Estimating the error of the beam approximation in the plane stability problem for a rectangular plate with a central crack

The plane stability problem for a rectangular, linearly elastic, isotropic plate with a central crack is solved. The dependence of the critical load on the crack length is studied using exact (the three-dimensional linearized theory of stability of elastic bodies) and approximate (beam approximation) approaches. The results produced by the beam approach are evaluated.Translated from Prikladnaya Mekhanika, Vol. 40, No. 11, pp. 117–126, November 2004.This revised version was published online in April 2005 with a corrected cover date.     

New models of Cahn-Hilliard-Gurtin equations

In this article, we further generalize the models of Cahn-Hilliard equations proposed by Gurtin and based on a balance law for microforces. We then study the existence and uniqueness of solutions and the boundedness of the order parameter.Received: 26 May 2003, Accepted: 29 August 2003, Published online: 3 February 2004PACS: 02.30.Jr, 64.75. + g Correspondence to: M. Efendiev     

Critical time for acoustic wavesin weakly nonlinear poroelastic materials

The final time of existence (critical time) of acoustic waves is a characteristic feature of nonlinear hyperbolic models. We consider such a problem for poroelastic saurated materials of which the material properties are described by Signorini-type constitutitve relations for stresses in the skeleton, and whose material parameters depend on the current porosity. In the one-dimensional case under consideration, the governing set of equations describes changes of extension of the skeleton, a mass density of the fluid, partial velocities of the skeleton and of the fluid and a porosity. We rely on a second order approximation. Relations of the critical time to an initial porosity and to an initial amplitude are discussed. The connection to the threshold of liquefaction is indicated.Received: 10 August 2004, Accepted: 3 December 2004, Published online: 4 March 2005PACS: 62.50, 81.40, 62.65 Dedicated to Prof J. L. Ericksen on the occasion of his 80th birthday     

Nonlinear vibration of a rotating cantilever beam in a surrounding magnetic field

The nonlinear vibrations of a rotating cantilever beam made of magnetoelastic materials surrounded by a uniform magnetic field are investigated. The kinetic energy, potential energy and work done by the electromagnetic force are obtained. A nonlinear dynamic model, based on the Hamilton principle, which includes the stretching vibration and bending vibration is presented. The Galerkin method is adopted to discretize the dynamic equations. The proposed method is validated by comparison with the literature. The nonlinear behaviors of the responses are studied. Then simulations for different kinds of magnetic field are conducted. The effects of magnetic field parameters, including the amplitude, plane angle, spatial angle and time-varying frequency, on the dynamic behaviors of the stretching motion and bending motion are investigated in detail. The results illustrate that the interaction effects between the rotating cantilever beam and the magnetic field will increase the vibration amplitude and fluctuation of the beam. In particular, we found that: collinear magnetic fields with equal amplitude lead to the same dynamic responses; the amplitude of magnetic field intensity increases the dynamic responses remarkably; the response amplitude changes nonlinearly with the plane angle and spatial angle of the magnetic field; and the increase of time-varying frequency enhances dynamic responses of the rotating cantilever beam.     

Endless elastic beam travelling on a moving rough surface with zones of stick and sliding

Nonlinear Dynamics - We study the planar deformation of a beam that travels across a given control domain supported by a moving rough plane, which is a prototype for various technological...     

On Rank One Connectedness, for Planar Objective Functions

We give a geometrical treatment of rank one connectedness, for planar objective functions. A decomposition of the Cauchy Green matrix introduces the Poincaré half plane, and the non-Euclidean distance between points of the half plane is central in formulating the condition of rank one connectedness. This revised version was published online in August 2006 with corrections to the Cover Date.     

Évolution quasi-statique d'un fil souple inextensible sur un plan avec frottement sec : cas discretQuasi-static motion of a supple,homogenous and inextensible string on a horizontal plane with dry friction: discret case

The differential inclusion describing the quasi-static motion of a supple, homogeneous and inextensible string on a horizontal plane with dry friction (Coulomb's law) is a one dimensional evolution model of a continuous medium, with non-linear geometry, obeying a “plastic-rigid” law. With a view to numerical simulation, we treat the discrete case: the string is assimilated to a chain constituted by rigid rods perfectly articulated around ball-joints. We give variational formulation of the problem and prove existence and uniqueness of solutions. We construct an algorithm that describes the instantaneous solutions when the initial configuration of the string is given. Then, some examples are treated. To cite this article: H. Sayah, C. R. Mecanique 332 (2004).     

