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2004 Vol. 36, No. 5

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Research on waverider configuration method
In hypersonic flow, as the increase of Mach number, thewave drag and friction drag also enlarge, and this will form a hysonic $L/D$``barrier''. But waverider can efficiently overcome this ``barrier''. Inthis paper we develop a wedge-elliptical cone waverider configurationmethod, study on front body-scramjet engine integration design, and create ahypersonic waverider. In terms of numerical result and wind test data, it isdifferent from traditional waveriders that this waverider can offer not onlyhigh $L/D$ ratio, but also the uniform flow field with high temperature andhigh press which is requireed by scramjet engine.
2004, 36(5): 513-519. doi: 10.6052/0459-1879-2004-5-2003-208
A new topology description function based approach for structural topology optimization
In the present paper, a new approach for structural topologyoptimization based on implicit topology description functions (TDF) isproposed. TDF is used to describe the shape/topology of the structure, whichis approximated in terms of its nodal values. Then a relationship isestablished between the element stiffness and the values of the topologydescription function on its four nodes. In this way and with some non-localtreatments of the design sensitivities, not only the shape derivative butalso the topological derivative of the optimal design can be incorporated inthe numerical algorithm in a unified way. Numerical experiments demonstratethat by employing this approach, the computational efforts associated withTDF (level set) based algorithms can be saved. Clear optimal topologies andsmooth structural boundaries free from any sign of numerical instability canbe obtained simultaneously and efficiently.
2004, 36(5): 520-526. doi: 10.6052/0459-1879-2004-5-2003-436
An orthogonality relationship for thin plate theory and its variational principle
While Hamiltonian system was led to solution of elastictheory a new systematic methodology for theory of elasticity was establishedand a symplectic orthogonality relationship was presented (ZhongWanxie, 1995). For two-dimensional theory of elasticity a new dual vectorand a new dual differential matrix were presented by putting the old dualvector in a new order. It was discovered for isotropic materials that thesymplectic orthogonality relationship may be decomposed into 2 independentlyand symmetrically orthogonal sub-relationships (Luo Jianhui et al., 2002).The new orthogonality relationship includes the symplectic orthogonalityrelationship. The new orthogonal relationship was generalized intothree-dimensional elasticity problems in which a direction of coordinate isan orthogonal direction of materials (Luo Jianhui et al., 2003). Theresearch of a systematic methodology for bending theory of thin and thickplate has also been noticed. Some conclusion of the systematic methodologyfor bending theory of Reissner-Mindlin thick plate was obtained (Luo Jianhuiet al., 2004). Firstly, the Hamiltonian dual differential equations forthick plates were derived. Then, the functional expressions of Hamiltonianvariational principle were obtained by using the variable substitution andmultiplier method. At last, the new orthogonality relationship of thickplate theory was proposed. But the new orthogonality relationship of thickplate theory can not be degenerated into thin plate theory. Therefore it isnecessary to research the new orthogonality relationship of thin platetheory. Based on the analogy between plate bending problems and planeelasticity problems Hamiltonian system was applied to thin plate bendingproblems and its symplectic orthogonality relationship was presented (ZhongWanxie et al., 1999). For thin plate bending theory a new dual vector ispresented while the dual vectors based on the analogy are put in a neworder. A variational principle based on the new dual vector is proposed andalso demonstrated by a new method. The principal diagonal sub-matrixes ofthe dual differential matrix are zero matrixes. As a result of thepeculiarity of the dual differential matrix it is discovered that theorthogonality relationship of thin plate bending theory based on the analogymay be decomposed into 2 orthogonal sub-relationships. Based on the integralform (Luo Jianhui et al., 2002) of the systematic methodology forelasticity, the new orthogonal relationship is demonstrated. The neworthogonality relationship of theory of elasticity is generalized intoanisotropic thin plate bending theory. The theoretical achievements of theHamiltonian system for thin plates provide new effective tools for theresearch on analytical and finite element solutions of thin plates.
