应用数学和力学

Chaos and Sub-Harmonic Resonance of Nonlinear System Without Small Parameters

LIU Yan-bin, CHEN Yu-shu, CAO Qing-jie

2011, 32(1): 1-10. doi: 10.3879/j.issn.1000-0887.2011.01.001

Abstract(1825) PDF(910)

Abstract:
Melnikov method was especially important to detect the presence of transverse homoclinic orbits and occurrence of homoclinic bifurcations.Unfortunately traditional Melnikov methods strongly depend on small parameter,which could not exist in most of the practice physical systems.Those methods were limited in dealing with the system with strongly nonlinear.A procedure to study the chaos and sub-harmonic resonance of strongly nonlinear practice systems by employing homotopy method which was used to extend Melnikov functions to strongly nonlinear systems was presented.Applied to a given example,the procedure shows the efficiencies in the comparison of the theoretical results and numerical simulation.

Stochastic Stability of FitzHugh-Nagumo Systems Perturbed by Gaussian White Noise

ZHENG Yan, HUANG Jian-hua

2011, 32(1): 11-21. doi: 10.3879/j.issn.1000-0887.2011.01.002

Abstract(1515) PDF(753)

Abstract:
Stochastic stability of FitzHugh-Nagumo systems perturbed by Gaussian white noise was studied.The dynamics of stochastic FitzHugh-Nagumo systems was studied first,which is essential in establishing the existence and uniqueness of their invariant measures,which mix exponentially.Then,asymptotic behavior of invariant measures when the size of noise gets to zero was investigated.

Unsteady Generalized Couette Flow in Composite Microchannel

M. L. Kaurangini, Basant K. Jha

2011, 32(1): 22-32. doi: 10.3879/j.issn.1000-0887.2011.01.003

Abstract(1324) PDF(820)

Abstract:
A numerical study was reported to investigate the unsteady fully developed laminar fluid flow in microchannel parallel-plates partially filled with uniform porous medium and partially with a clear fluid. The flow was induced by the movement of one of the plates and pressure gradient.Brinkman-Extended Darcy model was utilized to model the flow in porous region while Stokes equation was used in the clear fluid region.A theoretical analysis was also presented for the steady fully developed flow to find the closed form expressions for interfacial velocity,the velocity and skin frictions at the bounding plates.During the course of numerical computations,it is observed that there is an excellent agreement between the closed form solutions for steady fully developed flow with numerical solution of unsteady flow at large values of time.

Numerical Simulation of Vortex Evolution Based on Adaptive Wavelet Method

ZHAO Yong, ZONG Zhi, ZOU Wen-nan

2011, 32(1): 33-43. doi: 10.3879/j.issn.1000-0887.2011.01.004

Abstract(1683) PDF(748)

Abstract:
The application of wavelet method to vortex motion's prediction was investigated.First,the wavelet method was used to solve two initial boundary problems so as to verify its abilities of controlling numerical errors and capturing local structures.Then,the adaptive wavelet method was used to simulate the vortex emerging process.The results show that the wavelet method can predict the vortex evolution precisely and effectively.The application of this method to turbulence is suggested at last.

MHD Stagnation Point Flow of a Micropolar Fluid Towards a Heated Surface

Muhammad Ashraf, M. M. Ashraf

2011, 32(1): 44-52. doi: 10.3879/j.issn.1000-0887.2011.01.005

Abstract(1612) PDF(721)

Abstract:
The problem of two dimensional stagnation point flow of an electrically conducting micropolar fluid impinging normally on a heated surface in the presence of a uniform transverse magnetic field was analyzed.The governing continuity,momentum,angular momentum,and heat equations together with the associated boundary conditions were reduced to dimensionless form using suitable similarity transformations.The reduced self similar non-linear equations were then solved numerically by an algorithm based on finite difference discretization.The results were further refined by Richardson's extrapolation.The effects of the magnetic parameter,the micropolar parameters,and the Prandtl number on the flow and temperature fields were predicted in tabular and graphical forms to show the important features of the solution.The study shows that the velocity and thermal boundary layers become thinner as the magnetic parameter is increased.The micropolar fluids display more reduction in shear stress as well as heat transfer rate than that exhibited by Newtonian fluids,which is beneficial in the flow and thermal control of polymeric processing.

Inverse Estimation for the Unknown Fouling Geometry on the Inner Wall of a Forced-Convection Pipe

CHEN Wen-lih, YANG Yu-ching, LEE Haw-long, Jose Leon Salazar

2011, 32(1): 53-65. doi: 10.3879/j.issn.1000-0887.2011.01.006

Abstract(1684) PDF(719)

Abstract:
A conjugate gradient method based inverse algorithm was applied to estimate the unknown fouling-layer profile on the inner wall of a pipe system using simulated temperature measurements taken within the pipe wall.It was assumed that no prior information was available on the functional form of the unknown profile;hence the procedure was classified as the function estimation in inverse calculation.The temperature data obtained from the direct problem were used to simulate the temperature measurements. The accuracy of the inverse analysis is examined by using simulated exact and inexact temperature measurements.Results show that an excellent estimation on the fouling-layer profile can be obtained for the test case considered.The technique presented can be used in a warning system to call for pipe maintenance when the thickness of fouling exceeds a pre-defined criterion.

An Analytical Solution for Laminar Flow Through a Leaky Tube

Mofid Gorjid, Morteza Alipanah, Majid Shateri, Elham Farnad

2011, 32(1): 66-71. doi: 10.3879/j.issn.1000-0887.2011.01.007

Abstract(2190) PDF(768)

Abstract:
The laminar flow through a leaky tube was investigated,and the momentum and conservation of energy equations were solved analytically.Using the Hagen-Poiseuille velocity profile and defining unknown functions for the axial and radial velocity components,pressure and mass transfer equations were obtained and their profiles were plotted according to different parameters.The results indicate that the axial velocity,the radial velocity,mass transfer parameter and pressure in the tube decrease as the fluid moves along the tube.

