On the energy conservation and critical velocities for the propagation of a ＂steady-shock＂ wave in a bar made of cellular material

The propagation of shock waves in a cellular bar is systematically studied in the framework of continuum solids by adopting two idealized material models, viz. the dynamic rigid, perfectly plastic, locking （D-R-PP-L） model and the dynamic rigid, linear hardening plastic, locking （D-R-LHP-L） model, both considering the effects of strain-rate on the material properties. The shock wave speed relevant to these two models is derived. Consider the case of a bar made of one of such material with initial length L 0 and initial velocity v i impinging onto a rigid target. The variations of the stress, strain, particle velocity, specific internal energy across the shock wave and the cease distance of shock wave are all determined analytically. In particular the ＂energy conservation condition＂ and the ＂kinematic existence condition＂ as proposed by Tan et al. （2005） is re-examined, showing that the ＂energy conservation condition＂ and the consequent ＂critical velocity＂, i.e. the shock can only be generated and sustained in R-PP-L bars when the impact velocity is above this critical velocity, is incorrect. Instead, with elastic deformation, strain-hardening and strain-rate sensitivity of the cellular materials being considered, it is appropriate to redefine a first and a second critical impact velocity for the existence and propagation of shock waves in cellular solids. Starting from the basic relations for shock wave propagating in D-R-LHP-L cellular materials, a new method for inversely determining the dynamic stress-strain curve for cellular materials is proposed. By using e.g. a combination of Taylor bar and Hopkinson pressure bar impact experimental technique, the dynamic stress-strain curve of aluminum foam could bedetermined. Finally, it is demonstrated that this new formulation of shock theory in this one-dimensional stress state can be generalized to shocks in a one-dimensional strain state, i.e. for the case of plate impact on cellular materials, by simply making proper replacements of the elastic and plastic constants.     

A note on ＂Block H-matrices and spectrum of block matrices＂

In this paper, we make further discussions and improvements on the results presented in the previously published work ＂Block H-matrices and spectrum of block matrices＂. Furthermore, a new bound for eigenvalues of block matrices is given with examples to show advantages of the new result.     

Stability of laminated composite circular conical shells under external pressure

In this paper,based on the mixed-type theory developed by the same authors.atheoretical analysis is presented for the stability of laminated composite circular conicalshells under external pressure.The formulas for critical external pressure are obtained byusing the potential energy variation principle.Very good agreement is shown between thetheoretical prediction of critical external pressure and the experimental data.Finally,theinfluence of some parameters on critical external pressure is discussed numerically.Themixed-type theory developed by the same authors and the results obtained in this paperare very useful in aerospace engineering design.     

A study on flow resistance in the entrance region of isosceles triangular ducts

In the present paper the variational solution of velocity profile for anincompressible laminar and fully developed flow in isosceles triangular ducts is derivedby applying the Kantovorich method.The theoretical and experimental results ofpressure loss are also given.The velocity distribution model,additional pressure losscoefficient and calculating method of inlet length in the entrance region of isoscelestriangular ducts are also derived,which are suitable for various kinds of vertex angles.The calculations and experiments are also performed for two models:the isoscelestriangular channels with vertex angles2α=45.1°and2α=60°.Comparisons aremade between the theoretical analysis in this paper and those of the other authors.Itcan be seen that the present analytical result is of high.accuracy and widepracticability,and agrees well with the authors’experiment.     

Simple waves for two-dimensional compressible pseudo-steady Euler system

A simple wave is defined as a flow in a region whose image is a curve in the phase space. It is well known that ＂the theory of simple waves is fundamental in building up the solutions of flow problems out of elementary flow patterns＂ see Courant and Friedrichs＇s chassical book ＂Supersonic Flow and Shock Waves＂. This paper mainly concerned with the geometric construction of simple waves for the 2D pseudo-steady compressible Euler system. Based on the geometric interpretation, the expansion or compression simple wave flow construction around a pseudo-stream line with a bend part are constructed. It is a building block that appears in the global solution to four contact discontinuities Riemann problems.     

Research on Haar Spectrum in fault diagnosis of rotating machinery

In this paper,Haar Transform(HT)is used in the fault diagnosis of rotatingmachinery,and the“Impulse Sharpness”is presented as a diagnostic index.At present,Fourier Spectrumanalysis is most widely used Compared with FFT,HT is more rapid incomputation and more effective in discrete approximation.It’s very suitable for theextraction of pulses in the signal.However,HT has some shortcomings.It’s greatlyaffected by the starting point and length of the sample.Here,the authors present a methodto improve the stability and comparability of Haar Spectrum.The fault imitating test ofrolling bearing is carried out,and the results obtained have verified the sensitivity of HaarSpectrum and Impulse Index to the fault.     

