2010 Vol. 31, No. 2

Display Method:
Classification of Parametric Constrained Bifurcation
WU Zhi-qiang, DING Ran, CHEN Yu-shu
2010, 31(2): 127-133. doi: 10.3879/j.issn.1000-0887.2010.02.001
Abstract(1312) PDF(1062)
If the constraint s boundary relates to the bifurcation parameter,a bifurcation is called parametric constrained one.Relying upon some substitution,parametric constrained bifurcation was trans formed to unconstrained bifurcation about new variables.Then general form of transition sets of the parametric constrained bifurcation was derived.The resultind icates thatonly constrained bifurcation set is influen ced by parametric constraints,other transition sets are the same as those of the nonparametric constrained bifurcation.Taking parametric constrained pitch fork bifurcation problems as examples,effects of param etric constraints on bifurcation classification were discussed further in detail.
Singularity Analysis of a Two-Dimensional Elastic Cable With 1: 1 Internal Resonance
QIN Zhao-hong, CHEN Yu-shu, LI Jun
2010, 31(2): 134-142. doi: 10.3879/j.issn.1000-0887.2010.02.002
Abstract(1267) PDF(1058)
Two-degree-of-freedom bifurcation equation s for elastic cable with 1: 1 internal resonance were investigated.The transition set of system was obtained by singularity theory for three cases.The whole parametric plane was divided into several different persistent regions by the tran sition set.The bifurcation diagrams in different persistent regions were obtained.
Perturbation Solution for Unsteady Flow in a Porous Channel With Expanding or Contracting Walls in the Presence of a Transverse Magnetic Field
SI Xin-hui, ZHENG Lian-cun, ZHANG Xin-xin, CHAO Ying
2010, 31(2): 143-149. doi: 10.3879/j.issn.1000-0887.2010.02.003
Abstract(1170) PDF(714)
An incom pressible flow in a porous channel with expanding or contacting walls in the presence of a transverse magnetic field was considered.Using similarity transform ations,the governing equations were reduced to nonlinear ordinary differential equations.The exact similarity solutions for values of parameters,expansion ratio and Hartm annn number were obtained by singular perturbation method,and the associated be haviorwas discussed in detail.
Effects of Slip,Viscous Dissipation and Joule Heating on the MHD Flow and Heat Transfer of a Second Grade Fluid Past a Radially Stretching Sheet
Bikash Sahoo
2010, 31(2): 150-162. doi: 10.3879/j.issn.1000-0887.2010.02.004
Abstract(1293) PDF(806)
The flow and heat transfer of an electrically conducting non-New tonian second grade fluiddue to an radially stretching surface with partial slip was considered.The partial slip was controlled by a dimensionless slip factor,which varied between zero(total adhesion) and infin-ity(full slip).Suitable similarity transform ations were used to reduce the resulting highly nonlinear partial differential equations into ordinary differential equations.The issue of paucity of boundary conditions was addressed and an effective numerical scheme was adopted to solve the obtained differential equations even without augmenting any extra boundary conditions.The important findings in this communication are the combined effects of the partial slip,magnetic interaction parameter and the second grade fluid parameter on the velocity and temperature fields.It is interesting to find that the slipincreases the momentum and thermal boundary layer thickness.As slip increases in magnitude,perm ittingmore fluid to slip past the sheet,the skin friction coefficient decreases in magnitude and approaches zero for higher values of the slip parameter,i.e.the fluid behaves as though it were inviscid.The presence of magnetic field has also substantial effects on velocity and temperature fields.
Study on Fusion Dynamics of Underwater Explosion Bubbles
ZHANG A-man, ZENG Ling-yu, WANG Shi-ping, YANG Shu-tao, YAO Xiong-liang, WEN Xue-you
2010, 31(2): 163-170. doi: 10.3879/j.issn.1000-0887.2010.02.005
Abstract(1159) PDF(949)
Fusion phenomenon of bubbles is comm on and significant in nature.Potential flow theory and boundary integral method were employed to simulate the fusion of underwater explosion bubbles.According to the numerical results and expermiental data from published works,three-dimensionalm odel of fusion bubble was established.Comparing the numerical results with experimen taldata,well coincidence was presented.Influences of characteristic parameters involved,such as distance,depth and so on,were especially investigated using the three-dmien sional program developed,and some favorable curves and conclusions were obtained.Some references were provided for the relevant research on fusion mechanics and dynamic characteristics of bubbles.