2004, 36(5): 527-532. doi: 10.6052/0459-1879-2004-5-2004-051
Unified reliability model for fuzziness and randomness of the basic variables and state variables in structure
Based on the randomness and fuzziness of the basicvariables and state variables, a unified reliability model is presented forthe fuzzy random structure. In the unified reliability model, a factor isintroduced to formulate the safe measure for the fuzzy random structure asthe same one for the random structure. After the membership function of thefuzzy variable is replaced by the equivalent probability density functionfrom the mathematical transition in the unified reliability model, theconventional reliability methods for random structure can be extended forthe fuzzy random structure directly. Due to the unchangeable possibilitydistribution of the fuzzy variable in the equivalent mathematic transition,the failure probability can be calculated precisely for the fuzzy randomstructure. And the unified reliability model for random fuzzy structure canbe extended to the structure with multiple variables from strength-stresstwo variables. Comparison in the illustrations shows that the presentedmethod is more suitable for engineering application than the existed methodsin the references.
2004, 36(5): 533-539. doi: 10.6052/0459-1879-2004-5-2004-012
Wave mode characteristics on piezo-electric stepped beam
In this paper, a systematic approach for the freevibration analysis and forced-response of the beam bonded with PZT patchesis presented employing the travelling wave method.The wave propagation characteristic of the stepped beam bonded with PZTpatches is studied based on distributed parameters theories. Neglecting theeffect of transverse shear and rotary inertia, harmonic wave solutions arefound for both flexible and axial vibration of beam models. Then, the systemis simplified into a node model considering multiple point discontinuitiesdue to attached masses, and actuated moment of PZT patches. And wavescattering matrices including wave reflection and transmission matrices innodes are formulated by applying the compatibility of displacements andequilibrium of forces at the junctions. Based on the above work, the conceptof the wave loop, which is the process when the vibration wave comes througha periods along the wave propagation paths, is introduced, and wave loopsand transmission matrices are derived accounting for general boundaryconditions. Therefore, the wave loops matrices combined with the aid offield transfer matrices provides a concise and efficient method to solve thefree vibration problem of beam bonded with PZT patches. The frequencies andresponse solutions are exact since the effects of attenuating wavecomponents are included in the formulation. Furthermore, the generalrelations between the flexural wave transmission factor and the position ofthe PZT actuator in structures is discussed too. The numerical results givetwo major conclusions: 1) the PZT patch bonded position near by thefixed-end in beam has the powerful actuated capability, because theattenuating wave components created by the active wave incident upon thediscontinuities boundary enhance the transmission effectiveness of theactive traveling wave propagation; 2) the modulus of the mode transmissionfactor has a close relation with the sensitivity of the nature frequencies.The bigger modulus of the mode transmission factor, the bigger sensitivitiesfactor of the nature frequencies is.In addition, a comparison of eigenvalues and frequency response functionobtained by finite element method (FEM) and the wave method respectively isalso presented. It is indicated that the result by the wave method is moreexact than one by FEM.
