Effects of Surface Waves and Marine Soil Parameters on Seabed Stability

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Depth‐integrated,non‐hydrostatic model with grid nesting for tsunami generation,propagation, and run‐up

Tsunamis generated by earthquakes involve physical processes of different temporal and spatial scales that extend across the ocean to the shore. This paper presents a shock‐capturing dispersive wave model in the spherical coordinate system for basin‐wide evolution and coastal run‐up of tsunamis and discusses the implementation of a two‐way grid‐nesting scheme to describe the wave dynamics at resolution compatible to the physical processes. The depth‐integrated model describes dispersive waves through the non‐hydrostatic pressure and vertical velocity, which also account for tsunami generation from dynamic seafloor deformation. The semi‐implicit, finite difference model captures flow discontinuities associated with bores or hydraulic jumps through the momentum‐conserved advection scheme with an upwind flux approximation. The two‐way grid‐nesting scheme utilizes the Dirichlet condition of the non‐hydrostatic pressure and both the horizontal velocity and surface elevation at the inter‐grid boundary to ensure propagation of dispersive waves and discontinuities across computational grids of different resolution. The inter‐grid boundary can adapt to bathymetric features to model nearshore wave transformation processes at optimal resolution and computational efficiency. A coordinate transformation enables application of the model to small geographic regions or laboratory experiments with a Cartesian grid. A depth‐dependent Gaussian function smoothes localized bottom features in relation to the water depth while retaining the bathymetry important for modeling of tsunami transformation and run‐up. Numerical experiments of solitary wave propagation and N‐wave run‐up verify the implementation of the grid‐nesting scheme. The 2009 Samoa Tsunami provides a case study to confirm the validity and effectiveness of the modeling approach for tsunami research and impact assessment. Copyright © 2010 John Wiley & Sons, Ltd.     

冲击载荷作用下柱壳链中的弹性波传播简化模型及其解析解

柱壳链能引起波形的弥散,具备操控波形的潜力。建立了柱壳链结构的等效连续介质模型和细观有限元模型,研究了质量块冲击作用下柱壳链中的弹性应力波传播过程及其几何弥散特性。基于考虑横向惯性修正的Rayleigh-Love波动方程,建立了柱壳链在质量块冲击下的控制方程,采用Laplace变换及其逆变换获得了位移场、速度场和应变场的解析解,所得结果与细观有限元模拟结果较好吻合。结果表明,在冲击过程中应变和速度峰值均逐渐减小,应变峰值、振荡幅度和波形前沿宽度与泊松比和惯性半径相关,泊松比和惯性半径越大,应变峰值越小,应变分布振荡越剧烈,波形前沿宽度越宽。     

Tunable three-dimensional nonreciprocal transmission in a layered nonlinear elastic wave metamaterial by initial stresses

In this work, the three-dimensional(3 D) propagation behaviors in the nonlinear phononic crystal and elastic wave metamaterial with initial stresses are investigated.The analytical solutions of the fundamental wave and second harmonic with the quasilongitudinal(qP) and quasi-shear(qS1 and qS2) modes are derived. Based on the transfer and stiffness matrices, band gaps with initial stresses are obtained by the Bloch theorem.The transmission coefficients are calculated to support the band gap prope...     

Surface wave generation in the process of finite deformation of the bottom of a basin

The process of generation of three-dimensional irrotational fluid motions induced by small local finite-duration displacements of part of the bottom of a basin is considered within the framework of wave linear theory for a basin of constant depth. The solution of the problem and an expression for the total wave field energy are obtained using integral transforms. The general properties of the process of unsteady wave generation induced by short-term and slow deformations of the bottom are analyzed. Within the framework of the piston generation model the energy characteristics of axisymmetric waves are compared for two time laws of bottom deformation of identical duration. In general, it is shown that under certain conditions the nature and intensity of the wave process depend on both the time law and the duration of the deformation process.Sevastopol. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 2, pp. 151–156, March–April, 1996.     

