On the Use of the Restitution Condition in Flexible Body Dynamics

The difference between the classical treatment offlexible body impact and the treatment of impact in flexiblemultibody dynamics is due to several fundamental reasons. Inthe classical impact theory, simple structures such as beamsand plates are used. Infinite dimensional models can bedeveloped for these simple structural elements to study theimpact dynamics and the wave propagation problem. Flexiblemultibody impact problems, on the other hand, involve bodieswith complex geometry that cannot be modeled using infinitenumber of degrees of freedom. Furthermore, the classicalimpact theory has been mainly concerned with the impactbetween a rigid mass that moves without constraints beforeit impacts a simple flexible structure. This is not amultibody simulation scenario in which the impact occursbetween kinematically constrained bodies that are subjectedto impulsive constraint forces in addition to the impactforces. These constraint forces can influence the motion ofthe two bodies immediately after impact, and as aconsequence, the simple classical theory scenario of impactdoes not apply. It is the objective of this paper to discussthe use of the restitution condition in flexible multibodyimpact problems and demonstrate that the use of thisapproach does not exclude the classical formulation.Nonetheless, the impulse momentum balance approach can serveas an effective and efficient procedure for solving theimpact problem in finite dimensional models that do not obeythe classical wave theory. Energy results of simplestructural elements are presented in order to demonstratethe consistency of using the impulse momentum balanceapproach in solving impact problems in finite dimensionalflexible body applications.     

Analysis of natural milk and milk poweder samples by NAA

As a part of the Iraqi Food Analysis Programme /I.F.A.P./ the concentration of Na, Mg, P, Cl, K, Ca, Zn, Se, Br, Rb and I in natural milk collected from different regions of Iraq, and in milk powder samples have been determined by using the NAA technique. It was found that except for the elements I, Rb and Br the concentration of the elements was approximately identical in both the natural milks and milk powders.     

Role of compositional changes on thermal,magnetic,and mechanical properties of Fe-P-C-based amorphous alloys

This work aimed to tune the comprehensive properties of Fe-P-C-based amorphous system through investigating the role of microalloying process on the crystallization behavior,glass forming ability(GFA),soft magnetic features,and mechanical properties.Considering minor addition of elements into the system,it was found that the simultaneous microalloying of Ni and Co leads to the highest GFA,which was due to the optimization of compositional heterogeneity and creation of near-eutectic composition.Moreover,the FeCoNiCuPC amorphous alloy exhibited the best anelastic/viscoplastic behavior under the nanoindentation test,which was owing to the intensified structural fluctuations in the system.However,the improved plasticity by the extra Cu addition comes at the expense of magnetic properties,so that the saturation magnetization of this alloying system is significantly decreased compared to the FeCoPC amorphous alloy with the highest soft magnetic properties.In total,the results indicated that a combination of added elemental constitutes,i.e.,Fe69Co5Ni5Cu1P13C7 composition,provides an optimized state for the comprehensive properties in the alloying system.     

Self-consistent treatment of spin and magnetization dynamic effect in spin transfer switching

The effect of itinerant spin moment (m) dynamic in spin transfer switching has been ignored in most previous theoretical studies of the magnetization (M) dynamics. Thus in this paper, we proposed a more refined micromagnetic model of spin transfer switching that takes into account in a self-consistent manner of the coupled m and M dynamics. The numerical results obtained from this model further shed insight on the switching profiles of m and M, both of which show particular sensitivity to parameters such as the anisotropy field, the spin torque field, and the initial deviation between m and M.     

A new operational vector approach for time-fractional subdiffusion equations of distributed order based on hybrid functions

This research study deals with the numerical solutions of linear and nonlinear time-fractional subdiffusion equations of distributed order. The main aim of our approach is based on the hybrid of block-pulse functions and shifted Legendre polynomials. We produce a novel and exact operational vector for the fractional Riemann–Liouville integral and use it via the Gauss–Legendre quadrature formula and collocation method. Consequently, we reduce the proposed equations to systems of equations. The convergence and error bounds for the new method are investigated. Six problems are tested to confirm the accuracy of the proposed approach. Comparisons between the obtained numerical results and other existing methods are provided. Numerical experiments illustrate the reliability, applicability, and efficiency of the proposed method.     

Non-polynomial spline method for the solution of two-dimensional linear wave equations with a nonlinear source term

In this paper, two classes of methods are developed for the solution of two space dimensional wave equations with a nonlinear source term. We have used non-polynomial cubic spline function approximations in both space directions. The methods involve some parameters, by suitable choices of the parameters, a new high accuracy three time level scheme of order O(h ⁴ + k ⁴ + τ ² + τ ² h ² + τ ² k ²) has been obtained. Stability analysis of the methods have been carried out. The results of some test problems are included to demonstrate the practical usefulness of the proposed methods. The numerical results for the solution of two dimensional sine-Gordon equation are compared with those already available in literature.     

Effect of iridium loading on HZSM-5 for isomerization of n-heptane

The effect of iridium loading on the properties and catalytic isomerization of n-heptane over Ir-HZSM-5 is studied. Ir-HZSM-5 was prepared by impregnation method and subjected to isomerization process in the presence of flowing hydrogen gas. XRD and BET studies show that the presence of iridium stabilizes the crystalline structure of HZSM-5, leading to more ordered framework structure and larger surface area. TGA and FTIR results substantiate that iridium species interacts with OH group on the surface of HZSM-5. Pyridine FT-IR study verifies the interaction between iridium and surface OH group slightly increased the Bro¨nsted and Lewis acid sites without changing the lattice structure of HZSM-5. The presence of iridium and the increase of strong Lewis acid sites on HZSM-5 were found to bring an increase about 4.1%, 33.2% and 11.8% in conversion, selectivity and yield of n-heptane isomerization, respectively.