Comparison of methods for calculating the shock hugoniot of mixtures

Various methods used to determine the shock Hugoniot of condensed phase multi-component mixtures are reviewed and compared to available experimental data. The assumptions inherent in the different models are presented in this overview and their implications are discussed. The comparisons of the various models demonstrate that the predicted shock Hugoniots are in good agreement with published data despite the simplifying assumptions that are associated with the models. Averaging models are shown to be among the simplest methods to implement and result in the closest agreement with experimental data.     

Microstructure in a Cubic to Orthorhombic Transition

Microstructures for a cubic to orthorhombic transition are constructed using a geometrically nonlinear, thermoelastic theory of martensitic transformations. Such microstructures are of interest because they provide low energy paths along which a specimen can transform. The particular microstructures considered are the twinned martensite, austenite–martensite, wedge, triangle, and diamond. More specifically, all possible twins are found along with the corresponding twinning elements and magnitude of the twin shear. Further, two kinds of austenite–martensite microstructures are studied: those with a single variant of martensite and those with twinned martensite. The regions in the space of transformation stretches in which each of these microstructures exist are determined, and the shape strains and habit plane normals are found as well. In addition, special microstructures, the wedge, triangle, and diamond, are constructed with both the austenite-single variant and austenite-twinned martensite microstructures. These special microstructures are of interest because they provide a mechanism through which the transformation may proceed more easily, and they are possible only in alloys with particular transformation stretches. Numerically computed level curves in the space of the stretches are presented on which the special microstructures are possible. These results may be useful in providing guidelines for alloy design.     

Forced capillary-gravity wave motion of two-layer fluid in three-dimensions

A class of problems associated with forced capillary-gravity wave motion in a channel are analyzed in the presence of surface and interfacial tensions in a two-layer fluid in both the cases of finite and infinite water depths. The two and three-dimensional Green functions associated with the capillary-gravity wave problems in the presence of surface and interfacial tensions are derived using the fundamental source potentials. Using the two-dimensional Green function along with Green’s second identity, the expansion formulae for the velocity potentials associated with the capillary-gravity wavemaker problems in two-dimensions are obtained. The two-dimensional results are generalized to derive the expansion formulae for the velocity potentials associated with the forced capillary-gravity wave motion in the presence of surface and interfacial tensions in three-dimensions. Certain characteristics of the eigen-system associated with the expansion formulae are derived. The velocity potentials associated with the free oscillation of capillary-gravity waves in a closed basin and semi-infinite open channel in the presence of surface and interfacial tensions are obtained. The utility of the forced motion in a channel is demonstrated by analyzing the capillary-gravity wave reflection by a wall in a channel in the presence of surface and interfacial tensions. Long wave equations associated with capillary-gravity wave motion in the presence of surface and interfacial tensions are derived under shallow water approximation and the associated dispersion relation are obtained. Various expansion formulae and Green functions derived in the present study will be useful for analyzing a large class of physical problems in ocean engineering and mathematical physics.     

Thermoelastic interactions without energy dissipation in an unbounded body with a spherical cavity subjected to harmonically varying temperature

The present work is concerned with the thermally induced vibration in a homogeneous and isotropic unbounded body with a spherical cavity. The Green and Nagdhi model of thermoelasticity without energy dissipation is employed. The closed form solutions for distributions of displacement, temperature and stresses are obtained. The solutions valid in the case of small frequency are deduced and the results are compared with the corresponding results obtained in other generalized thermoelasticity theories. Numerical results applicable to a copper-like material are also presented graphically and the nature of variations of the physical quantities with radial coordinate and with frequency of vibration is analyzed.     

根部柔性梁的不确定性建模与确认

首先导出了包含根部挠性参数的悬臂梁动力学方程近似解,将平动和转动柔性参数作为不确定性源,根据若干预紧力矩下的模态实验结果完成了柔性参数识别,并假定其服从正态随机分布,识别了均值与标准差,进而通过回归分析建立了不确定参数随预紧力矩变化的数学模型.最后通过新的模态实验结果对所建模型进行了确认,通过确认结果,明确了该模型的使用范围.     

A numerical study of rays in random media

Statistics of electromagnetic rays in a random medium are studied numerically by the Monte Carlo method. Two dimensional random surfaces with prescribed correlation functions are used to simulate the random media. Rays are then traced in these sample media. Statistics of the ray properties such as the ray positions and directions are computed. Histograms showing the distributions of the ray positions and directions at different points along the ray path as well as at given points in space are given. The numerical experiment is repeated for different cases corresponding to weakly and strongly random media with isotropic and anisotropic irregularities. Results are compared with those derived from theoretical investigations whenever possible.     

On the cross-section distortion of thin-walled beams with multi-cell cross-sections subjected to bending

This paper deals with distortion of the cross-section contour of thin-walled beams with simple multi-cell closed rectangular cross-sections. The cross-section distortion is considered in the limit case. It is assumed that beam plates are hinged together along their longitudinal edges. Double symmetric three and two-cell closed cross-sections are considered. The stresses and displacements are obtained in the closed analytical form. The additional stresses and displacements due to distortion with respect to the stresses and displacements of the ordinary theory of bending are obtained. The boundary conditions are given in the general form. Some illustrative examples are given.     