Dynamic Analysis of Redesigned Systems Using an Algebraic Method
WANG Wan-yi, LIAO Jen-yi, HOURNG Lih-wu
2010, 31(2): 171-179. doi: 10.3879/j.issn.1000-0887.2010.02.006
Abstract(1068) PDF(888)
Bymatrixm odification,the redesign of as tructural system was investigated.The inertia congruence trans formation was adopted to find the laten troots of a dynamic stiffness matrix,and a method for determining its eigenvalue was proposed.The characteristics of the laten tvector for a known latentroo,tand a method for computing it,were studied.The mode shapes of a redesigned structurem ust be handled differently based on whether the structure exhibits are persistentor non-persistent natural frequencies.
Axisymmetrical Analytical Solution for Vertical Vibration of End-Bearing Pile in Saturated Viscoelastic Soil Layer
YANG Xiao, PAN Yuan
2010, 31(2): 180-190. doi: 10.3879/j.issn.1000-0887.2010.02.007
Abstract(1298) PDF(1000)
Based on the elasticity and theory of saturated porous media,regarding the pile and the soil as a single phase elastic medium and a saturated viscoelastic medium,respectively,the dyn amical behavior of vertical vibration of an end-bearing pile in a saturated viscoelastic soil layer was investigated in frequency domain with the Hemlho ltzdecom position and variable separation method.The axisymm etrical analytical solutions for vertical vibrations of the pile in a saturated viscoelastic soil layer were obtained,and the an alytical expression of the dynam ical complex stiffness of the pile top was presented.The responses of dynamic stiffness factor and equ ivalent damping of pile top against the frequency are shown in figures by means of the numerical method,and the effects of the saturated soil parameters,modu lusration of the pile to soil,slenderness ratio of pile and piles.Poisson ratio,etc.on the stiffness factor and damping are examined.It is shown that,due to the effect of the transversal deformation of the pile and the action of radial force of the saturated viscoelastic soil to the pile,the dynamic stiffness factor and the damping derived from the axisymmetrical solution are greatly distinct from those derived from the classical Euler-Bernoullirod model,especially at some specific excitation frequencies.Therefore,there are some limitations for the applicability of the Euler-Bernoulli rod model for analys is of the vertical vibration of the pile,and themore accurate analysis should be based on the three dim ensionalmodel.
Multiaxial Fatigue Life Prediction of Kiln Roller Under the Axis Line Deflection
SHEN Yi-ping, WANG Song-lai, LI Xue-jun, B. S. Dhillon
2010, 31(2): 191-198. doi: 10.3879/j.issn.1000-0887.2010.02.008
Abstract(1166) PDF(793)
Multiaxial fatigue life of the roller in rolling contact with whee lswith respect to axis line deflection was investigated.The multiaxial fatigue criterion proposed by Wang and Brown,together with rainflow countingm ethod and the Miner-Pamlgren's rule,were applied for cumulative damage estmiation and life prediction.As axis line deflection of overlong kilns generally results in asymm etricload distribution on each roller,the load ratio was in troduced to describe deflection for quantitative stress anaylsis,which was performed with in the finite element code ANSYS.And the tangen tial frictional stress walch lated in terms of the rolling contact area condition.By taking on eroller as an example,the plotted fatigue life curve versus load ratio discovers how axis line deflection affects fatigue life.The study is quitesign ificant to prevent fatigue failure of the roller,and canprovide bas is to adjust and optimize axis line of rotary kiln.
Semi-Analytical Solution to One-Dimensional Consolidation in Unsaturated Soils
QIN Ai-fang, SUN De-an, TAN Yong-wei
2010, 31(2): 199-209. doi: 10.3879/j.issn.1000-0887.2010.02.009
Abstract(1295) PDF(1005)
Aseries of semi-analytical solutions to one-dmiensional consolidation in unsaturated soil were obtained.First,the air governing equation by Fredlund for unsaturated soil consolidation was simplified.Then,by applying the Laplace transform and Cayley-Hamilton theorem to the air and water governing equations of simplified,Darcy's law and Fick's law,the transfer function between the state vectors at top and at any depth was constructed.Finally,by in troducing the boundary conditions,the excess pore-water pressure and excess pore-air pressure and the soil settlement were obtained under several kinds of boundary condition sunder the large-area uniform in stantaneous loading.By adopting the Crumpmethod,the inversion of Laplace transform was performed,and the semi-analytical solutions to the excess pore-water and excess pore-air pressures and the soil settlement were obtained in the tmie domain.In the case of one surface which is permeable to air and water,comparison sbetween the semi-analytical solutions and the analytical solutions indicate that the semi-an alytical solutions are correct by a typical example.In the case of one surface which is permeable to air but imperm eable to water,comparisons between the semi-analytical solutions and the results of the finite difference method indicate that the semi-analytical solution is correct too,else the conso lidation characteristics are analysed.The research is useful to the studies on unsaturated soil consolidation.
