Showing papers in "Applied Mathematics and Mechanics-english Edition in 2005"

Mathematical foundation of a new complexity measure

Abstract: For many continuous bio-medical signals with both strong nonlinearity and non-stationarity, two criterions were proposed for their complexity estimation: (1) Only a short data set is enough for robust estimation; (2) No over-coarse graining preprocessing, such as transferring the original signal into a binary time series, is needed.C 0 complexity measure proposed by us previously is one of such measures. However, it lacks the solid mathematical foundation and thus its use is limited. A modified version of this measure is proposed, and some important properties are proved rigorously. According to these properties, this measure can be considered as an index of randomness of time series in some senses, and thus also a quantitative index of complexity under the meaning of randomness finding complexity. Compared with other similar measures, this measure seems more suitable for estimating a large quantity of complexity measures for a given task, such as studying the dynamic variation of such measures in sliding windows of a long process, owing to its fast speed for estimation.

Dependence of modulus of elasticity and thermal conductivity on reference temperature in generalized thermoelasticity for an infinite material with a spherical cavity

Abstract: The equations of generalized thermoelasticity with one relaxation time with variable modulus of elasticity and the thermal conductivity were used to solve a problem of an infinite material with a spherical cavity. The inner surface of the cavity was taken to be traction free and acted upon by a thermal shock to the surface. Laplace transforms techniques were used to obtain the solution by a direct approach. The inverse Laplace transforms was obtained numerically. The temperature, displacement and stress distributions are represented graphically.

Interactions between two sedimenting particles with different sizes

Abstract: An improved implementation of Distributed Lagrange multiplier/fictitious domain method was presented and used to simulate the interactions between two circular particles sedimenting in a two-dimensional channel. The simulation results were verified by comparison with experiments. The results show that the interactions between two particles with different sizes can be described as drafting, kissing, tumbling and separating. Only for small diameter ratio, the two particles will interact undergoing repeated DKT (Drafting, Kissing and Tumbling) process. Otherwise, the two particles will separate after their tumbling. The results also show that, during the interaction process, the motion of the small particle is strongly affected while the large particle, is affected slightly.

New boundary element method for torsion problems of cylinder with curvilinear cracks

Abstract: The Saint-Venant torsion problems of a cylinder with curvilinear cracks were considered and reduced to solving the boundary integral equations only on cracks. Using the interpolation models for both singular crack tip elements and other crack linear elements, the boundary element formulas of the torsion rigidity and stress intensity factors were given. Some typical torsion problems of a cylinder involving a straight, kinked or curvilinear crack were calculated. The obtained results for the case of straight crack agree well with those given by using the Gauss-Chebyshev integration formulas, which demonstrates the validity and applicability of the present boundary element method.

Modified h-r mixed variational principle for magnetoelectroelastic bodies and state-vector equation

Abstract: Based upon the Hellinger-Reissner (H-R) mixed variational principle for three-dimensional elastic bodies, the modified H-R mixed variational theorem for magnetoelectroelastic bodies was established. The state-vector equation of magnetoelectroelastic plates was derived from the proposed theorem by performing the variational operations. To lay a theoretical basis of the semi-analytical solution applied with the magnetoelectroelastic plates, the state-vector equation for the discrete element in plane was proposed through the use of the proposed principle. Finally, it is pointed out that the modified H-R mixed variational principle for pure elastic, single piezoelectric or single piezomagnetic bodies are the special cases of the present variational theorem.

Dynamic propagation problem on dugdale model of mode iii interface crack

Abstract: By the theory of complex functions, the dynamic propagation problem on Dugdale model of mode III interface crack for nonlinear characters of materials was studied. The general expressions of analytical solutions are obtained by the methods of self-similar functions. The problems dealt, with can be easily transformed into Riemann-Hilbert problems and their closed solutions are attained rather simply by this approach. After those solutions were utilized by superposition theorem, the solutions of arbitrarily complex problems could be obtained.

Adaptive interval wavelet precise integration method for partial differential equations

Abstract: The quasi-Shannon interval wavelet is constructed based on the interpolation wavelet theory, and an adaptive precise integration method, which is based on extrapolation method is presented for nonlinear ordinary differential equations (ODEs). And then, an adaptive interval wavelet precise integration method (AIWPIM) for nonlinear partial differential equations(PDEs) is proposed. The numerical results show that the computational precision of AIWPIM is higher than that of the method constructed by combining the wavelet and the 4th Runge-Kutta method, and the computational amounts of these two methods are almost equal. For convenience, the Burgers equation is taken as an example in introducing this method, which is also valid for more general cases.