Anti-Plane Analysis of a Semi-Infinite Crack in a Piezoelectric Strip

GUO Jun-hong, LIU Ping, LU Zi-xing, QIN Tai-yan

2011, 32(1): 72-78. doi: 10.3879/j.issn.1000-0887.2011.01.008

Abstract(1718) PDF(758)

Abstract:
Using the complex variable function method and the technique of conformal mapping,the fracture problem of a semi-infinite crack in a piezoelectric strip was studied under the anti-plane shear stress and in-plane electric load.The analytical solutions of the field intensity factors and the mechanical strain energy release rate were presented with the assumption that the surface of the crack was electrically impermeable.When the height of the strip tends to infinity,the analytical solutions of an infinitely large piezoe-lectric solid with a semi-infinite crack were obtained.Moreover,the present results can be reduced to the well-known solutions for a purely elastic material in the absence of electric loading.In addition,numerical examples were conducted to analyze the influences of loaded crack length,the height of the strip and applied mechanical/electric loads on the mechanical strain energy release rate.

Orthogonal Basic Deformation Mode Method for Zero-Energy Mode Suppression of Hybrid Stress Element

ZHANG Can-hui, WANG Dong-dong, LI Tong-shan

2011, 32(1): 79-92. doi: 10.3879/j.issn.1000-0887.2011.01.009

Abstract(1744) PDF(661)

Abstract:
A set of basic deformation modes for hybrid stress finite element were directly derived from the element displacement field.Subsequently by employing the so-called united orthogonal conditions a new orthogonalization method was also proposed.The resulting orthogonal basic deformation modes exhibit simple and clear physical meanings.In addition,they do not involve any material parameters and thus can be efficiently used to examine the element performance and serve as a unified tool to assess different hybrid elements.Therafter a convenient approach for identification of spurious zero-energy modes was presented through using the positive definiteness property of flexibility matrix.Moreover,based upon the orthogonality relationship between the given initial stress modes and the orthogonal basic deformation modes,an alternative method of assumed stress modes to formulate a hybrid element free of spurious modes was discussed.It was also found that the orthogonality of the basic deformation modes was the sufficient and necessary condition for suppression of spurious zero-energy modes.Numerical examples of 2D 4-node quadrilateral element and 3D 8-node hexahedral element were illustrated in details to demonstrate the efficacy of the proposed orthogonal basic deformation mode method.

Powell’s Optimal Identification of Material Constants of Thin-Walled Box Girders Based on Fibonacci Series Search Method

ZHANG Jian, YE Jian-shu, ZHOU Chu-wei

2011, 32(1): 93-102. doi: 10.3879/j.issn.1000-0887.2011.01.010

Abstract(1580) PDF(780)

Abstract:
For thin-walled curve box girders,dynamic Bayesian error function of material constants of the structure was founded.Combined with one-dimensional Fibonacci series automatic search scheme of optimal step length,the Powell's optimization theory was utilized to perform the stochastic identification of material constants of thin-walled curve box.Then the steps of parameters'identification were presented in detail and the Powell's identification procedure of material constants of thin-walled curve box was compiled,in which the mechanical analysis of thin-walled curve box was completed based on finite curve strip element(FCSE)method.Through some classic examples,it is obtained that the Powell's identification of material constants of thin-walled curve box has numerical stability and convergence,which demonstrates that the present method and the compiled procedure are correct and reliable.And during parameters'iterative processes,the Powell's theory is irrelevant with the calculation of FCSE's partial differentiation, which proves high computation efficiency of the studied methods.The stochastic performances of systematic parameters and systematic responses are simultaneously deliberated in dynamic Bayesian error function. The one-dimensional optimization problem of the optimal step length is solved by adopting Fibonacci series search method and there is no need to determine the region in which the optimized step length lies.

Finite Dimensional Approximation to Global Minimizers in Functional Spaces With R-Convergence

CHEN Xi, YAO Yi-rong, ZHENG Quan

2011, 32(1): 103-112. doi: 10.3879/j.issn.1000-0887.2011.01.011

Abstract(1545) PDF(717)

Abstract:
New concept of convergence(R-convergence)of a sequence of measures was applied to characterize global minimizers in functional space as a sequence of approximating solutions in finite-dimensional spaces.A deviation integral approach was used to find such solutions.For a constrained problem,a penalized deviation integral algorithm was proposed to convert it to unconstrained ones.A numerical example on optimal control problem with non convex state constrains was given to show that the algorithm is efficient.

Numerical Simulations of Richtmyer-Meshkov Instability Using Conservative Front-Tracking Method

M. A. Ullah, GAO Wen-bin, MAO De-kang

2011, 32(1): 113-126. doi: 10.3879/j.issn.1000-0887.2011.01.012

Abstract(1545) PDF(651)

Abstract:
Numerical simulations of two Richtmyer-Meshkov(RM)instability experiments were presented using the conservative front tracking method developed in[Mao D.J Comput Phys,2007,226(2): 1550-1588],and compare them with that obtained in[Holmes R L,et al.J Fluid Mech,1995,301: 51-64].The simulations are generally in good agreement with that of Holmes et al.The simulations also captured the nonlinear and compressive phenomena,the self-interactions of the transmitted and reflected wave edges,which was pointed out in Holmes et al's work as the cause of the deceleration of the interfaces.However,the perturbation amplitudes and amplitude growth rates of the interfaces obtained with our conservative front-tracking method are a bit larger than that obtained by Holmes et al.

2011 Vol. 32, No. 1