Improved preconditioned conjugate gradient method and its application in F. E. A. for engineering

In this paper two theorems with theoretical and practical significance are given in respect to the preconditioned conjugate gradient method(PCCG).The theorems discuss respectively the qualitative property of the iterative solution and the construction principle of the iterative matrix.The authors put forward a new incompletely LU factorizing technique for non-M-matrix and the method of constructing the iterative matrix.This improved PCCG is used to calculate the ill-conditioned problems and large-scale three-dimensional finite element problems,and simultaneously contrasted with other methods.The abnormal phenomenon is analyzed when PCCG is used to solve the system of ill-conditioned equations,It is shown that the method proposed in this paper is quite effective in solving the system of large-scale finite element equations and the system of ill-conditioned equations.     

Packing properties of binary mixtures in disordered sphere systems

Mixtures of binary spheres are numerically simulated using a relaxation algorithm to investigate the effects of volume fraction and size ratio, A complete profile of the packing properties of binary spheres is given. The density curve with respect to the volume fraction has a triangular shape with a peak at 70% large spheres. The density of the mixture increases with the size ratio, but the growth becomes slow in the case of a large size disparity, The volume fraction and size ratio effects are reflected in the height and movement, respectively, of specific peaks in the radial distribution functions. The structure of the mixture is further analyzed in terms of contact types, and the mean coordination number is demonstrated to be primarily affected by ＂large-small＂ contacts. A novel method for estimating the average relative excluded volume for binary spheres by weighting the percentages of contact types is proposed and extended to polydisperse packings of certain size distributions. The method can be applied to explain the density trends of polydisperse mixtures in disordered sphere systems,     

DAMAGE MODEL OF CONTROL FISSURE IN PERILOUS ROCK

Hitherto, perilous rock is the weakest topic in disasters studies. Specially, damage of control fissure under loads is one key technique in study of develop mechanism of perilous rock. Damage division of end area of control fissure was defined by authors, then calculation methods of timed-Poisson's ratio and timed-Young's modulus were established in damage mechanics theory. Further, the authors set up damage constitutive equation of control fissure, which founds important basis to numerical simulation for control fissure to develop.     

Manipulation of polymer foam structure based on CO2-induced changes in polymer fundamental properties

Foaming of polymers with CO2 has attracted increasing attention in polymer processing studies. Some of the fundamental properties of polymer/CO2 systems is discussed in this short review, including solubility and diffusivity of CO2 in the polymer, polymer crystallization, interfacial tension between the polymer and the gas, and rheology of the CO2/polymers melt. These properties understandably affect the foaming process, and the structures of the foam products. Meanwhile, these properties can be changed via manipulation of CO2 in polymer. The proposed idea is to manipulate the foaming process and the foam structure by CO2-induced changes in these properties. Two cases from the authors＇ laboratory are presented for elucidating how to use the changes to manipulate the foaming process.     

Comprehensive form of solution for Lamb＇s dynamic problem expressed by Green＇s functions＊

By the analysis for the vectors of a wave field in the cylindrical coordinate and Sommerfeld＇s identity as well as Green＇s functions of Stokes＇ solution pertaining the conventional elastic dynamic equation, the results of Green＇s function in an infinite space of an axisymmetric coordinate are shown in this paper. After employing a supplementary influence field and the boundary conditions in the free surface of a senti-space, the authors obtain the solutions of Green＇s function for Lamb＇s dynamic problem. Besides, the vertical displacement uzz and the radial displacement urz can match Lamb＇s previous results, and the solutions of the linear expansion source u~r and the linear torsional source uee are also given in the paper. The authors reveal that Green＇s function of Stokes＇ solution in the semi-space is a comprehensive form of solution expressing the dynamic Lamb＇s problem for various situations. It may benefit the investigation of deepening and development of Lamb＇s problems and solution for pertinent dynamic problems conveniently.     

ON THE CONVERGENCE PROBLEMS OF ISHIKAWA AND MANN ITERATIVE PROCESSES WITH ERROR FOR Φ-PSEUDO CONTRACTIVE TYPE MAPPINGS

The purpose of this paper is to introduce the concept of Φ-pseudo contractive type mapping and to study the convergence problem of Ishikawa and Mann iterative processes with error for this kind of mappings. The results presented in this paper improve and extend many authors’recent results.     

Applications of active acoustics in particle technology

Earlier work by the authors in which active sound pressure signals and impulsive pressure disturbances were used to measure flow rates in gas solid systems was briefly reviewed. Work in progress with an emerging technology in which Helmholtz resonance is applied to the measurement of volume is outlined.     

Analytical model of sound transmission through laminated composite cylindrical shells considering transverse shear deformation

Composite structures are often used in the aerospace industry due to the advantages offered by a high strength to weight ratio. Sound transmission through an infinite laminated composite cylindrical shell is studied in the context of the transmission of airborne sound into the aircraft interior. The shell is immersed in an external fluid medium and contains internal fluid. Airflow in the external fluid medium moves with a constant velocity. An exact solution is obtained by simultaneously solving the first-order shear deformation theory （FSDT） of a laminated composite shell and the acoustic wave equations. Transmission losses （TL） obtained from numerical solutions are compared with those of other authors. The effects of structural properties and flight conditions on TL are studied for a range of values, especially, the Mach number, stack sequences, and the angle of warp. Additionally, comparisons of the transmission losses are made between the classical thin shell theory （CST） and FSDT for laminated composite and isotropic cylindrical shells.     

