Motion of an External Load over a Semi-Infinite Ice Sheet in the Subcritical Regime

The three-dimensional problem of steady-state forced vibrations of fluid and semiinfinite ice sheet under the action of a local external load traveling along the rectilinear sheet edge at a constant velocity is considered. Two cases are analyzed. In the first case the fluid surface outside the ice sheet is free and in the second the fluid is confined by a rigid vertical wall and the ice sheet edge adjacent to the wall can be both clamped and free. The ice sheet is simulated by a thin elastic isotropic plate floating on the surface of fluid of finite depth. The load traveling velocity is assumed to be not higher than the minimum phase velocity of the flexural-gravity waves (subcritical regime). The solution to the linear problem is obtained by means of the integral Fourier transform and matching the expansions of the velocity potential in the vertical eigenfunctions. Examples of the numerical investigation of the ice sheet and fluid displacements are given.     

Action of a Periodic Load on an Elastic Floating Plate

The problem of the behavior of an elastic floating plate in the form of a strip under the action of a periodic surface load is solved using the Wiener-Hopf technique. The shortwave approximation is found in explicit form. The effect of the frequency and nature of the acting load on the vibration amplitudes of the fluid and the plate is investigated numerically. It is found that for certain loads no waves propagate in the fluid and the vibrations of the plate are localized in the neighborhood of the acting load. Conditions under which local vibration can be realized are found.__________Translated from Izvestiya Rossiiskoi Academii Nauk, Mekhanika Zhidkosti i Gaza, No. 2, 2005, pp. 132–146.Original Russian Text Copyright © 2005 by Tkacheva.     

Effect of a Shock Pulse on a Floating Ice Sheet

The vibrations of a viscoelastic plate lying on an elastic liquid base subjected to pulse loading have been studied theoretically and experimentally. The effect of the variable depth of the reservoir, plate thickness, and strain relaxation time on the value of the plate vibration amplitude and the length and curvature of the flexural gravity wave profile are analyzed. Good agreement of theoretical and experimental results is obtained.     

Equilibrium of a Transversally Isotropic Body with an Elliptic Crack under Thermal Action

A nonuniform thermal effect on the surface of an elliptic crack in a transversally isotropic medium is studied. Use is made of the previous result on the analogy between elastic and thermoelastic problems for an arbitrary smooth flat crack in isotropic and transversally isotropic materials. A numerical analysis is performed to study how the stress intensity factors depend on the parameters and orientation of the crack     

Versal Deformation and Local Bifurcation Analysis of Time-Periodic Nonlinear Systems

In this study a local semi-analytical method of quantitativebifurcation analysis for time-periodic nonlinear systems is presented.In the neighborhood of a local bifurcation point the system equationsare simplified via Lyapunov–Floquet transformation whichtransforms the linear part of the equation into a dynamically equivalenttime-invariant form. Then the time-periodic center manifoldreduction is used to separate the `critical' states and reduce thedimension of the system to a possible minimum. The center manifoldequations can be simplified further via time-dependent normal formtheory. For most codimension one cases these nonlinear normal forms arecompletely time-invariant. Versal deformation of thesetime-invariant normal forms can be found and the bifurcation phenomenoncan be studied in the neighborhood of the critical point. However, ingeneral, it is not a trivial task to find a quantitatively correctversal deformation for time-periodic systems. In order to do so, onemust find a relationship between the bifurcation parameter of theoriginal time-periodic system and the versal deformation parameter ofthe time-invariant normal form. Essentially one needs to find theeigenvalues of the fundamental solution matrix of the time-periodicproblem in terms of the system parameters, which, in general, cannot bedone due to computational difficulties. In this work two ideas areproposed to achieve this goal. The eigenvalues of the fundamentalsolution matrix can be related to the versal deformation parameter bysensitivity analysis and an approximation of any desired order can beobtained. This idea requires a symbolic computational procedure whichcan be very time consuming in some cases. An alternative method issuggested for faster results in which a second or higher order curvefitting technique is used to find the relationship. Once thisrelationship is established, closed form post-bifurcation steady-statesolutions can be obtained for flip, symmetry breaking, transcritical andsecondary Hopf bifurcations. Unlike averaging and perturbation methods,the proposed technique is applicable at any bifurcation point in theparameter space. As physical examples, a simple and a double pendulumsubjected to periodic parametric excitation are considered. A simple twodegrees of freedom model is also studied and the results are comparedwith those obtained from the traditional averaging method. All resultsare verified by numerical integration. It is observed that the proposedtechnique yields results which are very close to the numericalsolutions, unlike the averaging method.     

