为了模拟半平面问题的远域辐射阻尼,以时域边界元法(TD-BEM)理论为基础,根据应力波在弹性介质中的传播特性,在时域内提出了一种新的单元,即自适应半无限边界单元,专门用于离散远域半无限边界.该单元外侧节点是一个始终处于...     

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.     

Maxwell泥床上线性长波衰减的研究

用Maxwell模型作为非牛顿泥床本构,建立了一组新的Boussinesq型方程组,以描述波-泥相互作用下水波的传播. 基于该方程,解析给出了一维线性长波衰减率的表达式. 当泥层模型退化到牛顿流体时,该结果与前人文献的结果一致. 当无量纲松弛时间λ较大时,衰减率随泥深近似地出现周期性的极值现象,这些极值位置对应泥层中各阶模态的衰减率峰值.      

Rayleigh lamb waves in micropolar isotropic elastic plate

The propagation of waves in a homogeneous isotropic micropolar elastic cylindrical plate subjected to stress free conditions is investigated. The secular equations for symmetric and skew symmetric wave mode propagation are derived. At short wave limit, the secular equations for symmetric and skew symmetric waves in a stress free circular plate reduces to Rayleigh surface wave frequency equation. Thin plate results are also obtained. The amplitudes of displacements and microrotation components are obtained and depicted graphically. Some special cases are also deduced from the present investigations. The secular equations for symmetric and skew symmetric modes are also presented graphically.     

Review of Computational Aeroacoustics Algorithms

This paper presents a review of recent advancements in computational methodology for aeroacoustics problems. High-order finite difference methods for computation of linear and nonlinear acoustic waves are the primary focus of the review. Schemes for numerical simulation of linear waves include explicit optimized and DRP finite-difference operators, compact schemes, wavenumber extended upwind schemes and leapfrog-like algorithms. Both spatial approximations and time-integration techniques, which include low-dissipation low-dispersion Adams-Bashforth and Runge-Kutta (RK) methods, are examined. Wave propagation properties are analysed in the wavenumber and frequency space. Different approaches to eliminate short-wave spurious numerical waves are also reviewed. Methods for simulating nonlinear acoustic phenomena include essentially non-oscillatory (ENO) schemes, numerical adaptive filtering for high-order explicit and compact finite-difference operators, MacCormack and adaptive compact nonlinear algorithms. A literature survey of other CAA methods is provided in the introductory part.     

Free vibration of microstretch thermoelastic plate with one relaxation time

The propagation of waves in microstretch thermoelastic homogeneous isotropic plate subjected to stress free thermally insulated and isothermal conditions is investigated in the context of conventional coupled thermoelasticity (CT) and Lord and Shulman (L–S) theories of thermoelasticity. The secular equations for both symmetric and skew-symmetric wave mode propagation have been obtained. At short wavelength limits, the secular equations for symmetric and skew-symmetric modes reduce to Rayleigh surface wave frequency equation. The amplitudes of dilatation, microrotation, microstretch and temperature distribution for the symmetric and skew symmetric wave modes are computed analytically and presented graphically for different theories of thermoelasticity. The theoretical and numerical computations are found to be in close agreement.     

Assessment of TVD schemes for inviscid and turbulent flow computation

A systematic study has been conducted to assess the performance of the TVD schemes for practical flow computation. The viewpoint adopted here is to treat the TVD schemes as a combination of the standard central difference scheme with numerical dissipation terms. The controlled amount of numerical dissipation modifies the computed fluxes to ensure that the solution is oscillation-free. Four variants of TVD schemes, two with upwind dissipation terms and two with symmetric dissipation terms, have been studied and compared with the conventional Beam-Warming scheme for inviscid and turbulent axisymmetric flow computations. The results obtained show that all four variants can accurately resolve the shock and flow profiles with fewer grid points than the Beam-Warming scheme. The convergence rates of the TVD schemes are also substantially superior to that of the Beam-Warming scheme. The combination of high accuracy, good robustness and improved computational efficiency offered by the TVD schemes makes them attractive for computing high-speed flow with shocks. In terms of the relative performances it is found that the symmetric schemes converge slightly faster but that the upwind schemes are less sensitive to the number of grid points being employed.     