Prediction of Quasi-Brittle Fracture of Concrete and Rock Structures Using Laboratory-Sized Specimens

A simple method is developed for predicting the fracture behaviour of struetures made of quasi-brittle materials sueh as eonerete and roek using the data from laboratory-sized speeimens. The method is based on the reeently-developed boundary effeet concept and associated asymptotic model. It is demonstrated that the ＂apparent＂ size dependence of fraeture behaviour of concrete and rock is in fact due to the influence of specimen boundaries. Various size effect phenomena that are often observed in fracture meehanies tests of eoncrete and roek are related to each other, and the asymptotie boundary effect model can explain all the observed ＂size＂ effeet phenomena. Four types of experimental results available in the literature （ineluding the data measured on （1） the speeimens of identical size with different crack-to-size （α） ratios, （2） specimens of different sizes with different a-ratios, （3） different types of specimens and （4） geometrieally similar speeimens） are used to verify the asymptotic boundary effect model, and it is found that the predictions of the model agree very well with the experimental results. Furthermore, the important fracture properties, fracture toughness KIC and strength f, of quasi-brittle materials sueh as eonerete and roek can also be calculated using the formulae provided in the model.     

PROGRESS IN THREE-DIMENSIONALLY ORDERED SELF-ASSEMBLY OF COLLOIDAL SiO2 PARTICLES

Three-dimensionally ordered self-assembly of monodispersed colloidal SiO2 particles involving a structure with periodic alternation of refractive indices represents an advanced field of particuology, colloidal chemistry, materials science, optical physics and information science. Study on such self-assembly not only lays the foundation for the development of advanced functional materials, but also is significant in understanding the principles of nano- and micro-scele processes. Recent progress in three-dimensionally ordered self-assembly of colloidal SiO2 particles is reviewedinclusive of the authors‘‘ investigations.     

THE THEOREM OF THE STABILITY OF NONLINEAR NONAUTONOMOUS SYSTEMS UNDER THE FREQUENTLY-ACTING PERTURBATION—LIAPUNOV’S INDIRECT METHOD

In this paper the stability of nonlinear nonautonomous systems under the frequently-acting perturbation is studied.This study is a forward development of the study of thestability in the Liapunov sense;furthermore,it is of significance in practice sinceperturbations are often not single in the time domain.Malk in proved a general theoremabout thesubject.To apply the theorem,however,the user has to construct a Liapunovfunction which satisfies specified conditions and it is difficult to find such a function fornonlinear nonautonomous systems.In the light of the principle of Liapunov’s indirectmethod,which is an effective method to decide the stability of nonlinear systems in theLiapunov sense,the authors have achieved several important conclusions expressed in theform of theorems to determine the stability of nonlinear nonautonomous systems under thefrequently-acting perturbation.     

EFFECT OF FABRICATION ON HIGH CYCLE FATIGUE PROPERTIES OF COPPER THIN FILMS

The influence of fabrication on the tensile and fatigue behavior of copper films manufactured by 3 kinds of fabrication methods was investigated. The tensile and high cycle fatigue tests were performed using the test machine developed by authors. Young＇s moduli （72, 71 and 69 GPa, respectively） are lower than the literature values （108-145 GPa）, while the yield strengths were as high as 358, 350 and 346 MPa, respectively and the ultimate strengths as 462, 456 and 446 MPa, respectively. There is not much difference in the tensile properties of the 3 kinds of films. There is little difference in the fatigue properties of the 3 kinds of films but one of them has shorter fatigue life than others in high cycle region and longer fatigue life than others in low cycle region.     

Numerical investigation on the flowfield of ＂swallowtail＂ cavity for supersonic mixing enhancement

A ＂swallowtail＂ cavity for the supersonic combustor was proposed to serve as an efficient flame holder for scramjets by enhancing the mass exchange between the cavity and the main flow. A numerical study on the ＂swallow- tail＂ cavity was conducted by solving the three-dimensional Reynolds-averaged Navier-Stokes equations implemented with a k-e turbulence model in a multi-block mesh. Turbu- lence model and numerical algorithms were validated first, and then test cases were calculated to investigate into the mechanism of cavity flows. Numerical results demonstrated that the certain mass in the supersonic main flow was sucked into the cavity and moved spirally toward the combustor walls. After that, the flow went out of the cavity at its lateral end, and finally was efficiently mixed with the main flow. The comparison between the ＂swallowtail＂ cavity and the conventional one showed that the mass exchanged between the cavity and the main flow was enhanced by the lateral flow that was induced due to the pressure gradient inside the cavity and was driven by the three-dimensional vortex ring generated from the ＂swallowtail＂ cavity structure.     

Mann and Ishikawa iterative approximation of solutions form-accretive operator equations

The purpose of this paper is to study the Mann and Ishikawa iterative approximation of solutions for m-accretive operator equations in Banach spaces. The results presented in this paper extend and improve some authors’ recent results.