The Stress Intensity Factor for an Elliptic Crack Under a Piecewise-Constant Load

A closed approximate solution is given for the stress intensity factor (SIF) at the front of an elliptic crack under uniform loading on the elliptic ring. The solution is constructed by modifying Rice's variational formula that integrally relates the SIFs for two different states on the crack faces. The first state is a combination of the second and principal states such that the total SIF is zero. In this case, Rice's formula reduces to the virtual-displacement principle for a combined loading on the crack faces.     

The Action of an Arbitrary Load on the Surface of an Orthotropic Half-Space

The exact solution to the first boundary-value problem for a half-space is constructed on the basis of the general solution of the equilibrium equations for an orthotropic medium (nine elastic constants). The stress–strain state of an orthotropic half-space whose surface is under an arbitrarily applied concentrated force is described as an example. The well-known solution for the isotropic case is obtained by the same scheme, which confirms the reliability of the result.     

Dependence of the Critical Load on the Geometric Characteristics of a Hinged Plate with a Crack

The plane problem of three-dimensional stability of a hinged plate with a central crack under uniaxial loading along the crack is considered. The net approach is used to solve the problem. The variational difference and gradient methods are used, respectively, to construct a difference scheme and to solve difference problems. The dependence of the critical load on two parameters — the crack length and the thickness ratio — is derived. Formulas for calculation of the critical load are given     

Symbolic Computation of Local Stability and Bifurcation Surfaces for Nonlinear Time-Periodic Systems

In this paper we present a spectral technique for building asymptotic expansions which describe periodic processes in conservative and self-excited systems without assuming the oscillations to be weakly nonlinear. The small parameter of the expansion is connected with the ratio of the amplitudes of higher than the first harmonics in contrast to the traditional parameter connected with weak nonlinearity. In the case of an oscillator with power nonlinearity the frequency of the main harmonic and the complex amplitudes of higher harmonics are computed as the expansions of either integer (for weakly nonlinear oscillations) or algebraic (for strong nonlinearity) functions of the complex amplitude of the first harmonic depending on the character of the initial conditions and the maximum power of the nonlinear term in the equation. In the simplest case of weakly nonlinear oscillations the complete asymptotic expansion is shown to be valid in the whole domain of the periodic motions of definite type until the separatrix is reached. The expressions for the first terms of the expansion for concrete examples coincide with the expressions obtained both with the use of other methods and by expanding the exact solutions. For some special cases of the strongly nonlinear oscillations the comparison of the results with known exact solutions is carried out as well as the criteria of convergence of the expansions are determined.     

Behavior of a Semi-Infinite Ice Cover Under a Uniformly Moving Load

This paper consideres the behavior of a semi-infinite ice cover on the surface of an ideal incompressible fluid of finite depth under the action of a load moving with constant velocity along the edge of the cover at some distance from it. The ice cover is modeled by a thin elastic plate of constant thickness. In a moving coordinate system, the deflection of the plate is assumed to be steady. An analytic solution of the problem is obtained using the Wiener–Hopf technique. The wave forces, the deflection of the plate, and the elevation of the free surface of the fluid at different velocities of the load are investigated.     

Delayed Fracture of a Laminated Viscoelastic Plate with a Through Crack under a Time-Dependent Load

The delayed fracture of a viscoelastic plate with a rectilinear mode I crack under a time-dependent load is studied. The plate is made of a laminated composite with an isotropic elastic reinforcing component and a viscoelastic matrix. The composite is modeled by an orthotropic homogeneous linearly viscoelastic medium with some averaged characteristics. To determine the viscoelastic characteristics of the composite, the Volterra principle and the method of continued fractions are used. The study is made within the framework of the theory of delayed fracture for viscoelastic bodies.     