Effect of a biasing electric field on the propagation of symmetric Lamb waves in piezoelectric plates

This paper is concerned with the effect of a biasing electric field on the propagation of Lamb waves in a piezoelectric plate. On the basis of three dimensional linear elastic equations and piezoelectric constitutive relations, the differential equations of motion under a biasing electric field are obtained and solved. Due to the symmetry of the plate, there are symmetric and antisymmetric modes with respect to the median plane of the piezoelectric plate. According to the characteristics of symmetric modes (odd potential state) and antisymmetric modes (even potential state), the phase velocity equations of symmetric and antisymmetric modes of Lamb wave propagation are obtained for both electrically open and shorted cases. The effect of a biasing electric field on the phase velocity, electromechanical coupling coefficient, stress field and mechanical displacement of symmetric and antisymmetric Lamb wave modes are discussed in this paper and an accompanying paper respectively. It is shown that the biasing electric field has significant effect on the phase velocity and electromechanical coupling coefficient, the time delay owning to the velocity change is useful for high voltage measurement and temperature compensation, the increase in the electromechanical coupling coefficient can be used to improve the efficiency of transduction.     

Inhomogeneous plane waves in compressible viscous fluids

The propagation of inhomogeneous plane waves in a compressible viscous fluid is considered. The frequency and the slowness vector are both allowed to be complex. There are seen to be two types of solutions: (a) two transverse waves, which involve no density or pressure fluctuations, (b) a longitudinal wave, which involves no fluctuations in vorticity. For each type, a propagation condition is obtained giving the (complex) squared length of the slowness vector as a function of frequency. Each depends also on the viscosities. It is seen how to recover the incompressible case as the limit in which the inviscid acoustic wave speed tends to infinity. Each wave is shown to be linearly stable for real frequencies. These waves are attenuated in space and time but nevertheless it is possible to define constant weighted mean values (over a cycle of the propagating part of the wave) of the energy density, energy flux and dissipation. The energy-dissipation equation and the propagation conditions are used to derive relationships between these constant weighted means, some of which are generalizations to compressible fluids of previously known results for incompressible fluids. Explicit expressions in terms of frequency are given for the weighted means.     

Leaky and non-leaky behaviours of guided waves in CF/EP sandwich structures

The aim of this study is to investigate the leaky and non-leaky behaviours of guided waves, between the composite skin and the core in CF/EP sandwich structures, focusing on the fundamental symmetric like and anti-symmetric like guided wave modes and Rayleigh waves. In investigating the core effect on the guided wave propagation different types of cores are used, namely Nomex honeycomb (HRH 10 1/8-3) 10 and 20 mm in thickness and foam (Divinycell^®  PVC). The behaviour of the guided wave modes is characterised and the conversion mechanism to the Rayleigh wave is investigated. Further, leaky and non-leaky behaviours of guided waves upon interacting with debonded areas are explored, where the ability of guided waves to identify debonding of different sizes was assessed. Finite element analysis simulations are presented to support the experimental analysis, where propagation of ultrasonic waves and their interaction with debonded areas are quantitatively examined.     

One dimensional steepening of waves in non-ideal relaxing gas

In this paper, we studied the behavior of different modes of wave propagation and breaking of wave front by employing the theory of singular surfaces in a plane and radially symmetric flow of a non-ideal relaxing gas. The one dimensional steepening of waves is considered and the transport equation for the jump discontinuity of velocity gradient is obtained. The effects of relaxation and van der Waals excluded volume of the medium on the jump discontinuity of velocity gradient are analyzed.     

Propagation of Lamb waves in transversely isotropic thermoelastic diffusive plate

The constitutive relations and field equations for anisotropic generalized thermoelastic diffusion are derived and deduced for a particular type of anisotropy, i.e. transverse isotropy. Green and Lindsay (GL) theory, in which, thermodiffusion and thermodiffusion–mechanical relaxations are governed by four different time constants, is selected for study. The propagation of plane harmonic thermoelastic diffusive waves in a homogeneous, transversely isotropic, elastic plate of finite width is studied, in the context of generalized theory of thermoelastic diffusion. According to the characteristic equation, three quasi-longitudinal waves namely, quasi-elastodiffusive (QED-mode), quasi-massdiffusive (QMD-mode) and quasi-thermodiffusive (QTD-mode) can propagate in addition to quasi-transverse waves (QSV-mode) and the purely quasi-transverse motion (QSH-mode), which is not affected by thermal and diffusion vibrations, gets decoupled from the rest of the motion of wave propagation. The secular equations corresponding to the symmetric and skew symmetric modes of the plate are derived. The amplitudes of displacements, temperature change and concentration for symmetric and skew symmetric modes of vibration of plate are computed numerically. Anisotropy and diffusion effects on the phase velocity, attenuation coefficient and amplitudes of wave propagation are presented graphically in order to illustrate and compare the analytically results. Some special cases of frequency equation are also deduced from the existing results.     

