应用数学和力学

2011 Vol. 32, No. 4

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Modelling of Three-Dimensional Dynamic Stall

Lü Chao, WANG Tong-guang

2011, 32(4): 375-382. doi: 10.3879/j.issn.1000-0887.2011.04.001

Abstract(1798) PDF(852)

Abstract:
The dynamic stall process in three-dimensional (3D) case on a rectangular wing undergoing a constant rate ramp-up motion was introduced to provide qualitative analysis about the onset and development of the phenomenon of the stall.Subsequently,on the base of having enhanced the understanding of the mechanism of the dynamic stall,a 3D dynamic stall model was constructed with the emphasis of the onset,growth and the convection of dynamic stall vortex on the 3D wing surface.The results show that this engineering dynamic stall model can simulate the 3D unsteady aerodynamic performance appropriately.

Approximate Solutions to the MHD Falkner-Skan Flow Over a Permeable Wall

SU Xiao-hong, ZHENG Lian-cun

2011, 32(4): 383-390. doi: 10.3879/j.issn.1000-0887.2011.04.002

Abstract(1756) PDF(946)

Abstract:
The magnetohy drodynamic (MHD) Falkner-Skan boundary layer flow over a permeable wall in the presence of a transverse magnetic field was examined.The approximate solutions and skin friction coefficients of the MHD boundary layer flow were obtained by using DTM-Padéwhich couples the differential transform method (DTM) with the Padéapproximation.The approximate solutions were expressed in the form of a power series that can be easily computed by employing an iterative procedure.The results of the approximate solution were tabulated,plotted for the values of different parameters and compared with the numerical ones obtained by employing the shooting technique.It is found that results of the approximate solution agree very well with those of numerical solution,which verifies the reliability and validity of the present work.Moreover,the effects of various physical parameters on the boundary layer flow were presented graphically and discussed.

MHD Stagnation-Point Flow and Heat Transfer Towards a Stretching Sheet With Induced Magnetic Field

F. M. Ali, R. Nazar, N. M. Arifin, I. Pop

2011, 32(4): 391-399. doi: 10.3879/j.issn.1000-0887.2011.04.003

Abstract(1688) PDF(878)

Abstract:
The problem of steady magnetohydrodynamic (MHD) stagnation point flow of an incompressi-ble viscous fluid over a stretching sheet was studied.The effect of induced magnetic field was taken into account.The nonlinear partial differential equations were transformed into ordinary differential equations via the similarity transformation.The transformed boundary layer equations were solved numerically using the shooting method.Numerical results are obtained for various magnetic parameter β and Prandtl number Pr.The effects of induced magnetic field on the skin friction coefficient,local Nusselt number,velocity and temperature profiles for both a/c＞1 and a/c＜1,where a and c are positive constants,are presented graphically and discussed in detail.

Modelling Two Different Therapy Strategies for Drug T-20 on HIV-1 Patients

SONG Bao-jun, LOU Jie, WEN Qing-zhi

2011, 32(4): 400-416. doi: 10.3879/j.issn.1000-0887.2011.04.004

Abstract(1639) PDF(833)

Abstract:
A mathematical model that describes the antiretroviral therapy of the fusion inhibitor enfuvirtide on HIV-1 patients and the effect of enfuvirtide (formerly T-20) using impulsive differential equations were developed,taking into account two different drug elimination kinetics:first order and Michaelis-Menten.The model was a non-autonomous system of differential equations.For the time-dependent system,the disease-free equilibrium and its stability when therapy was taken with perfect adherence were focused on.Analytical thresholds for dosage and dosing intervals were determined to ensure that the disease-free equilibrium remains stable.The effects of supervised treatment interruption were also explored.It is shown that supervised treatment interruption may be worse than no therapy at all,thus strongly supporting no interruption strategies.

Simulation of Tumor Microvasculature and Microenvironment Response to Anti-Angiogenic Treatment by Angiostatin and Endostatin

WU Jie, DING Zu-rong, CAI Yan, XU Shi-xiong, ZHAO Gai-ping, LONG Quan

2011, 32(4): 417-427. doi: 10.3879/j.issn.1000-0887.2011.04.005

Abstract(1425) PDF(862)

Abstract:
The effects of anti-angiogenesis treatment by angiostain and endostatin on normalization of tumor microvasculature and microenvironment was investigated,based on mathematical modeling and numerical simulation of tumor anti-angiogenesis and tumor haemodynamics.The results show that,after antiangiogenesis treatment:1) the proliferation,growth and branching of neo-vessels is effectively inhibited,the extent of vascularization in tumors is accordingly reduced;2) the overall blood perfusion inside tumor is declined;the plateau of tumor interstitial fluid pressure is relieved;the interstitial fluid oozing out from the tumor periphery into the surrounding normal tissue is reduced;the intravasations across vasculature is remarkably decreased.

Analytical Solutions for the Transverse Distributions of Stream-Wise Velocity in Turbulent Flow in Rectangular Channel With Partially Vegetations

HUAI Wen-xin, GENG Chuan, ZENG Yu-hong, YANG Zhong-hua

2011, 32(4): 437-444. doi: 10.3879/j.issn.1000-0887.2011.04.006

Abstract(1720) PDF(870)

Abstract:
The lateral distribution of longitudinal velocity in steady uniform turbulent flow in partially vegetated rectangular channel was studied.Plants were assumed as immovable medium.The resistance caused by vegetation was expressed by the theory of poroelasticity.With the consideration of the influence of secondary flow,the momentum equation could be settled.The momentum equation was simplified due to the characters of steady uniform flow.The momentum equation was nondimensionalized to obtain a smooth solution for the lateral distribution of longitudinal velocity.The research shows the secondary current intensity coefficient is in the same order of magnitude under different flow conditions.To verify the model,the acoustic Doppler velocimeter (Micro ADV) is used to measure the velocity field in a rectangular open channel partially with emergent artificial rigid vegetation.Comparisons between the measured data,from both the experiment and the Japanese researchers' paper,and the computed results show that the method did well in predicting the transverse distributions of stream-wise velocity in turbulent flow in rectangular channel with partially vegetations.