2004, 36(5): 540-548. doi: 10.6052/0459-1879-2004-5-2003-204
Scattering of flexural waves in mindlin's plates of soft ferromagnetic materials with a cutout
The problem of elastic waveguide and dynamic stressconcentrations in plates with a cutout is the important subject in solidmechanics. The cutout in structures has influence directly on the loadingcapacity and the lifetime of structures, therefore, some researchers havedevoted to theoretical analysis and experimental research in the world.Considered dynamic stress concentration or intensity factors, the classicaltheory of thin plate has disadvantage. Thick plate theory proposed byMindlin made up for the shortage classical theory of thin plate includingthe effect of transverse shear deformation and rotator inertia. Thesatisfying result is gained in engineering. In the 1960's, with wavefunction expansion method, Pao Yih-Hsing first studied the problem of theflexural wave scattering and dynamic stress concentrations in Mindlin'sthick plates with circular cavity and gave an analytical solution andnumerical results.With the development of modern science and technology, the ferromagneticmaterials have been applied to superconduct nuclear power station andmagnetic levitation trains. It has better physical and mechanical property.The stress on the contour of a cavity or crack in ferromagnetic materialsmay be increase in a uniform magnetic field. It has a influence on thecarrying capacity and the lifetime of structures. According to the manyreferences, the dynamical behavior of ferromagnetic elastic structures canbe significantly affected by the presence of a uniform magneticfield.Based on the theory of magneto-elastic interaction, Japaneseresearchers analyzed scattering of flexural wave and the dynamic bendingmoment intensity factors in cracked Mindlin plates of ferromagneticmaterials and gave numerical results. They used Fourier transforms to reducethe mixed boundary value problem to a Fredholm integral equation that can besolved numerically.In this paper, based on the equation of wave motion in Mindlin's plate ofmagneto-elastic interaction, using wave function expansion method, thescattering of flexural wave and dynamic stress concentrations in a plate offerromagnetic materials with a cutout are investigated. According toanalysis and numerical results, the magnetic induction intensity has greatinfluence on the dynamic stress concentration factors at low frequency.
2004, 36(5): 549-556. doi: 10.6052/0459-1879-2004-5-2003-531
Frequency response of a cylindrical cavity in poro-viscoelastic saturated medium
This paper discusses the frequency response of a poroviscoelasticsaturated medium to axially symmetric harmonious surface traction and fluidpressure over the boundary of a cavity in the form of a circular liningcavity of infinite length. A constitutive model presented by Carcione isintroduced to describe the creep and relaxation behavior of medium. Thecavity is taken as partially sealed with partial permeable boundaryconsidering the relative permeability of the liner and the medium. Theanalytical solutions of stresses, displacement and pore pressure amplitudeare derived in frequency domain by introducing two scalar potentialfunctions. A parametric study is made based on the solutions to illustratethe influence of the minimum quality factor concerning the creep andrelaxation behavior of porous medium, the permeability parameter concerningthe partial permeable behavior of boundary, and relative rigidity of linerand medium on the frequency response of the cavity. It is indicated thatthere are strong correlations among these parameters and the attenuation ofradial displacement, stress, and pore pressure amplitude.
2004, 36(5): 557-563. doi: 10.6052/0459-1879-2004-5-2003-386
One local bifurcation of nonlinear system based on magnetorheological damper
Magnetorheological (MR) fluids is a kind of smartmaterials, it can be transformed from Newton fluids into visco-plastic solidby varying the strength of the magnetic field. The dampers made by MR fluidshave a number of attractive features, for example, inexpensive tomanufacture, small power requirements, reliability, stability, and cancontinually change its state. The process of change is very quick, less thana few milliseconeds, and can be easily controlled. MR dampers have beenrecognized as having many attractive characteristics for use in vibrationcontrol applications, it is a kind of ideal semi-active control devices. MRdamper is widely used in the civil engineering, vehicle suspension systemand its structural characteristics have been extensively studied. But, up tonow, the dynamic behaviors about MR damper semi-active control system,specially, its bifurcation behaviors and global dynamics have not beendiscussed.The problem of bifurcation behavior for the MR damper nonlinear system isdiscussed. A dynamic model of the system with nonlinear MR damper force ispresented. The system's normal form and universal unfolding of the doublezero eigenvalue are achieved. The complex dynamic behavior of the nonlinearsystem will be shown by the analysis. By theoretical analysis, it is shownthat the design of parameters has a close relation with the system'sstability; the range of selected parameters are achieved when the system isstable, based on the condition of bifurcation parameters, bifurcation curve,bifurcation set and phase portraits. From numerical simulating analysis, thecomplex dynamics behavior is shown, and the result is in correspondence withthe theoretic analysis.