Generalized variational principles on nonlinear theory of elasticity with finite displacements

Two generalized variational principles on nonlinear theory of elasticity with finitedisplacements in which the σ_(ij),e_(i j)and u_i are all three kinds of independent functionsare suggested in this paper.It isproved that these two generalized variational principles areequivalent to each other if the stress-strain relation is satisfied as constraint.Some specialcases,i.e.generalized variational principles on nonlinear theory of elasticity with smalldeformation,on linear theory with finite deformation and on linear theory with smalldeformation together with the corresponding equivalent theorems are also obtained.All ofthem are related to the three kinds of independent variables.     

Convective heat transfer in a square channel with angled ribs on two opposite walls

Detailed quantitative maps of the heat transfer distribution in a square channel with angled rib turbulators are measured by means of infrared (IR) thermography associated with the heated-thin-foil technique. Air flows in the channel where square ribs are mounted on two opposite walls at an angle of either 30° or 45° with respect to the duct axis. Two rib pitches, two different rib arrangements and two heating conditions are investigated. Results are presented in terms of local and averaged Nusselt numbers, which are normalised with the classical Dittus and Boelter correlation, for three different Reynolds numbers.     

Natural harmonic oscillations of a heavy fluid in basins of complex shape

The natural harmonic oscillations of a heavy fluid in uniform-depth basins of complex shape, including those with three or more symmetry axes, are investigated within the shallow-water approximation. The waves are assumed to be gently sloping. The modes found are compared with the similar modes in an elliptic basin representing the class of basins with two symmetry axes. The mode characteristics associated with the number of basin symmetry axes and the basin shape are explored. Basins with two symmetry axes whose shape differs considerably from the elliptic, in particular, nonconvex basins, are considered. Both rotating and non-rotating basins are studied. The possibility of approximating the amplitudes of certain rotating-basin mode classes by Bessel functions is discussed.     

Supersonic Gas Flows in Radial Nozzles

Results of experimental investigations and numerical simulations of supersonic gas flows in radial nozzles with different nozzle widths are presented. It is demonstrated that different types of the flow are formed in the nozzle with a fixed nozzle radius and different nozzle widths: supersonic flows with oblique shock waves inducing boundary layer separation are formed in wide nozzles, and flows with a normal pseudoshock separating the supersonic and subsonic flow domains are formed in narrow nozzles (micronozzles). The pseudoshock structure is studied, and the total pressure loss in the case of the gas flow in a micronozzle is determined.     

Nonlinear dynamics and chaos in coupled shape memory oscillators

Shape memory and pseudoelastic effects are thermomechanical phenomena associated with martensitic phase transformations, presented by shape memory alloys. This contribution concerns with the dynamical response of coupled shape memory oscillators. Equations of motion are formulated by assuming a polynomial constitutive model to describe the restitution force of the oscillators and, since they are associated with a five-dimensional system, the analysis is performed by splitting the state space in subspaces. Free and forced vibrations are analyzed showing different kinds of responses. Periodic, quasi-periodic, chaos and hyperchaos are all possible in this system. Numerical investigations show interesting and complex behaviors. Dynamical jumps in free vibration and amplitude variation when temperature characteristics are changed are some examples. This article also shown some characteristics related to chaos–hyperchaos transition.     

Two-phase micro- and macro-time scales in particle-laden turbulent channel flows

The micro-and macro-time scales in two-phaseturbulent channel flows are investigated using the direct numerical simulation and the Lagrangian particle trajectorymethods for the fluid-and the particle-phases,respectively.Lagrangian and Eulerian time scales of both phases are calculated using velocity correlation functions.Due to flowanisotropy,micro-time scales are not the same with the theoretical estimations in large Reynolds number(isotropic) turbulence.Lagrangian macro-time scales of particle-phaseand of fluid-phase seen by particles are both dependent onparticle Stokes number.The fluid-phase Lagrangian integral time scales increase with distance from the wall,longerthan those time scales seen by particles.The Eulerian integral macro-time scales increase in near-wall regions but decrease in out-layer regions.The moving Eulerian time scalesare also investigated and compared with Lagrangian integraltime scales,and in good agreement with previous measurements and numerical predictions.For the fluid particles themicro Eulerian time scales are longer than the Lagrangianones in the near wall regions,while away from the walls themicro Lagrangian time scales are longer.The Lagrangianintegral time scales are longer than the Eulerian ones.Theresults are useful for further understanding two-phase flowphysics and especially for constructing accurate predictionmodels of inertial particle dispersion.     

Incremental boundary value problems in the presence of coupling of elastic and plastic deformations: A rock mechanics oriented theory

In some elastoplastic systems (typically rocklike media) the elastic properties are affected by plastic yielding. This “coupling” phenomenon is dealt with in this paper in the context of the incremental theory of plasticity with nonassociated (lacking normality) flow laws. Some extremum properties and uniqueness conditions are given for solution of the rate problem. Stability conditions are established. The results achieved are equally applicable to media with nonassociative flow rules without coupling, with or without worksoftening, and are believed to be novel in this more traditional area. The results are cast into algebraic formulations for finite element models, in view of their practical applications.     