Some exact solutions for a class of compressible non-linearly elastic materials

In this paper we consider exact solutions for plane and axisymmetric deformations for a class of compressible elastic materials we call coharmonic. The coharmonic materials are derived from the harmonic materials by using Shield's inverse deformation theorem. The governing equations for the coharmonic material show the same kind of simplification associated with the harmonic materials. The equations reduce to first-order linear equations depending on an arbitrary harmonic function. They are intractable in general, so various ansätze are investigated. Boundary value problems for the coharmonic materials are compared with the same problems for harmonic materials. For certain boundary value problems, the harmonic materials exhibit well-known problematic behaviour which limits their use as models of material behaviour. The corresponding solutions for the coharmonic materials do not display these non-physical features.     

正交各向异性厚板的边界元解法

本文利用 Hormander 算子法和平面波分解法导出了计入剪切变形的正交各向异性厚板的基本解。建立了计入剪切变形的正交各向异性厚板的边界积分方程。文中详细地讨论了基本解的数值计算,并用边界元法分析了一些算例。     

Numerical modeling of coupled seabed scour and pipe interaction

Scouring of the seabed by ice masses poses great threat to structural integrity and safety of buried structures such as oil and gas pipes. Large ridge motions and large seabed deformations complicate study of the seabed scouring and pipe interaction using classical Lagrangian methods. We present a new numerical approach for modeling the coupled seabed scour problem and its interaction with embedded marine pipes. In our work, we overcome the common issues associated with finite deformation inherently present within the seabed scour problem using a rheological approach for soil flow. The seabed is modeled as a viscous non-Newtonian fluid, and its interface described implicitly through a level-set function. The history-independent model allows for large displacements and deformations of the ridge and seabed, respectively. Numerical examples are presented to demonstrate the capabilities of the method with regard to seabed scouring and the ensuing large soil deformation.     

A numerical model for run‐up of breaking waves

In the present paper, the numerical method for the three‐dimensional run‐up, given in Johnsgard and Pedersen [‘A numerical model for three‐dimensional run‐up’, Int. J. Numer. Methods Fluids, 24 , 913–931 (1997)], is extended to include wave breaking. In the fundamental problem of run‐up of a uniform bore, the present model is compared with analytical solutions from the literature. The numerical solutions converge, but very slowly. This is not due to the numerical model, but rather to the structure of the solutions themselves. Numerical results for two realistic but simplified tsunami cases are also presented. In the first case, two‐dimensional simulations are performed concerning the run‐up of a tsunami in Portugal, in the second case, the three dimensional wave pattern generated after a slide in Tafjord, Norway in 1931, is studied. A discussion of different aspects of the model is summarized at the end of the paper. Copyright © 1999 John Wiley & Sons, Ltd.     

Shock initiated instabilities in underwater cylindrical structures

An experimental investigation to understand the mechanisms of dynamic buckling instability in cylindrical structures due to underwater explosive loadings is conducted. In particular, the effects of initial hydrostatic pressure coupled with a dynamic pressure pulse on the stability of metallic cylindrical shells are evaluated. The experiments are conducted at varying initial hydrostatic pressures, below the critical buckling pressure, to estimate the threshold after which dynamic buckling will initiate. The transient underwater full-field deformations of the structures during shock wave loading are captured using high-speed stereo photography coupled with modified 3-D Digital Image Correlation (DIC) technique. Experimental results show that increasing initial hydrostatic pressure decreases the natural vibration frequency of the structure indicating loss in structural stiffness. DIC measurements reveal that the initial structural excitations primarily consist of axisymmetric vibrations due to symmetrical shock wave loading in the experiments. Following their decay after a few longitudinal reverberations, the primary mode of vibration evolves which continues throughout later in time. At the initial hydrostatic pressures below the threshold value, these vibrations are stable in nature. The analytical solutions for the vibration frequency and the transient response of cylindrical shell are discussed in the article by accounting for both (1) the added mass effect of the surrounding water and (2) the effect of initial stress on the shell imposed by the hydrostatic pressure. The analytical solutions match reasonably well with the experimental vibration frequencies. Later, the transient response of a cylindrical shell subjected to a general underwater pressure wave loading is derived which leads to the analytical prediction of dynamic stability.     