2004, 36(5): 564-568. doi: 10.6052/0459-1879-2004-5-2003-417
Investigation of the dynamic stall about the pitching airfoil
The static stall about the airfoil at the high angle ofattack deteriorate the characteristics of aerodynamics rapidly. But thisphenomena can be delayed effectively by the dynamic stall caused by theunsteady motion. The dual-step Roe schema developed by Rogers wasused to solve the incompressible Navier-Stokes equations. Computationallysimulated the dynamic stall about the pitching NACA0015 airfoil withidentical pitching rate ($\alpha =0^{\circ} \sim 60^{\circ})$, at Low Reynoldsnumber ($Re=4.8 \times 10^{4}$). And compared with Walker's experimentalresults to correct the CFD results. The developments of the mainvortex, the second vortex and the third vortex, and the lift coefficientalteration to the angle of attack during the process were studied. Finally,the effects of the different pitching rate to the dynamic stall werecompared.
2004, 36(5): 569-576. doi: 10.6052/0459-1879-2004-5-2004-203
Experimental investigations of lateral jet interactions in supersonic flows
Experimental investigation of the lateral jet interaction have beenperformed in supersonic flows to study the effects of jet pressures, angleof attacks, leeward side jet or windward side jet on the jet interactioncharacteristics. The results indicated that with increasing of jetpressures, the high pressure region before lateral jet extended forward, andthe wraparound effect strengthened. In the case of angle of attacks, thehigh pressure region before the leeward side jet enlarged, the region of jetwraparound effect moving forward, and the jet interaction control was moreeffective.
2004, 36(5): 577-582. doi: 10.6052/0459-1879-2004-5-2004-003
Numerical simulation for the flow front of viscous incompressible fluid
In the past decade, Wang's control volume approach hasbeen the dominated method to simulate the advancing front of melt ininjection molding. It demands one and only one control volume be filledwithin one time step no matter how fine or rough the mesh is. The time stepdecision deduced from geometry is lack of theory support and difficult totest its stability. This limitation results in the loss of simulatedprecision for rough mesh and tedious calculation for fine mesh. This workpresents a new method to simulate the advancing front of viscousincompressible fluid in injection molding. The governing equations are interms of generalized Hele-Shaw flow for the viscous, incompressible,non-Newtonian fluid under non-isothermal conditions. The moving fluiddescription is transformed into a transport equation about fill factor inthe whole domain to be filled. The fill factor at each time step isdetermined by Taylor expansion, while the derivatives in the expansion iscalculated with the recursive formula derived by Galerkin method. Differentfrom Wang's approach, the time step in this present method is determined by thepre-error and high order derivative of fill factor which involving velocityfield and the previous conditions of neighboring control volumes. This workproves that the method is stable if the time step is carefully chosen. Basedon this theory, a program was developed to simulate the advancing meltfronts in injection molding. For verification of the numerical resultsobtained from the developed program, the simulation results are comparedwith the experimental results obtained from the test mold set designed byHan in the current study using the same commercial-grade PP and processconditions. Comparisons are also carried out between this present method and thetraditional method. Compared with Wang's approach, this present method canimprove the simulated precision for rough mesh and reduce the calculationfor fine mesh.
2004, 36(5): 583-588. doi: 10.6052/0459-1879-2004-5-2001-417
A Study on the Water Flow in Baiyangdian Lake
A study on the influence of wind stress on the flowcharacter of water in Baiyangdian Lake is carried out, and we arrive at someimportant conclusions. These are: (1) wind stress can be regarded as themain driving force of the water circulation flow; (2) the water flowdirection of surface layer is the same direction as the wind moves, whiledirection of the layers below is on the contrary or is almost inversed; (3)the flow character of water beneath the surface layer is complex. Doubleeddies can be seen evidently on the second horizontal layer; (4) thetopography influences the vertical flow heavily, double eddies can also beseen in the complex vertical direction. The dynamic character of water inBaiyangdian Lake is studied in this paper, which laid a solid foundation forthe further researches on biology.
