Applied Mathematics and Mechanics (English Edition)

Classification of parametrically constrained bifurcations

吴志强丁然陈予恕

2010, 31(2): 135-142. doi:10.1007/s10483-010-0201-z

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If the constraint boundary relates to a bifurcation parameter, a bifurcation is said to be parametrically constrained. Relying upon some substitution, a parametrically constrained bifurcation is transformed to an unconstrained bifurcation about new variables. A general form of transition sets of the parametrically constrained bifurcation is derived. The result indicates that only the constrained bifurcation set is influenced by parametric constraints, while other transition sets are the same as those of the corresponding nonparametrically constrained bifurcation. Taking parametrically constrained pitchfork bifurcation problems as examples, effects of parametric constraints on bifurcation classification are discussed.

Singularity analysis of a two-dimensional elastic cable with 1:1 internal resonance

秦朝红陈予恕李军

2010, 31(2): 143-150. doi:10.1007/s10483-010-0202-z

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A two-degree-of-freedom bifurcation system for an elastic cable with 1:1 internal resonance is investigated in this paper. The transition set of the system is obtained with the singularity theory for three cases. The whole parametric plane is divided into several different persistent regions by the transition set. The bifurcation diagrams in different persistent regions are obtained.

Perturbation solution to unsteady flow in a porous channel with expanding or contracting walls in the presence of a transverse magnetic field

司新辉郑连存张欣欣晁莹

2010, 31(2): 151-158. doi:10.1007/s10483-010-0203-z

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An incompressible flow in a porous channel with expanding or contacting walls in the presence of a transverse magnetic field is considered. Using similarity transformations, the governing equations are reduced to the nonlinear ordinary differential equations. The exact similar solutions for the different cases of the expansion ratio and the Hartmann number are obtained with a singular perturbation method, and the associated behavior is 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): 159-173. doi:10.1007/s10483-010-0204-7

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The flow and heat transfer of an electrically conducting non-Newtonian second grade fluid due to a radially stretching surface with partial slip is considered. The partial slip is controlled by a dimensionless slip factor, which varies between zero (total adhesion) and infinity (full slip). Suitable similarity transformations are used to reduce the resulting highly nonlinear partial differential equations into ordinary differential equations. The issue of paucity of boundary conditions is addressed and an effective numerical scheme is 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 slip increases the momentum and thermal boundary layer thickness. As the slip increases in magnitude, permitting more 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 a magnetic field has also substantial effects on velocity and temperature fields.

Fusion dynamics of underwater explosion bubbles

张阿漫曾令玉王诗平杨树涛姚熊亮闻雪友

2010, 31(2): 175-182. doi:10.1007/s10483-010-0205-z

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Fusion of bubbles is a common and significant phenomenon in the nature. In this work, the potential flow theory and the boundary integral method are employed to simulate the fusion of underwater explosion bubbles. Based on the numerical and experimental results in the literature, a three-dimensional model of bubble fusion is established. A good agreement is shown between the numerical results and experimental data. Influences
of characteristic parameters such as distance and depth are specifically investigated by using the developed three-dimensional program, resulting in favorable curves and conclusions. This work provides references for the relevant research on fusion mechanics and dynamic characteristics of bubbles.

Dynamic analysis of redesigned systems using algebraic method

王萬益廖建義洪勵吾

2010, 31(2): 183-192. doi:10.1007/s10483-010-0206-x

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This study investigates the redesign of a structural system with the matrix modification. The inertia congruence transformation is adopted to find the latent roots of a dynamic stiffness matrix, and a method for determining its eigenvalue is proposed. The characteristics of the latent vector for a known latent root and a method for computing it are studied. The mode shapes of the redesigned structure must be differently handled based on whether the structure exhibits persistent or non-persistent natural frequencies.

Axisymmetrical analytical solution for vertical vibration of end-bearing pile in saturated viscoelastic soil layer

杨骁潘元

2010, 31(2): 193-204. doi:10.1007/s10483-010-0207-7

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Based on elasticity and the theory of saturated porous media, and regarding the pile and the soil as a single phase elastic and a saturated viscoelastic media, respectively, the dynamical behavior of vertical vibration of an end-bearing pile in a saturated viscoelastic soil layer is investigated in the frequency domain using the Helmholtz decomposition and variable separation method. The axisymmetrical analytical solutions for vertical vibrations of the pile in a saturated viscoelastic soil layer are obtained, and the analytical expression of the dynamical complex stiffness of the pile top is presented. Responses of dynamic stiffness factor and equivalent damping of pile top with respect to the frequency are shown in figures using a numerical method. Effects of the saturated soil parameters, modulus ratio of the pile to soil, slenderness ratio of pile and pile’s 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 radial force of the saturated viscoelastic soil acting on the pile, the dynamic stiffness factor and the damping derived from the axisymmetrical solution are greatly different from those derived from the classical Euler-Bernoulli rod model, especially at some specific excitation frequencies. Therefore, there are limitations on applicability of the Euler-Bernoulli rod model in analyzing vertical vibration of the pile. More accurate analysis should be based on a three-dimensional model.

