<Emphasis Type="Italic">J</Emphasis><Subscript>2</Subscript> invariant relative orbits via differential correction algorithm

This paper describes a practical method for finding the invariant orbits in J ₂ relative dynamics. Working with the Hamiltonian model of the relative motion including the J ₂ perturbation, the effective differential correction algorithm for finding periodic orbits in three-body problem is extended to formation flying of Earth’s orbiters. Rather than using orbital elements, the analysis is done directly in physical space, which makes a direct connection with physical requirements. The asymptotic behavior of the invariant orbit is indicated by its stable and unstable manifolds. The period of the relative orbits is proved numerically to be slightly different from the ascending node period of the leader satellite, and a preliminary explanation for this phenomenon is presented. Then the compatibility between J ₂ invariant orbit and desired relative geometry is considered, and the design procedure for the initial values of the compatible configuration is proposed. The influences of measure errors on the invariant orbit are also investigated by the Monte–Carlo simulation. The project supported by the Innovation Foundation of Beihang University for Ph.D. Graduates, and the National Natural Science Foundation of China (60535010).     

An experimental—Numerical evaluation of the<Emphasis Type="Italic">T</Emphasis><Stack><Subscript>ε</Subscript><Superscript>*</Superscript></Stack> integral for a three-dimensional crack front

TheT _ε ^* integral was calculated on the surface of single edge notched, three-point bend (SE(B)) specimens using experimentally obtained displacements. Comparison was made withT _ε ^* calculated with the measured surface displacements andT _ε ^* calculated at several points through the thickness of a finite element (FE) model of the SE(B) specimen. Good comparison was found between the surfaceT _ε ^* calculated from displacements extracted from the FE model and the surfaceT _ε ^* calculated from experimentally obtained displacements. The computedT _ε ^* integral was also observed to decrease as the crack front was traversed from the surface to the mid-plane of the specimen. Mid-planeT _ε ^* values tend to be approximately 10% of the surface values.     

Reduction of<Emphasis Type="Italic">K</Emphasis><Subscript>I</Subscript> and<Emphasis Type="Italic">K</Emphasis><Subscript>II</Subscript> by the shape-memory effect in a TiNi shape-memory fiber-reinforced epoxy matrix composite

Shape-memory TiNi fiber-reinforced/epoxy matrix composites have been fabricated, and the suppression of crack-tip stress intensity and the change in fracture toughness have been systematically investigated. Stress-strain data for these composite specimens with notches at various angles and different crack lengths in the transverse direction have been measured in tensile tests. The stress intensity factor at the crack tip is experimentally determined from photoelastic fringe patterns. The decreases inK values are attributed to the compressive stress field in the matrix induced when the pre-strains of the TiNi fiber contract to their initial length upon heating above the austenitic final temperature. We present the influences of the pre-strain of TiNi fibers and the compressive domain size between a crack tip and fiber on theK value.     

Assessment of <Emphasis Type="Italic">Σ−Y</Emphasis><Subscript>liq</Subscript> model predictions for air-assisted atomisation

In a series of recent works, R. Borghi and co-workers proposed a new Eulerian model of two-phase turbulent flows which introduced a transport equation for the average area of the liquid–gas interface. This work is devoted to the assessment of this model’s ability to predict the effects of liquid properties and injection regimes on the atomisation quality. Air-assisted atomisation, for which extensive experimental data are available, is chosen as a test case. It is shown that the model predictions are in good agreement with the observed trends for a wide range of variations of the liquid properties, such as density and surface tension, as well as the injection regimes, defined by the liquid and gas jet exit velocities.      

Effects of measurement techniques on the experimental characterization of crack tip opening angle-Δ<Emphasis Type="Italic">a</Emphasis> resistance curves

One of the most promising approaches to characterizing the stable tearing process for lower constraint configurations in metallic materials has been indicated to be the crack tip opening angle (CTOA) criterion. In this paper we examine the effect of measurement distance selection and the impact of measurement procedures/analysis on the experimental CTOA-Δa resistance curve behavior of a Ti-6Al-4V and an Al5083 alloy. A new, systematic procedure for carrying out the experimental, surface CTOA measurement process has been used, which has uncovered artifacts of measurement distance selection that have not been presented prior to this study. By studying the CTOA-Δa behavior using a rigidly defined and consistent method, it is apparent that the measurement distance behind the crack tip at which angles are measured has a direct impact on the shape of the early transitional behavior of the CTOA-Δa behavior as well as the critical, experimental CTOA values produced.     

Bifurcations of Limit Cycles in a <Emphasis Type="Italic">Z</Emphasis><Subscript>8</Subscript>-Equivariant Planar Vector Field of Degree 7

The weakened Hilberts 16th problem for symmetric planar perturbed polynomial Hamiltonian systems is considered. An example of Z₈-equivariant planar perturbed Hamiltonian systems is constructed. By using bifurcation theory of planar dynamical systems and the method of detection functions, under the help of numerical analysis, it is shown that there exist parameter groups such that this perturbed Hamiltonian polynomial vector field of degree 7 has at least7²=49 limit cycles with Z₈ symmetry. It also gives rise to different configurations of limit cycles forming compound eyes.Dedicated to Professor Shui-Nee Chow on the occasion of his 60th birthday.     

An <Emphasis Type="Italic">In Situ</Emphasis> Ultrasonic Technique for Simultaneous Measurement of Longitudinal and Shear Wave Speeds in Solids

Ultrasonic wave speed measurements are widely used to infer the elastic properties of solids. In the standard method, longitudinal and shear transducers are used separately to measure the corresponding wave speeds in a material. A new experimental method is introduced for simultaneously measuring the longitudinal and the shear wave speeds using a single set of longitudinal or shear transducers. The method can also be used to measure the wave speeds in situ during deformation by placing the transducers along the loading axis. The transducers are housed in a specially designed fixture such that they are not subjected to loading. The technique is demonstrated by performing uniaxial compression experiments on fully dense isotropic solids (where the wave speeds are not expected to change during deformation) and in polymeric foams (where the wave speeds are affected by damage).