Propagation of Harmonic Waves in a Cylindrical Shell (Timoshenko Model)

Equations for studying the axisymmetric deformation of a cylindrical shell are derived on the basis of Timoshenko shell theory. A dispersion equation is set up to study natural harmonic waves in a cylindrical isotropic shell. A numerical approach to plotting dispersion diagrams is proposed. The wave velocities obtained coincide with analytical solutions     

The Wavelet-Based Technique in Dispersive Wave Propagation

The paper expounds a wavelet-based technique. The techniques is applied to the dispersive wave equation by describing wave propagation by a composition of fundamental (harmonic) wavelets. The linear Klein–Gordon equation is analyzed and associated approximate wavelet solutions are considered for fixed resolution levels. Discretized wavelet families are computed explicitly using a basis of time harmonic wavelets. Some applications at various low resolution levels show that the technique proposed provides new opportunities for wave propagation analysis     

孤立波与淹没平板相互作用的三维波面和水动力实验研究

在波浪水池中进行了孤立波作用下有限长度和有限宽度淹没平板的三维模型水池实验. 首次应用多目视觉立体重构技术测量局部三维自由表面变形, 该系统的有效测量水平范围为1.7 m$\times $1.6 m. 用4个三分力测力传感器组成水下测力系统, 在不影响波面的情况下测量孤立波对平板的作用力和力矩. 针对波浪不破碎的情况, 选择0.4 m水深和0.16 m波高的来波条件, 平板淹没深度为0.1 m. 实验结果表明, 孤立波经过淹没平板时自由面有明显的三维变形, 导致孤立波波幅的时空变化. 波幅在平板尾缘中心线处达到最大值, 并沿展向逐渐减小. 利用多目视觉立体重构系统得到的波面变化过程与浪高仪给出定点波面时间序列相互印证, 表明建立标识码波面测量方法是有效的. 孤立波对淹没平板作用的水动力载荷变化分为6个典型阶段, 并与利用波面三维重构得到的波面测量标识码并讨论. 基于多目视觉立体重构技术得到了垂向力和俯仰力矩极值点出现时的三维波面形态. 建立的多目视觉立体重构系统将为海洋工程结构物的水池物理模型实验提供新的波面测量手段.      

Wave propagation in a pre-stressed highly elastic body: two exact solutions for Boussinesq problems

Two problems of wave propagation induced by surface loads in a compressible neo-Hookean half-space, initially at rest under a uniform pre-stress, are considered. One problem concerns a plane-strain situation, the other, one of axial symmetry. An accepted general procedure, that of superposing infinitesimal deformations upon the possibly large deformations due to pre-stress, is carried out completely in terms of tractable exact solutions for both the surface behavior and the full field, and analytical expressions for all wave speeds.

The results show that for a tensile pre-stress above a critical value, a negative Poisson effect occurs; for compressive pre-stresses, Rayleigh waves disappear at a critical value. Indeed, all wave speeds in the deformed configuration (effective wave speeds), as well as the solutions, for both problems are clearly sensitive to material properties and to both the magnitude and nature (compressive or tensile) of the pre-stress. In particular, the constraint imposed by plane strain appears to enhance this sensitivity.     

水下散体颗粒滑坡产生海啸波的实验研究

海底滑坡海啸作为仅次于地震海啸的重要海啸形态,常常发生于靠近海岸带的陆架和陆坡等区域,且由于其近岸灾害影响显著、物理机制复杂、难以监测和预警等特点,给靠近海岸带的居民造成了巨大的生命财产损失．关于水上滑坡海啸的实验研究相对比较充分,而对水下滑坡海啸和部分淹没滑坡海啸的研究则相对较少．本研究在大型波浪水槽中进行了斜坡上散体水下滑坡激发海啸的机理实验,研究了滑坡体的滑移距离、海啸波的形成过程以及海啸波的幅值、波速、非线性等特征,系统地认识了滑坡体质量、水深以及滑坡角度对滑坡海啸波高的影响规律,并提出了改进的水下滑坡海啸特征参数经验公式．     

