Papers by Keyword: Refraction

Abstract: The beautiful colors of the rainbow have always fascinated humans and especially children are inspired to various artworks such as drawing, canvas painting, poster, wall decals and so on. Since refraction and reflection of light cannot be seen taking place in raindrop during rainbow formation, children are unaware of all these details. Although throughout the year past, there are many literatures on theoretical and mathematical aspects of rainbow formation, however there are very few studies in education context to teach about this phenomenon to the children in particular by observing and measuring. Therefore, in this paper we are proposing a model that can be used for hands-on learning with high school students about the formation of spectrum in glass sphere. With the help of the model students can see the angle at which different color lights are deviated by the glass sphere and finally, students can also relate the concept learnt from this lesson to real life phenomenon about spectrum formation by rain drop.

Abstract: The results of mathematical modeling of the dynamic interaction of a plane longitudinal shock wave with a plane interface between two isotropic nonlinear elastic materials are presented. The mechanical properties of deformable solid are given by the elastic Murnaghan model. The dynamic processes of deformations distribution are studied in the framework of the theory of singular surfaces. The numerical solutions of the corresponding self-similar problem with strong and weak deformations discontinuities in the reflected and refracted wave packages have been obtained on the basis of the developed scheme of computational experiment.

Abstract: X-ray refraction is based on optical deflection of X-rays, similar to the well-known small angle X-ray scattering, but hundreds of times more intense, thus enabling shorter measurement time. We show that X-ray refraction techniques are suitable for the detection of pores, cracks, and in general defects. Indeed, the deflected X-ray intensity is directly proportional to the internal specific surface (i.e., surface per unit volume) of the objects. Although single defects cannot be imaged, the presence of populations of those defects can be detected even if the defects have sizes in the nanometer range.We present several applications of X-ray refraction techniques to composite materials:- To visualize macro and microcracks in Ti-SiC metal matrix composites (MMC);- To correlate fatigue damage (fibre de-bonding) of carbon fibre reinforced plastics (CFRP) to X-ray refraction intensity;- To quantify the impact damage by spatially resolved single fibre de-bonding fraction as a function of impact energy in CFRP laminates.An example of classic high-resolution computer tomography of an impact-damaged CFRP will also be presented, as a benchmark to the present state-of-the-art imaging capabilities. It will be shown that while (absorption) tomography can well visualize and quantify delamination, X-ray refraction techniques directly yield (spatially resolved) quantitative information about fibre de-bonding, inaccessible to absorption tomography.

Abstract: X-ray residual stress analysis is a widespread nondestructive technique to investigate the residual stress and residual stress gradient in thin films and protective coatings.In the present contribution we introduce a new method based on the noncomplanar measurement geometry that allow to span large area of sin² ψ and penetration depth values without sample inclination. The refraction correction and absorption is considered in details for the noncomplanar measurements. The proposed technique is applied to determine stress gradients of blasted hard TiN coatings.

Abstract: Using the reflection and refraction coefficient of SH wave at the interface of strata, we derived the phase shift of total reflection and refraction SH-wave, The results show that, the phase shift reflection than the phase shift refraction, phase shift of reflection 2 times the phase shift of refraction.

Abstract: With vision feedback the binocular micro stereovision system based on stereo light microscope (SLM) makes it possible to achieve 2D/3D high accuracy auto-positioning, 3D information extraction, 3D shape reconstruction and 3D measurement. Therefore, it is extensively used in micro robot navigation, micromanipulation, micro assembly and bioengineering, etc. To improve the key problems of low accuracy, refraction and occlusion in micro stereovision measurement, a novel micro stereo vision system is built based on optical theory and digital image processing. Then, the nonlinear correlation between optical paths of the micro stereo vision system is studied and the environment adaptive nonlinear model is established. On this basis, the coupling mechanism of multi-refraction and occlusion with micro-projection nonlinear model is proved, and multi-refraction variable refractive index correction and micro stereo occlusion reconstruction algorithms are developed. It realizes synchronization observation in larger field of view, rapid non-contact accuracy positioning and 3D measurement based on stereovision to solve the pivotal problems of accuracy positioning and measure in the chip encapsulation, micro assembly and the micro manipulation.

Abstract: Using the model of micropolar generalized magneto-thermo-elasticity, the coupled transverse and micro-rotational wave at an interface between two micropolar solid mediums is discussed in the presence of a constant magnetic field. The model can be applied to the coupled theory as well as to five generalizations: the Lord-Shulman theory with one relaxation time, the Green-Lindsay theory with two relaxation times, the Green-Naghdi theories of type II(without energy dissipation) and of type III, and the theory with dual-phase-lag. Using continuous conditions at the interface, the amplitude ratios of reflected and refracted longitudinal displacement waves, longitudinal micro-rotational waves and the coupled transverse and micro-rotational waves are studied for incident coupled transverse and micro-rotational wave. The effect of thermal relaxation is discussed for C-D theory, G-L theory and L-S theory. The numerical results show that the effects of thermal relaxation times are very significant on the amplitude ratios.

Abstract: The reflection and refraction of harmonic SH waves at the interface between a homogeneous solid and a one-dimensional phononic crystal is studied. The effects of wave frequencies on the refraction coefficients are investigated. The results show that for lower frequencies, most part of the energy is reflected into the homogeneous solid and that the frequency has little effects on the energy distribution at the interface. While for higher frequencies, SH waves cannot propagate in some directions because of the existence of the directional band gaps, which results in the discontinuity in the refraction coefficient curve. For waves passing through the interface, the higher the frequency is, the smaller the refraction coefficient is.

Abstract: The micropolar elasticity theory takes into consideration the granular character of the medium, describes deformations by a microrotation and a microdisplacement. A model can be applied to the coupled theory as well as to five generalizations, such as L-S theory, G-L theory, H-I theory, G-N theory of type (II) and C-T theory. And if some parameters in this model are taken as given values, we can easily deduce the known models of Kelvin-Voigt model and other generalized micropolar/magneto/thermo/viscoelastic theory model. Employing the model of micropolar generalized magneto-thermo-elasticity, reflection and refraction of longitudinal displacement wave at interface of two welded micropolar elastic media are studied. The amplitude ratios of reflected and refracted micropolar magneto-thermoelastic longitudinal displacement waves, longitudinal microrotational waves and the coupled transverse and microrotational waves are studied for incident longitudinal displacement wave. The numerical results show that the effects of thermal relaxation times are very significant on the amplitude ratios.

Abstract: Using the model of generalized micropolar magneto-thermo-elasticity, reflection and refraction of longitudinal displacement wave at interface of two welded micropolar elastic media are studied. The model can be applied to the coupled theory as well as to five generalizations, such as L-S theory, G-L theory, H-I theory, G-N theory of type (II) and C-T theory. And if some parameters in this model are taken as given values, we can easily deduce the known models of Kelvin-Voigt model and other generalized micropolar/magneto/thermo/viscoelastic theory model. Using continuous conditions at the interface, the amplitude ratios of reflected and refracted micropolar magneto-thermoelastic longitudinal displacement waves, longitudinal microrotational waves and the coupled transverse and microrotational waves are studied for incident longitudinal displacement wave. The numerical results show that the effect of magnetic field is very significant on the amplitude ratios.