Study on coupling model of (seepage-field) and stress-field for rolled control concrete dam

Abstract: Based on the construction interfaces in rolled control concrete dam(RCCD), the methods were proposed to calculate the influence thickness of construction interfaces and the corresponding physical mechanics parameters The principle on establishing the coupling model of seepage-field and stress-field for RCCD was presented A 3-D Finite Element Method(FEM) program was developed Study shows that such parameters as the thickness of construction interfaces, the elastic ratio and the Poisson's ratio obtained by tests and theoretical analysis are more reasonable, the coupling model of seepage-field and stress-field for RCCD may indicate the coupling effect between the two fields scientifically, and the developed 3-D FEM program can reflect the effect of the construction interfaces more adequately According to the study, many scientific opinions are given both to analyze the influence of the construction interfaces to the dam's characteristics and to reveal the interaction between the stress-field and the seepage-field

An effective boundary element method for analysis of crack problems in a plane elastic plate

Abstract: A simple and effective boundary element method for stress intensity factor calculation for crack problems in a plane elastic plate is presented. The boundary element method consists of the constant displacement discontinuity element presented by Crouch and Starfield and the crack-tip displacement discontinuity elements proposed by YAN Xiangqiao. In the boundary element implementation the left or the right crack-tip displacement discontinuity element was placed locally at the corresponding left or right each crack tip on top of the constant displacement discontinuity elements that cover the entire crack surface and the other boundaries. Test examples (i. e., a center crack in an infinite plate under tension, a circular hole and a crack in an infinite plate under tension) are included to illustrate that the numerical approach is very simple and accurate for stress intensity factor calculation of plane elasticity crack problems. In addition, specifically, the stress intensity factors of branching cracks emanating from a square hole in a rectangular plate under biaxial loads were analysed. These numerical results indicate the present numerical approach is very effective for calculating stress intensity factors of complex cracks in a 2-D finite body, and are used to reveal the effect of the biaxial loads and the cracked body geometry on stress intensity factors.

Equivalence of refined theory and decomposed theorem of an elastic plate

Abstract: A connection between Cheng's refined theory and Gregory's decomposed theorem is analyzed. The equivalence of the refined theory and the decomposed theorem is given. Using operator matrix determinant of partial differential equation, Cheng gained one equation, and he substituted the sum of the general integrals of three differential equations for the solution of the equation. But he did not prove the rationality of substitute. There, a whole proof for the refined theory from Papkovich-Neuber solution was given. At first expressions were obtained for all the displacements and stress components in term of the midplane displacement and its derivatives. Using Lur'e method and the theorem of appendix, the refined theory was given. At last, using basic mathematic method, the equivalence between Cheng's refined theory and Gregory's decomposed theorem was proved,i. e., Cheng's bi-harmonic equation, shear equation and transcendental equation are equivalent to Gregory's interior state, shear state and Papkovich-Fadle state, respectively.

Higher order boussinesq-type equations for water waves on uneven bottom

Abstract: Higher order Boussinesq-type equations for wave propagation over variable bathymetry were derived. The time dependent free surface boundary conditions were used to compute the change of the free surface in time domain. The free surface velocities and the bottom velocities were connected by the exact solution of the Laplace equation. Taking the velocities on half relative water depth as the fundamental unknowns, terms relating to the gradient of the water depth were retained in the inverse series expansion of the exact solution, with which the problem was closed. With enhancements of the finite order Taylor expansion for the velocity field, the application range of the present model was extended to the slope bottom which is not so mild. For linear properties, some validation computations of linear shoaling and Booij's tests were carried out. The problems of wave-current interactions were also studied numerically to test the performance of the enhanced Boussinesq equations associated with the effect of currents. All these computational results confirm perfectly to the theoretical solution as well as other numerical solutions of the full potential problem available.

Linear quadratic nonzero-sum differential games with random jumps

Abstract: The existence and uniqueness of the solutions for one kind of forward-backward stochastic differential equations with Brownian motion and Poisson process as the noise source were given under the monotone conditions. Then these results were applied to nonzero-sum differential games with random jumps to get the explicit form of the open-loop Nash equilibrium point by the solution of the forward-backward stochastic differential equations.