Reflection of a beam of elastic waves by a periodic surface profile

Reflection of elastic waves from a traction-free solid-air boundary of periodic saw-tooth profile is investigated analytically and experimentally. For an incident plane wave the surface displacements on the profile are computed as the solution of a singular integral equation. The reflected field is subsequently obtained by using an integral representation. Incident beams of finite width are represented by Fourier superpositions of plane waves. The dependence of the reflected signal spectra on the incident beam width is examined closely near the fundamental surface resonance frequency. Experimental spectra which were obtained using two different diameter transducers, are compared to the corresponding theoretical spectra. It is found that the depth of the spectral minima depends on the incident beam width. Both analytical and experimental results exhibit the splitting of an incident beam of elastic waves into two reflected beams. The beam splitting is more pronounced for a narrower incident beam and for frequencies close to a resonance frequency of the profile.     

水击谐波流场中乳化油液滴粒径的PIV测量

为了掌握乳化油液滴在水击谐波流场中的碰撞、破裂、聚集和变形等微观形态的变化规律,采用粒子图像测速(PIV)技术对水平方管中乳化油液滴的水击谐波流场进行了测量,分析了在水击谐波流场中,不同激振力作用下乳化油液滴的粒径变化。测量结果表明,在水击谐波流场作用下,乳化油液滴平均粒径的增长率随着激振力的减小而减小,随着作用时间的增大呈增加趋势,直至粒径处于一种动态平衡;乳化液滴随着激振力增大到达波节聚集位置的时间减少,可见增大水击谐波激振力有利于乳化液滴的聚集并合并为大尺度的液滴,从而有效地提高了水击谐波流场作用下的油水分离效果。     

平面波输入下海水-海床-结构动力相互作用分析

海洋工程结构的地震反应分析是保证海洋工程结构地震安全的重要环节.由于其所处的复杂环境, 该问题涉及到流固耦合和土-结相互作用.本文基于海水、饱和海床、基岩流固耦合统一计算框架,采用Davidenkov模型和修正的Masing准则考虑饱和海床的非线性,在脉冲SV波垂直入射下, 进行了海域场地和海洋工程结构的动力响应分析. 首先,对比分析了线性自由场和非线性自由场输入情形的海域场地非线性反应,结果表明线性自由场输入时反应不合理,自由场分析和场地分析应该采用相一致的本构模型. 然后,对比分析了海床分别为线性和非线性情形时,海域场地以及海水-海床-结构体系的反应特征. 与线性海床情形相比,非线性对海床反应的影响主要由如下两方面因素控制: 一方面,非线性导致饱和海床模量减小, 饱和海床与基岩间的波阻抗比减小,由基岩到饱和海床间的反射系数和透射系数增加, 导致反应增大; 另一方面,非线性导致阻尼加大, 使海床反应减小. 对于本文算例而言,阻尼对非线性海床结果的影响占主导作用.      

Wave propagation analysis of a functionally graded magneto-electro-elastic nanobeam rest on Visco-Pasternak foundation

Wave propagation analysis of a nanobeam made of functionally graded magneto-electro-elastic materials with rectangular cross section rest on Visco-Pasternak foundation is studied in this paper. For modeling the axial, rotation and transverse deformations, Timoshenko beam model is used. Fundamental magneto-electro-elastic equations of the model are derived for a general functionally graded beam excited to electric and magnetic potentials. Surface elasticity is employed for more confident modeling the behavior of nanobeam. Using Hamilton principle and calculation of kinetic and strain energies, the equations of motion are derived. Considering the harmonic wave propagation of infinite domain yields characteristic equation of the system in terms of different parameters of model. The effects of different parameters such as non-homogeneous index, wave number and residual surface stress are investigated on the different phase velocities corresponding to modes of deformation. One can find that increasing the non-homogeneous index and wave number leads to decrease in wave propagation phase velocities.