Multiaxial fatigue life prediction of kiln roller under axis line deflection

沈意平王送来李学军 B.S.DHILLON

2010, 31(2): 205-214. doi:10.1007/s10483-010-0208-x

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This paper investigates the multiaxial fatigue life of the roller in rolling contact with wheels with respect to axis line deflection. The multiaxial fatigue criteria proposed by Wang and Brown, together with the rainflow counting method and Miner-Palmgren’s rule, are applied to the cumulative damage estimation and life prediction. As the axis line deflection of overlong kilns generally results in asymmetric load distribution on each roller, the load ratio is introduced to describe the deflection for quantitative stress analyses. The stress analyses are performed within the finite element code ANSYS. The tangential friction stress is calculated in terms of the condition of the rolling contact area. By taking one roller as an example, the plotted fatigue life versus load ratio curve discovers how the axis line deflection affects the fatigue life. This study is significant to prevent the fatigue failure of the roller and can provide basis to adjust and optimize the axis line of the rotary kiln.

Semi-analytical solution to one-dimensional consolidation in unsaturated soils

秦爱芳孙德安谈永卫

2010, 31(2): 215-226. doi:10.1007/s10483-010-0209-9

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In this paper, a series of semi-analytical solutions to one-dimensional consolidation in unsaturated soils are obtained. The air governing equation by Fredlund for unsaturated soils consolidation is simplified. By applying the Laplace transform and the Cayley-Hamilton theorem to the simplified governing equations of water and air, Darcy’s law, and Fick’s law, the transfer function between the state vectors at top and at any depth is then constructed. Finally, by the boundary conditions, the excess pore-water pressure, the excess pore-air pressure, and the soil settlement are obtained under several kinds of boundary conditions with the large-area uniform instantaneous loading. By the Crump method, the inverse Laplace transform is performed, and the semi-analytical solutions to the excess pore-water pressure, the excess pore-air pressure, and the soils settlement are obtained in the time domain. In the case of one surface which is permeable to air and water, comparisons between the semi-analytical solutions and the analytical solutions indicate that the semi-analytical solutions are correct. In the case of one surface which is permeable to air but impermeable to water, comparisons between the semi-analytical solutions and the results of the finite difference method are made, indicating that the semi-analytical solution is also correct.

Steady-state growing crack-tip field characteristics of mode III elastic-viscoplastic/rigid interface cracks

梁文彦王振清杨增杰

2010, 31(2): 227-235. doi:10.1007/s10483-010-0210-9

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The existence of viscosity effect at the interface of double dissimilar materials has an important impact on the distribution of the interface crack-tip field and the properties variety of the interface itself. The singularity and viscosity are considered in the crack-tip. The elastic-viscoplastic governing equations of double dissimilar materials at the interface crack-tip field are established. The displacement potential function and boundary condition of interface crack-tip are introduced. The numerical analysis of elastic-viscoplastic/rigid interface for mode III is worked out. The stress-strain fields are obtained at the crack-tip and the variation rules of solutions are discussed according to each parameter. The numerical results show that the viscosity effect is a main factor of the interface propagating in the crack-tip field, and the interface crack-tip is a viscoplastic field governed by the viscosity coefficient, Mach number (Ma), and singularity exponent.

Nonlinear aeroelastic coupled trim and stability analysis of rotor-fuselage

胡新宇韩景龙喻梅

2010, 31(2): 237-246. doi:10.1007/s10483-010-0211-9

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Based on the Hamilton principle and the moderate deflection beam theory, discretizing the helicopter blade into a number of beam elements with 15 degrees of freedom, and using a quasi-steady aero-model, a nonlinear coupled rotor/fuselage equation is established. A periodic solution of blades and fuselage is obtained through aeroelastic coupled trim using the temporal finite element method (TEM). The Peters dynamic inflow model is used for vehicle stability. A program for computation is developed, which produces the blade responses, hub loads, and rotor pitch controls. The correlation between the analytical results and related literature is good. The converged solution simultaneously satisfies the blade and the vehicle equilibrium equations.

Solutions to semilinear p-Laplacian Dirichlet problem in population dynamics

R.A.MASHIYEV G.ALISOY S.OGRAS

2010, 31(2): 247-254. doi:10.1007/s10483-010-0212-6

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In this article, we study a semilinear p-Laplacian Dirichlet problem arising in population dynamics. We obtain the Morse critical groups at zero. The results show that the energy functional of the problem is trivial. As a consequence, the existence and bifurcation of the nontrivial solutions to the problem are established.

Delay-dependent robust stability and H∞ analysis of stochastic systems with time-varying delay

孙继涛王庆国高含俏

2010, 31(2): 255-262. doi:10.1007/s10483-010-0213-6

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This paper investigates the robust stochastic stability and H∞ analysis for stochastic systems with time-varying delay and Markovian jump. By using the freeweighting matrix technique, i.e., He’s technique, and a stochastic Lyapunov-Krasovskii functional, new delay-dependent criteria in terms of linear matrix inequalities are derived for the the robust stochastic stability and the H∞ disturbance attenuation. Three numerical examples are given. The results show that the proposed method is efficient and much less conservative than the existing results in the literature.

A VU-decomposition method for a second-order cone programming problem

陆媛庞丽萍夏尊铨

2010, 31(2): 263-270. doi:10.1007/s10483-010-0214-6

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A VU-decomposition method for solving a second-order cone problem is presented in this paper. It is first transformed into a nonlinear programming problem. Then, the structure of the Clarke subdifferential corresponding to the penalty function and some results of its VU-decomposition are given. Under a certain condition, a twice continuously differentiable trajectory is computed to produce a second-order expansion of the objective function. A conceptual algorithm for solving this problem with a superlinear convergence rate is given.

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