Wave propagation along a non-principal direction in a compressible pre-stressed elastic layer

The dispersive behavior of small amplitude waves propagating along a non-principal direction in a pre-stressed, compressible elastic layer is considered. One of the principal axes of stretch is normal to the elastic layer and the direction of propagation makes an angle θ with one of the in-plane principal axes. The dispersion relations which relate wave speed and wavenumber are obtained for both symmetric and anti-symmetric motions by formulating the incremental boundary value problem for a general strain energy function. The behavior of the dispersion curves for symmetric waves is for the most part similar to that of the anti-symmetric waves at the low and high wavenumber limits. At the low wavenumber limit, depending on the pre-stress and propagation angle, it may be possible for both the fundamental mode and the next lowest mode to have finite phase speeds, while other higher modes have an infinite phase speed. At the high wavenumber limit, the phase speeds of the fundamental mode and the higher modes tend to the Rayleigh surface wave speed and the limiting wave speeds of the layer, respectively. Numerical results are presented for a Blatz–Ko material and the effect of the propagation angle is clearly illustrated.     

Waves in an inhomogeneous plasma with Hall dispersion

The evolution of steady-state periodic solutions of the Korteweg-de Vries equation (the socalled cnoidal waves), propagating along the direction of the gravitational force with an arbitrary orientation of the magnetic field, is studied for plasma characterized by Hall dispersion and Joule dissipation, using the magnetohydrodynamic approximation. The wavelength is regarded as much shorter than the characteristic scale of the inhomogeneity. The dependence of the wave amplitude on the distance to the source of the wave is considered for various limiting cases. The behavior of the wave depends on the temperature distribution in the medium. In the particular case of an isothermal atmosphere, the problem is solved analytically for a cold plasma in the absence of dissipation. The amplitude of both fast and slow waves increases when the wave travels upward and diminishes when the wave travels downward. The nonlinearity of the wave (i.e., the parameter characterizing the deviation of the wave from sinusoidal form) diminishes in the case of fast magnetoacoustic waves when the wave travels upward and increases when the wave travels downward. The situation is reversed for slow magnetoacoustic waves.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 139–144, September–October, 1976.The author is grateful to V. B. Baranov for constant interest in the work and valuable comments.     

非均匀水流水域波浪的传播变形

将两个不同的、考虑波流相互作用和能量耗散项的、依赖时间变化的双曲型缓坡方程分别化 为一组等价的控制方程组,具体分析了底摩阻项对相对频率和波数矢的影响,从而选择了合 适的数学模型. 将所选择的缓坡方程化为依赖时间变化的抛物型方程,并用ADI法进 行数值求解,建立了缓变水深水域非均匀水流中波浪传播的数值模拟模型. 通过和波流共线 的解析解的比较,说明数值解和解析解相一致. 结合Arthur(1950)水流这一经典算例,定 量地讨论了考虑联合折射-绕射作用后的波数和仅考虑折射作用的波数的差别及其对波高分 布的影响. 在基本同样的条件下, 本文的数值解与他人的计算结果一致.     

Development of optimized weighted‐ENO schemes for multiscale compressible flows

The present paper deals with the development of optimized weighted–ENO schemes to improve the resolution of a class of compressible flows characterized by a wide disparity of scales, typical of compressible turbulence and/or aeroacoustic phenomena, and shock waves. The approach relies on a least square minimization of both the dispersion and dissipation error components together with the use of symmetric stencil support. Extensive numerical simulations of sound propagation, shock–sound interaction and isotropic compressible turbulence have been carried out, and the results confirm that the optimized schemes yield a resolution in wave number space greater than the non‐optimized ones. Copyright © 2003 John Wiley & Sons, Ltd.