On the steady vibrations of elastic materials with voids

This paper is concerned with the linear elastodynamics of homogeneous and isotropic materials with voids. First, the singular solutions corresponding to concentrated forces in the case of steady vibrations are established. Then, representations of Somigliana type for the displacement field and the change in the volume fraction field are presented. Radiation conditions of Sommerfeld type are derived. The potentials of single layer and double layer are used to reduce the boundary value problems to singular integral equations for which Fredholm's basic theorems are valid. Existence and uniqueness results for exterior problems are established.     

Special virtual fields for the direct determination of material parameters with the virtual fields method. 3. Application to the bending rigidities of anisotropic plates

This paper deals with the direct identification of bending rigidities of thin anisotropic plates. These parameters are extracted from an heterogeneous strain field which takes place onto the top surface of a bent plate. The loading conditions are such that no closed-form solution is available for the deflection/slope/curvature fields. The procedure presently used is the virtual fields method with “special” virtual fields. It is shown that the unknown parameters are directly extracted with this method since no iterative calculations are required. The parameters are in fact directly equal to the virtual work of the applied loading with the special virtual displacement fields. The headlines of the method are recalled in the first part of the paper. They are then applied in the case of anisotropic bent plates. The accuracy and the stability of the procedure are finally discussed through some relevant examples.     

Plane stress state problems for notched bodies whose plastic properties depend on the form of the stress state

We consider one possible approach to the problem of describing the dependence of material plastic strain characteristics on the stress hydrostatic component arising in many porous, fractured, and other inhomogeneous materials. The plastic strain of the media under study is investigated under the plasticity assumption in the corresponding generalized form with the use of the form parameter of the stress state. The plasticity constitutive relations are stated on the basis of the plastic flow law associated with the accepted plasticity condition. For the conditions of plane stress state in the framework of the material rigid-plastic model, a system of partial differential equations is obtained and conditions for its hyperbolicity are determined. The relations for determining the stress fields and velocity fields in plastic domains are obtained, and their properties are investigated. The problem of tension of a strip with symmetric angular notches is solved, where the stress fields are determined and the continuous displacement rate field is constructed. The problem of uniform symmetric tension of a plane with a circular hole is considered. The stress fields in a strip with symmetric circular notches are examined. A comparison with solutions for plastically incompressible media whose properties are invariant with respect to the form of the stress state is performed.     

固支加筋方板的大挠度塑性动力响应

本文详细分析了爆炸载荷作用下固支回筋方板的大挠度塑性动力响应，给出了各种可能的运动模拟以及相应的差别条件，导出了最大残余变形的计算式，与文献［３］的试验结果比较表明，在多数情况下符合良好。     

The alternating between complete synchronization and hybrid synchronization of hyperchaotic Lorenz system with time delay

The various cases of synchronization in two identical hyperchaotic Lorenz systems with time delay are studied. Based on Lyapunov stability theory, the sufficient conditions for achieving synchronization of two identical hyperchaotic Lorenz systems with time delay are derived, and a simple scheme only with a single linear controller is proposed. When the parameters in the response system are known, the alternating between complete synchronization and hybrid synchronization (namely, coexistence of antiphase and complete synchronization) is observed with the control feedback gain varying. Furthermore, when the parameters in the response system are unknown, for the same feedback controller, the complete synchronization and the hybrid synchronization can be obtained, respectively, as the associated parameters updated laws of the unknown parameters are chosen. Numerical simulation results are presented to demonstrate the proposed chaos synchronization scheme.     

Influence of a wavy boundary on turbulence.

Measurements of turbulence with laser Doppler velocimetry (LDV) are compared for turbulent flows over a flat surface and a surface with sinusoidal waves of small wavelength. The wavy boundary was highly rough in that the flow separated. The Reynolds number based on the half-height of the channel and the bulk velocity was 46,000. The wavelength was 5 mm and the height to wavelength ratio was 0.1. The root-mean-squares of the velocity fluctuations are approximately equal if normalized with the friction velocity. This can be explained as a consequence of the approximate equality of the correlation coefficients of the Reynolds shear stress. Calculations with a direct numerical simulation (DNS) are used to show that the fluid interacts with the wall in quite different ways for flat and wavy surfaces. They show similarity in that large quadrant 2 events in the outer flow, for both cases, are associated with plumes that emerge from the wall region and extend over large distances. Measurements of skewness of the streamwise and wall-normal velocity fluctuations and quadrant analyses of the Reynolds shear stresses are qualitatively similar for flat and wavy surfaces. However, the skewness magnitudes and the ratio of the quadrant 2 to quadrant 4 contributions are larger for the wavy surface. Thus, there is evidence that turbulent structures are universal in the outer flow and for quantitative differences in the statistics that reflect differences in the way in which the fluid interacts with the wall.