Damage Detection Method in Complicated Beams With Varying Flexural Stiffness

FENG Kan, LI Zheng, GAO Gui-yun, SU Xian-yue

2011, 32(4): 445-454. doi: 10.3879/j.issn.1000-0887.2011.04.007

Abstract(1884) PDF(746)

Abstract:
A damage detection method for complicated beam-like structures was proposed based on the subsection strain energy method (SSEM),and its applicable condition was introduced.For a beam with continuously varying flexural stiffness and an edge crack,the SSEM was applied to detect the crack location effectively by numerical modal shapes.As a complicated beam,the glass fiber-reinforced composite model of a wind turbine blade was studied by an experimental modal analysis.The SSEM was used to calculate the damage index from the measured modal parameters,and to locate the damage position in the blade model successfully.The results indicate that the SSEM based on the modal shapes can be used to detect the damage in complicated beams or beam-like structures in engineering applications.

Uniqueness Theorem,Theorem of Reciprocity and Eigen Value Problems in the Linear Theory of Porous Piezoelectricity

Anil K. Vashishth, Vishakha Gupta

2011, 32(4): 455-469. doi: 10.3879/j.issn.1000-0887.2011.04.008

Abstract(1781) PDF(766)

Abstract:
The uniqueness theorem and theorem of reciprocity in the linearized theory of porous piezoelectricity were established with the assumption of positive definiteness of elastic and electric field.General theorems in the linear theory of porous piezoelectric materials were proved for the quasi-static electric field approximation.The uniqueness theorem was also proved without using positive definiteness of elastic field.An eigen value problem,associated with free vibrations of porous piezoelectric body,was studied employing abstract formulation.Some properties of involved operators were also studied.The problem of frequency shift due to small disturbances,based on an abstract formulation,was studied using variational and operator approach.A perturbation analysis of a special case is also given.

Free Vibration of Circular Cylindrical Shell With Constrained Layer Damping

CAO Xiong-tao, ZHANG Zhi-yi, HUA Hong-xing

2011, 32(4): 470-482. doi: 10.3879/j.issn.1000-0887.2011.04.009

Abstract(1771) PDF(805)

Abstract:
The free vibration characteristic of circular cylindrical shell with passive constrained layer damping (PCLD) was presented.Wave propagation approach rather than finite element method,transfer matrix method and Rayleigh-Ritz method were used to solve the vibration of PCLD circular cylindrical shell with simply supported boundary condition at two ends.The governing equations of motion for the orthotropic cylindrical shell with PCLD were derived on the base of Sanders thin shell theory.Numerical results show that the present method is more effective in comparison with other methods.The effect of the thickness of viscoelastic core and constrained layer,the elastic modulus ratio of orthotropic constrained layer and complex shear modulus of viscoelastic core on frequency parameter and loss factor is discussed.

Stresses in a Rotating Heterogeneous Viscoelastic Composite Cylinder With Variable Thickness

A. M. Zenkour

2011, 32(4): 483-496. doi: 10.3879/j.issn.1000-0887.2011.04.010

Abstract(1447) PDF(719)

Abstract:
An analytical solution for the rotation problem of a two-layer composite elastic cylinder under plane strain assumption was presented.The external cylinder had variable-thickness formulation and made of a heterogeneous orthotropic material.It was contained by a fiber-reinforced viscoelastic homogeneous isotropic solid core of uniform-thickness.The thickness and elastic properties of the external cylinder were taken as power functions of the radial direction.On application of the boundary and continuity conditions,the radial displacement and stresses for the rotating composite cylinder were determined.The effective moduli and Illyushin's approximation methods were used to obtain the viscoelastic solution of this problem.The effects of heterogeneity,thickness variation,constitutive and time parameters on the radial displacement and stresses were investigated.

Two New Predictor-Corrector Algorithms for Second-Order Cone Programming

ZENG You-fang, BAI Yan-qin, JIAN Jin-bao, TANG Chun-ming

2011, 32(4): 497-508. doi: 10.3879/j.issn.1000-0887.2011.04.011

Abstract(1733) PDF(886)

Abstract:
Based on the ideas of infeasible interior-point methods and predictor-corrector algorithms,two interior-point predictor-corrector algorithms for second-order cone programming (SOCP) were presented.They use the Newton direction and the Euler direction as the predictor directions,respectively.The corrector directions belong to the category of the Alizadeh-Haeberly-Overton (AHO) directions.The two new algorithms were suitable to cases of feasible and infeasible interior iterative points.A simpler neighborhood of central path for the SOCP was proposed,which was the pivotal difference from other interior-point predictor-corrector algorithms.Under some assumptions,the algorithms possess global,linear and quadratic convergence.The complexity bound O (rln (ε₀/ε)) was obtained,where r denotes the number of second-order cones in SOCP problem.The numerical results show that the proposed algorithms are effective.