Steady-State Growing Crack-Tip Field Characteristics of Mode Ⅲ Elastic-Viscoplastic/Rigid Interface Cracks
LIANG Wen-yan, WANG Zhen-qing, YANG Zeng-jie
2010, 31(2): 210-217. doi: 10.3879/j.issn.1000-0887.2010.02.010
Abstract(1299) PDF(855)
The singularity and viscosity in crack-tip were considered,and the elastic-viscoplastic governing equations of double dissimilar materials at interface crack-tip field were established.The displacement potential function and boundary condition of in terface crack-tip were introduced,and the numerical analysis of rigid-elastic viscoplastic in terface for mode was worked out.The stress-strain fields were obtained at the crack-tip and the variations of solutions were discussed according to each parameter.The numerical results show that the viscosity effect is am ain factor of in terface propagating crack-tip field,and the interface crack-tip is a viscop lastic field that is governed by viscosity coefficient,Mach number and singular factor.
Nonlinear Aeroelastic Coupled Trim and Stability Analysis of Rotor-Fuselage
HU Xin-yu, HAN Jing-long, YU Mei
2010, 31(2): 218-226. doi: 10.3879/j.issn.1000-0887.2010.02.011
Abstract(1413) PDF(900)
Based on the principle of Hamilton and the moderate deflection beam theory,discretizing the blade into a number of beame lements which had 15 degrees of freedom,using quasi-steady aero model,the nonlinear coupledrotor/fuselage equation was founded.The periodic solution of blades and fuselage were obtained through aeroe lastic coupledtrim using temporal finite element method.Peters.dynamic inflow modelwas adopted for vehicle stability.A calculation program was builtup,which offered the blade responses,hubloads and the rotor pitch controls.The correlation between analytical results and related literatures is good.The converged solution simultaneously satisfies the blade and the vehicle equilibrium equations.
Solutions to Semilinear p-Laplacian Dirichlet Problem Arising in Population Dynamics
R. A. Mashiyev, G. Alisoy, S. Ogras
2010, 31(2): 227-235. doi: 10.3879/j.issn.1000-0887.2010.02.012
Abstract(943) PDF(723)
The semilinear p-Laplacian Dirichlet problem arising in population dynamics was studied.The Morse critical groupsat zero of the energy function of the problem being trivial was obtained.As a consequence,existence and bifu rcation of nontrivial solutions to the problem were established.
Delay-Dependent Robust Stability and H Analysis of Stochastic Systems With Time-Varying Delay
SUN Ji-tao, WANG Qing-guo, GAO Han-qiao
2010, 31(2): 236-244. doi: 10.3879/j.issn.1000-0887.2010.02.013
Abstract(997) PDF(845)
Robust stochastic stability and Hanalys is for stochastic systems with time-varying delay and Markovian jumpwere investigated.A stochastic Liapunov-Krasovskii functional was introduced for stability analysis.By using the free-weighting matrices technique (i e.He.s technique),new delay-dependent criteria in terms of linear matrix inequality were derived for robust stochastic stability and the Hdistu rbance a ttenuation.Three numerical examples were given toshow that the proposed method wase fficient and muchless conserva tive than the existing results in the literature.
VU-Decomposition Method for a Second-Order Cone Programming Problem
LU Yuan, PANG Li-ping, XIA Zun-quan
2010, 31(2): 245-252. doi: 10.3879/j.issn.1000-0887.2010.02.014
Abstract(1645) PDF(830)
A VU-decomposition method for solving a second-order coneproblem was presented.First of all,this problem was trans formed into a nonlinear programming problem.Then the structure of Clarke subdifferen tial corresponding to penalty function and some results of its VU-decomposition were given.Under certain condition,a twice continuously differen tiable trajectory could be computed for yielding a second-order expansion of the objective functionf.A conceptual algorithm for solving this problem with a superlinear convergence rate was given.