Dynamic modeling for airship equipped with ballonets and ballast

Abstract: Total dynamics of an airship is modeled. The body of an airship is taken as a submerged rigid body with neutral buoyancy,i. e., buoyancy with value equal to that of gravity, and the coupled dynamics between the body with ballonets and ballast is considered. The total dynamics of the airship is firstly derived by Newton-Euler laws and Kirchkoff's equations. Furthermore, by using Hamiltonian and Lagrangian semidirect product reduction theories, the dynamics is formulated as a Lie-Poisson system, or also an Euler-Poincare system. These two formulations can be exploited for the control design using energy-based methods for Hamiltonian or Lagrangian system.

Numerical study on the stability and mixing of vertical round buoyant jet in shallow water

Abstract: The k-epsilon model was applied to establish the mathematical model of vertical round buoyant jet discharging into confined depth, and it was solved using the Hybrid Finite Analytic Method (HFAM). The numerical predictions demonstrate two generic flow patterns for different jet discharge and environmental parameters: (i) a stable buoyant flow discharge with the mixed fluid leaving the near-field warm in a surface warm water layer; (ii) an unstable buoyant flow discharge with recirculation and re-entrainment of warm water in the near field. Furthermore, the mixing characters of vertical round buoyant jet were numerically predicted. Both the stability criterion and numerical predictions of bulk dilutions are in excellent agreement with Lee and Jirka's experiments and theory.

Laminar dissipative flow in a porous channel bounded by isothermal parallel plates

Abstract: The effects of viscous dissipation on thermal entrance heat transfer in a parallel plate channel filled with a saturated porous medium, is investigated analytically on the basis of a Darcy model. The case of isothermal boundary is treated. The local and the bulk temperature distribution along with the Nusselt number in the thermal entrance region were found. The fully developed Nusselt number, independent of the Brinkman number, is found to be 6. It is observed that neglecting the effects of viscous dissipation would lead to the well-known case of internal flows, with Nusselt number equal to 4.93. A finite difference numerical solution is also utilized. It is seen that the results of these two methods, analytical and numerical, are in good agreement.

Dynamic stability of axially moving viscoelastic beams with pulsating speed

Abstract: Parametric vibration of an axially moving, elastic, tensioned beam with pulsating speed was investigated in the vicinity of subharmonic and combination resonance. The method of averaging was used to yield a set of autonomous equations when the parametric excitation frequency is twice or the combination of the natural frequencies. Instability boundaries were presented in the plane of parametric frequency and amplitude. The analytical results were numerically verified. The effects of the viscoelastic damping, steady speed and tension on the instability boundaries were numerically demonstrated. It is found that the viscoelastic damping decreases the instability regions and the steady speed and the tension make the instability region drift along the frequency axis.

Numerical simulation study on rock breaking mechanism and process under high pressure water jet

Abstract: The numerical simulation method to study rock breaking process and mechanism under high pressure water jet was developed with the continuous mechanics and the FEM theory. The rock damage model and the damage-coupling model suited to analyze the whole process of water jet breaking rock were established with continuum damage mechanics and micro damage mechanics. The numerical results show the dynamic response of rock under water jet and the evolvement of hydrodynamic characteristic of jet during rock breaking is close to reality, and indicates that the body of rock damage and breakage under the general continual jet occurs within several milliseconds, the main damage form is tensile damage caused by rock unload and jet impact, and the evolvement of rock damage shows a step-change trend. On the whole, the numerical results can agree with experimental conclusions, which manifest that the analytical method is feasible and can be applied to guide the research and application of jet breaking rock theory.

Scattering of Harmonic Anti-Plane Shear Waves by an Interface Crack in Magneto-Electro-Elastic Composites

Abstract: The dynamic behavior of an interface crack in magneto-electro-elastic composites under harmonic elastic anti-plane shear waves is investigated for the permeable electric boundary conditions. By using the Fourier transform, the problem can be solved with a pair of dual integral equations in which the unknown variable was the jump of the displacements across the crack surfaces. To solve the dual integral equations, the jump of the displacements across the crack surface was expanded in a series of Jacobi polynomials. Numerical examples were provided to show the effect of the length of the crack, the wave velocity and the circular frequency of the incident wave on the stress, the electric displacement and the magnetic flux intensity factors of the crack. From the results, it can be obtained that the singular stresses in piezoelectric/piezomagnetic materials carry the same forms as those in a general elastic material for anti-plane shear problem.