2004, 36(5): 589-595. doi: 10.6052/0459-1879-2004-5-2004-084
An analytical method for the plane problem of doubly periodic circular cross-section fiber composite materials
Combining the theory of doubly periodic and doublyquasi-periodic Riemann boundary value problems and Eshelby's equivalentinclusion method, an analytical method for the plane problem of compositematerials with a doubly periodic array of circular cross-section fibers ispresented. The stresses expressions in series are obtained in the fibers andmatrix and a comparison with the finite element calculations is done. Thetransverse tensile and shear moduli are predicted for a unidirectionalfiber-reinforced composite with an doubly periodic array of circular fibers.It is found that for a composite with hard fibers and a soft matrix under asame fiber volume fraction, the effective moduli for a square array offibers are larger than those for a hexagonal array of fibers. The presentmethod provides an efficient tool for analyzing the mechanical properties ofinhomogeneous materials and designing microstructures of compositematerials, and can also be used to evaluate the precision of other numericaland approximate methods such as the finite element method.
2004, 36(5): 596-603. doi: 10.6052/0459-1879-2004-5-2003-424
A numerical method for analyzing multiple void-crack interaction in a plane elastic media
This paper presents an approach to modeling a generalsystem containing multiple interacting cracks and voids in a plane elasticmedia. By extending Bueckner's principle suited for a crack to a generalsystem containing multiple interacting cracks and voids, the originalproblem is divided into a homogeneous problem (the one without cracks andvoids) subjected to remote loads and a multiple void-crack problem in anunloaded body with applied tractions on the surfaces of cracks and voids.Thus, the results in terms of stress intensity factors (SIFs) can beobtained by considering the latter problem, which is analyzed easily bymeans of the Hybrid Displacement Discontinuity Method (HDDM) proposedrecently by the author. Many test examples are included to illustrate thatthe method is very simple and effective for analyzing arbitrarymultiple cracks and voids in a plane elastic media.
2004, 36(5): 604-610. doi: 10.6052/0459-1879-2004-5-2004-061
An iterative combined approximation approach for structural static reanalysis of topological modifications
This paper presents an iterative combined approximation(ICA) approach for structural static reanalysis of all types of topologicalmodifications. The proposed procedure is basically an approximate two-stepmethod. First, the newly added degrees of freedom (DOFs) are assumed to belinked to the original DOFs of the modified structure by means of the Guyanreduction so as to obtain the condensed equation. Second, the displacementsof the original DOFs of the modified structure are solved using the ICAapproach. And the displacements of the newly added DOFs resulting fromtopological modification can be recovered. In order to illustrate theapplication of the present method, the layout optimal design of stiffenersin the plate-shell structure is given. In the layout optimization, thestrain energy sensitivity of the element and the rejection ratio areintroduced. In each iteration, a number of elements may be deleted. To savecomputational effort, the ICA is used to perform the reanalysis to updatethe modified displacements of the structure. The results show that the ICAmethod is effective for structural static reanalysis of the topologicalmodifications even though the large topological modifications are made, andit is easy to implement on a computer.
2004, 36(5): 611-616. doi: 10.6052/0459-1879-2004-5-2003-194
The numerical analysis formulation of the viscoelastic solid modeled by fractional operator
The numerical method of mechanical problems for the viscoelastic solids withRiemann-Liouville fractional derivative model is presented in this paper.Instead of using finite Grunwald definition of fractional derivative toapproximate the Riemann-Liouville's, this work has developed a numericalalgorithm directly from Riemann-Liouville's definition by taking advantagesof the features of its integrand kernel, assuming the approximating functionfor the integrand and making use of Newmark-type numerical methods. Thenumerical formulations are used to analyze the transient dynamic responsefor a viscoelastic oscillator and the finite element analysis procedures.The sample results show that the proposed method possesses the advantages offast convergence, higher accuracy, higher stability and easy for applicationand further modification.