具有半刚性节点性质的平面刚架弹簧单元的研究

联合应用力法与逐段刚化法推导出具有半刚性节点性质的弹簧节点梁单元和平面刚架弹簧单元的单元刚度方程. 该方法具有物理概念清楚,推导过程简便、巧妙的特点. 本文所建立的弹簧节点梁单元和平面刚架弹簧单元可以应用在具有半刚性节点性质的工程结构的承载力分析与计算中.     

Elastic equations for a cylindrical section of a tree

Considering a cylindrical section of a tree subjected to loads independent of x₃ as a relaxed Saint-Venant's problem, it was shown that plane sections remain plane. Since plane sections remain plane, the displacement equations for the neutral fiber derived using either the relaxed Saint-Venant's problem or elementary beam theory are equivalent. The stresses in the plane of the transverse cross-section were found to equal to zero. Therefore, it is appropriate to use elementary beam theory to estimate the three-dimensional stress functions when the wood is considered to be homogeneous. In addition the three-dimensional displacement equations allow the required elastic coefficients in cylindrical coordinates to be measured from full size samples.     

Stochastic stability of parametrically excited random systems

Multidegree-of-freedom dynamic systems subjected to parametric excitation are analyzed for stochastic stability. The variation of excitation intensity with time is described by the sum of a harmonic function and a stationary random process. The stability boundaries are determined by the stochastic averaging method. The effect of random parametric excitation on the stability of trivial solutions of systems of differential equations for the moments of phase variables is studied. It is assumed that the frequency of harmonic component falls within the region of combination resonances. Stability conditions for the first and second moments are obtained. It turns out that additional parametric excitation may have a stabilizing or destabilizing effect, depending on the values of certain parameters of random excitation. As an example, the stability of a beam in plane bending is analyzed.Published in Prikladnaya Mekhanika, Vol. 40, No. 10, pp. 135–144, October 2004.     

Unsteady drag on a sphere by shock wave loading

The dynamic drag coefficient of a sphere by shock wave loading is investigated numerically and experimentally. The diameter of the sphere is varied from 8 m to 80 mm in numerical simulation. The axisymmetric Navier-Stokes equations are solved on a fine grid, and the grid convergence of the drag coefficient is achieved. The numerical result is validated by comparing the experimental data of a 80 mm sphere, measured by the accelerometer in a vertical shock tube. It is found that the sphere experiences in the early interaction one order higher drag than in the steady state. A transient negative drag, mainly resulting from the focusing of shock wave on the rear side of the sphere, is observed only for high Reynolds number flows, and the drag becomes positive because of increased skin friction for low Reynolds number flows.Received: 10 March 2004, Accepted: 24 May 2004, Published online: 20 August 2004[/PUBLISHED]M. Sun: Send offprints requests to     

Flow of a generalized second grade non-Newtonian fluid with variable viscosity

A modified constitutive equation for a second grade fluid is proposed so that the model would be suitable for studies where shear-thinning (or shear-thickening) may occur. In addition, the dependence of viscosity on the temperature follows the Reynolds equation. In this paper, we propose a constitutive relation, (18), which has the basic structure of a second grade fluid, where the viscosity is now a function of temperature, shear rate, and concentration. As a special case, we solve the fully developed flow of a non-Newtonian fluid given by (11), where the effects of concentration are neglected.Received: 28 August 2003, Accepted: 3 March 2004, Published online: 25 June 2004 Correspondence to: M. Massoudi Dedicated to Professor Brian Straughan     

An experimental investigation of underexpanded jets from oval sonic nozzles

 Underexpanded jets from oval sonic nozzles were experimentally studied for various pressure ratios up to 20.3. The results revealed that the barrel type of shock structure was present only in the major axis plane except at low aspect ratios. The results also revealed that the jet spreading rate in the minor axis plane of the nozzle was much higher compared to that in the major axis plane, resulting in axis switching of jets. The cross sectional area of these jets were considerably higher compared to the axisymmetric jets indicating higher interface area for viscous mixing in the near field region and increased mixing in the far field region clear of shock structure. Received: 7 January 1997 / Accepted: 7 August 1997     

Étude par la PIV des structures à la périphérie d'une cavité rotor–stator aspiréeStudy of structures on the periphery of a rotor–stator cavity with suction by means of PIV

We experimentally study the three-dimensional structure of the spiral instability observed on the periphery of a opened rotor–stator cavity with suction. We use the stereoscopic Particles Images Velocimetry technique which gives sequences of maps of the three velocity components of fluid particles located in a meridian plane. This sequence is acquired with a low frequency during the running of a great number of structures. The originality of this study consists in an optimized temporal reclassifying of the maps on a single period that allows a three-dimensional reconstitution of the instability. To cite this article: D. Rémy et al., C. R. Mecanique 332 (2004).     

