The Richtmyer-Meshkov instability of a double-layer interface in convergent geometry with magnetohydrodynamics

The interaction between a converging cylindrical shock and double density interfaces in the presence of a saddle magnetic field is numerically investigated within the framework of ideal magnetohydrodynamics.Three fluids of differing densities are initially separated by the two perturbed cylindrical interfaces.The initial incident converging shock is generated from a Riemann problem upstream of the first interface.The effect of the magnetic field on the instabilities is studied through varying the field strength.It shows that the Richtmyer-Meshkov and Rayleigh-Taylor instabilities are mitigated by the field,however,the extent of the suppression varies on the interface which leads to non-axisymmetric growth of the perturbations.The degree of asymmetry of the interfacial growth rate is increased when the seed field strength is increased.

Double plate system with a discontinuity in the elastic bonding layer

The double plate system with a discontinuity in the elastic bonding layer of Winker type is studied in this paper. When the discontinuity is small, it can be taken as an interface crack between the bi-materials or two bodies （plates or beams）. By comparison between the number of multifrequencies of analytical solutions of the double plate system free transversal vibrations for the case when the system is with and without disconti- nuity in elastic layer we obtain a theory for experimental vibration method for identification of the presence of an interface crack in the double plate system. The analytical analysis of free transversal vibrations of an elastically connected double plate systems with discontinuity in the elastic layer of Winkler type is presented. The analytical solutions of the coupled partial differential equations for dynamical free and forced vibration processes are obtained by using method of Bernoulli＇s particular integral and Lagrange＇s method of variation constants. It is shown that one mode vibration corresponds an infinite or finite multi-frequency regime for free and forced vibrations induced by initial conditions and one- frequency or corresponding number of multi-frequency regime depending on external excitations. It is shown for every shape of vibrations. The analytical solutions show that the discontinuity affects the appearance of multi-frequency regime of time function corresponding to one eigen amplitude function of one mode, and also that time functions of different vibration basic modes are coupled. From final expression we can separate the newgeneralized eigen amplitude functions with correspon- ding time eigen functions of one frequency and multifrequency regime of vibrations.

SINGLE AND DOUBLE EDGE INTERFACE CRACK SOLUTIONS FOR ARBITRARY FORMS OF MATERIAL COMBINATION

In this paper interfacial edge crack problems are considered by the application of the finite element method. The stress intensity factors are accurately determined from the ratio of crack-tip-stress value between the target given unknown and reference problems. The reference problem is chosen to produce the singular stress fields proportional to those of the given unknown problem. Here the original proportional method is improved through utilizing very refined meshes and post-processing technique of linear extrapolation. The results for a double-edge interface crack in a bonded strip are newly obtained and compared with those of a single-edge interface crack for different forms of combination of material. It is found that the stress intensity factors should be compared in the three different zones of relative crack lengths. Different from the case of a cracked homogeneous strip, the results for the double edge interface cracks are found to possibly be bigger than those for a single edge interface crack under the same relative crack length.