无限冰介质中爆炸裂纹扩展机理与数值模拟

根据冰体力学性能,提出了无限淡水冰介质在爆炸冲击载荷下的压碎区及裂隙区的理论计算方法.利用大型有限元软件ANSYS/LS-DYNA模拟了爆炸载荷下无限区域冰体内裂纹扩展过程,模拟结果与实验结果基本一致,表明采用的损伤断裂模型能够较准确的反映无限冰介质动态力学性能及裂纹成形过程.数值模型可近似计算冰体中裂隙区的半径.数值计算值与理论计算值误差不超过5%,数值模拟结果与实验结果吻合,从而确定了无限区域冰体在-15℃时的基本破坏特征及范围.     

圆柱形界面相裂纹在扭转载荷作用下的动态断裂

本文研究了位于界面相中的圆柱形界面裂纹的扭转冲击问题.采用Laplace、Fourier变换和位错密度函数将混合边值问题转化为求解Cauchy核奇异积分方程,利用Laplace数值反演技术计算了动态应力强度因子.讨论了材料特性和结构的几何尺寸对动态应力强度因子的影响.结果表明,随着界面相厚度的增加,无量纲化的动态应力强度因子减小.当裂纹靠近剪切弹性模量大的材料时,无量纲化的动态应力强度因子增大,反之减小.界面相两侧不同的材料组合对裂尖动态应力强度因子的影响是随着剪切弹性模量和质量密度的比值的增加而减小.界面相中裂纹长度对裂尖动态应力强度因子的影响比其他因素的影响大.     

General Spatial Dynamic Problem for an Elliptic Crack under the Action of a Normal Shear Wave,with Consideration for the Contact Interaction of the Crack Faces

Consideration is given to the contact interaction of the faces of a stationary plane elliptical crack under the action of a harmonic shear wave normally incident on the crack surface. The dependence of the mode II and III stress intensity factors on the wave number is studied for different values of the friction coefficient     

Biaxial Load Effect on Crack Initiation for Orthotropic Materials

This paper is concerned with the study of the elastostatic fracture response of an orthotropic plate with an inclined crack and subjected at infinity to a biaxial uniform load. To this end an unconventional approach to the derivation of the complex variable expressions of the elastic fields is proposed. The above formulation has been used to solve the boundary value problem as superposition of Mode-I and Mode-II crack problems and it is shown that the near tip asymptotic expressions of stress and displacement fields are affected by non-singular terms originated by load biaxiality. The maximum circumferential tensile stress criterion is applied in order to investigate the effects of non-singular terms on the angle of crack extension.     

Initial-Value Problem on the Behavior of an Ice Cover under the Load in the Presence of Shear Current

Fluid Dynamics - The solution to the problem on the behavior of an ice cover on the surface of an ideal incompressible fluid of finite depth under a local pressure domain in the presence of a shear...     

On Time-Periodic Flow of a Viscous Liquid past a Moving Cylinder

We show existence, uniqueness and spatial asymptotic behavior of a two-dimensional time-periodic flow around a cylinder that moves orthogonal to its axis, with a time-periodic velocity, v. The result is proved if the size of the data is sufficiently small, and the average of v over a period is not zero.     

Numerical Study of Natural Convection Heat Transfer in an Inclined Porous Cavity with Time-Periodic Boundary Conditions

Kalabin et al. (Numer. Heat Transfer A 47, 621-631, 2005) studied the unsteady natural convection for the sinusoidal oscillating wall temperature on one side wall and constant average temperature on the opposing side wall. The present article is on the unsteady natural convective heat transfer in an inclined porous cavity with similar temperature boundary conditions as those of Kalabin et al. The inclined angle of the cavity is varied from 0° to 80°. The flow field is modeled with the Brinkman-extended Darcy model. The combined effects of inclination angle of the enclosure and oscillation frequency of wall temperature are studied for Ra* = 10³, Da = 10⁻³, , and Pr=1. Some results are also obtained with the Darcy–Brinkman–Forchheimer model and Darcy’s law and are compared with the present Brinkman-extended Darcy model. The maximal heat transfer rate is attained at the oscillating frequency f = 46.7π and the inclined angle .     

瞬态温度场作用下冰载荷计算

给出了关于冰的粘弹性微分本构模型的广义变分原理和冰载荷计算的有限元方法。修正的增量粘弹性矩阵有效地加速了迭代过程，计算了瞬态温度场下冰内压应力分布及对结构物作用力。其结果与实测数据定性吻合。