Selection of two-dimensional nonlinear strain waves in micro-structured mediaSelection d'ondes de déformation non linéaires à deux dimensions dans des milieux à microstructure

It is shown that the micro-displacement gradient allows the propagation of two-dimensional localized long nonlinear strain waves in a medium with microstructure. These waves may exist even in the presence of dissipation and energy input in the microstructured medium but with selected values of the wave amplitude and velocity. An increase or a decrease in the wave amplitude and velocity happens faster at the initial stage than that of the plane localized wave. However, their steady values selected by the energy input/output, are higher for the plane waves. To cite this article: A.V. Porubov et al., C. R. Mecanique 332 (2004).     

Influence of the resonator angular displacements in a hemispherical resonator gyro on the coupling between the working and beam-type vibrations

In [1], we have studied how the coupling between the working and beam type vibrations of the resonator affects the hemispherical resonator gyro operation. We show that such a coupling arises if the resonator is unbalanced. The beam type vibrations are considered as translational displacements of the resonator hemisphere in the plane orthogonal to the symmetry axis. In the present paper, we take into account the fact that the hemisphere translational displacement is accompanied by its rotation about the axis perpendicular to the displacement line. We show that in this case a more accurate balancing of the resonator is required to eliminate the coupling between the two vibration modes.     

Instabilities in a Two-Dimensional Combustion Model with Free Boundary

We prove instability of the planar travelling wave solution in a two-dimensional free boundary problem modelling the propagation of near- equidiffusional premixed flames in the whole plane. We reduce the problem to a fixed boundary fully nonlinear parabolic system. The spectrum of the linearized operator contains an interval [0,ω ^c ], ω ^c > 0, so we cannot construct backward solutions. We use an argument about stability of dynamical systems in Banach spaces in order to prove pointwise instability of the moving front. (Accepted: January 31, 2000)?Published online August 21, 2000     

中心刚体-变截面梁系统的动力学特性研究

对在平面内做大范围转动的中心刚体-变截面梁系统的动力学进行了研究.考虑柔性梁横向弯曲变形和纵向伸长变形, 且在纵向位移中计及由于横向变形而引起的纵向缩短项, 即非线性耦合变形项. 采用假设模态法描述变形, 运用第二类Lagrange方程推导得到系统刚柔耦合动力学方程. 在此基础上对做大范围旋转运动的中心刚体-楔形梁以及中心刚体-梯形梁模型的动力学进行了详细研究. 研究表明: 梁宽比、梁高比以及梯形梁变截面位置都对系统的动力学特性有很大影响.      

Real-time determination and controlof the laser-drilled holes depth

We present an optodynamical method for the real-time determination of the depth of laser-drilled holes. The method consists of the detection of shock waves generated during the interaction of the laser beam with the irradiated material using a piezoelectric transducer (PZT), and measurement of the shock waves propagation time through the sample using the PZT signal. The experimental observations reveal that the propagation time has an almost exponential decay with the number of pulses and is strongly dependent on the laser radiation wavelength. The quantity of ablated substrate material per laser pulse is a nonlinear function of the number of consecutive laser pulses incident on the same spot at the irradiated sample surface.Received: 29 September 2003, Accepted: 30 September 2004, Published online: 27 January 2005[/PUBLISHED]Correspondence to: M. Stafe and C. Negutu     

Direct determination of curvatures of bent plates using a double-glass-plate shearing interferometer

A single-exposure reflective moiré technique for the direct recording of curvature contours of laterally loaded plates is proposed. The specular reflection of a coherent, collimated beam of light by the loaded specimen is collected by a field lens and focussed onto a shearing interferometer. The shearing interferometer consists of two thin, identical plane-parallel glass plates, placed successively in the optical path near the focal plane and aligned at 45 deg to the optical axis. The two plates shear the narrow convergent beam from the lens twice optically, producing three sets of images—superposing one over the other—at the image plane. Curvature fringes result in the region overlapped by all three images.