2004, 36(5): 617-622. doi: 10.6052/0459-1879-2004-5-2003-355
Natural neighbour method based on the algorithm of local search
The natural neighbour method (or natural element method),which is based on the natural neighbour interpolation, is a method betweenmeshless and mesh. The discrete model of the domain ${\it\Omega} $ in naturalneighbourmethod(NNM) consists of a set of distinct nodes, and a polygonal descriptionof the boundary. The whole displacement interpolations are constructed withrespect to the nature neighbour nodes and Voronoi tessellation of the givedpoint. The natural neighbours of the gived point have been definitelydefined. The properties of the natural neigbour interpolation are excellent.For instance, the conditions of linear consistency, partition of unitity,positivity, and delta properties are all satisfied in natural neigbourinterpolation. The disadvantages in element-free Galerkin method(EFG), suchas, the difficulties of imposition of essential boundary and treatment ofmaterial discontinuity, the complex algorithm of matrix inverse in thecomputation of Moving Least Squares(MLS) shape function, the uncertainchoice of the weight functions can be avoided in NNM. But, NNM is usuallyregarded as a mesh-based method beacause the delaunay triangulations fromthe whole solution domain are still needed for neighbour-search. In stead ofsearching for the natural neighbors from delauny triangulation of the wholedomain, an algorithm quantifies the natural neighbour nodes of the givenpoint based on the locally delaunay triangles is proposed for theimprovement of the NNM. Similar to the EFG method, the procedure ofinterpolation and construction in the improved NNM is meshless. As a result,the improved NNM can possesses both the excellent properties of the naturalneigbour interpolation and advantages of the EFG method. Numerical resultsshow that the excellent agreement with exact solution is obtained in thismethod. Convergence studies in the numerical examples also show that thepresent method possesses an excellent rate of convergence for both thedisplacement and strain energy.
2004, 36(5): 623-628. doi: 10.6052/0459-1879-2004-5-2003-517
Nonexistence of ultra-subharmonic periodic solutions for a class of nonautonomous dynamic system
In the study of the nonlinear dynamics, Melnikov functionis widely used as a criterion to check whether subharmonic orultra-subharmonic bifurcation even chaos will occur in a perturbed Hamiltonsystem. However, for the most cases, the classical Melnikov method canmerely show the existence of subharmonic periodic orbits. Such a result isattributed to that only first order approximation is adopted in theclassical Melnikov method. So higher-order Melnikov method is developed todetermine the existence of the ultra-subharmonic periodic solution. In thispaper, a class of non-autonomous differential dynamic system is studied. Itis proved that if there exists a periodic solution in such a system, thesolution can only be subharmonic, and the existence of ultra-subharmonicperiodic solution is impossible. Moreover, the nonexistence of R-typeultra-subharmonic periodic solution defined for a specified planar system isalso confirmed. As an application of above conclusions, some typicalexamples are investigated. The results demonstrate that second-orderMelnikov method used to justify the existence of ultra-subharmonic periodicorbits in a planar perturbation system may lead to a wrong conclusion. Asimple geometric explanation is also provided.
2004, 36(5): 629-633. doi: 10.6052/0459-1879-2004-5-2003-523
The bifurcation analysis of the ems maglev vehicle-coupled-guideway system
The stable range of the guideway natural vibrationfrequencies is studied by analyzing the Hopf bifurcation of thevehicle-coupled-guideway maglev system. The maglev system is controlled bythe cascade controller and the connection of the controller's parameters andthe frequencies is given. Based on the stable controller, the Hopfbifurcation point corresponding changeless system parameters and variableguideway natural frequencies is calculated by the numerical arithmetic. Thestable range of the guideway natural frequencies is obtained using bothnumerical arithmetic and simulation method. The qualitative restrictionbetween the system mass, controller frequencies, stiffness of the secondsubsystem and the guideway natural frequencies is explained.
2004, 36(5): 634-640. doi: 10.6052/0459-1879-2004-5-2003-357