Geometrical nonlinear waves in finite deformation elastic rods

Abstract: By using Hamilton-type variation principle in non-conservation system, the nonlinear equation of wave motion of a elastic thin rod was derived according to Lagrange description of finite deformation theory. The dissipation caused due to viscous effect and the dispersion introduced by transverse inertia were taken into consideration so that steady traveling wave solution can be obtained. Using multi-scale method the nonlinear equation is reduced to a KdV-Burgers equation which corresponds with saddle-spiral heteroclinic orbit on phase plane. Its solution is called the oscillating-solitary wave or saddle-spiral heteroclinic orbit on phase plane. Its solution is called the oscillating-solitary wave or saddle-spiral shock wave. If viscous effect or transverse inertia is neglected, the equation is degraded to classical KdV or Burgers equation. The former implies a propagating solitary wave with homoclinic on phase plane, the latter means shock wave and heteroclinic orbit.

Moving inclined load at boundary surface

Abstract: The analytic expressions for the displacement components and stresses at a point of an orthotropic micropolar elastic medium with an overlying elastic half space as a result of moving inclined load of arbitrary orientation were obtained. The inclined load was assumed to be a linear combination of a normal load and a tangential load. The eigen value approach using Fourier transforms was employed and the transform was inverted by using a numerical technique. The numerical results were illustrated graphically for aluminium epoxy composite.

New approach to minimize dispersion induced by turn in capillary electrophoresis channel flows

Abstract: The mechanism of dispersion induced by turn in the capillary electrophoresis channel flows was analyzed firstly. Then the mathematical model of electroosmotic flow is built, and the dispersion of the flow, with different distribution of charge at inner and outer wall in the turns, was simulated numerically using the finite differential method. A new approach of altering the distribution of charge at inner and outer wall in the turns was presented, based on the computational results, to minimize the dispersion induced by turn. Meanwhile, an optimization algorithm to analyze the numerical results and determine the optimal distribution of charge in the turns was also developed. It is found that the dispersion induced by turn in the capillary electrophoresis channel flows could be significantly suppressed by this approach.

Multi-scale coherent structures in turbulent boundary layer detected by locally averaged velocity structure functions

Abstract: The time sequence of longitudinal velocity component at different vertical locations in turbulent boundary layer was finely measured in a wind tunnel. The concept of coarse-grained velocity structure functions, which describes the relative motions of straining and compressing for multi-scale eddy structures in turbulent flows, was put forward based on the theory of locally multi-scale average. Based on the consistency between coarse-grained velocity structure function and Harr wavelet transformation, detecting method was presented, by which the coherent structures and their intermittency was identified by multi-scale flatness factor calculated by locally average structure function. Phase-averaged evolution course for multi-scale coherent eddy structures in wall turbulence were extracted by this conditional sampling to educe scheme. The dynamics course of multi-scale coherent eddy structures and their effects on statistics of turbulent flows were studied.

Computational technique for flow in blood vessels with porous effects

Abstract: A finite element solution for the Navier-Stokes equations for steady flow under the porosity effects through a double branched two-dimensional section of a three-dimensional model of a canine aorta was obtained. The numerical solution involves transforming a physical coordinates to a curvilinear boundary fitted coordinate system. The steady flow, branch flow and shear stress under the porous effects were discussed in detail. The shear stress at the wall was calculated for Reynolds number of 1000 with branch to main aortic flow rate ratio as a parameter. The results are compared with earlier works involving experimental data and it has been observed that our results are very close to the exact solutions. This work is in fact an improvement of the work of Sharma et al. (2001) in the sense that computational technique is economic and Reynolds number is large.

Nonlinear vibration for moderate thickness rectangular cracked plates including coupled effect of elastic foundation

Abstract: Based on Reissner plate theory and Hamilton variational principle, the nonlinear equations of motion were derived for the moderate thickness rectangular plates with transverse surface penetrating crack on the two-parameter foundation. Under the condition of free boundary, a set of trial functions satisfying all boundary conditions and crack's continuous conditions were proposed. By employing the Galerkin method and the harmonic balance method, the nonlinear vibration equations were solved and the nonlinear vibration behaviors of the plate were analyzed. In numerical computation, the effects of the different location and depth of crack, the different structural parameters of plates and the different physical parameters of foundation on the nonlinear amplitude frequency response curves of the plate were discussed.

Long time behavior for solution of initial boundary value problem of one class of systems with multidimensional inhomogeneous gbbm equations

Abstract: The following initial-boundary value problem for the systems with multidimensional inhomogeneous generalized Benjamin-Bona-Mahony (GBBM) equations is reviewed. The existence of global attractors of this problem was proved by means of a uniform priori estimate for time.

3-d dynamic response of transversely isotropic saturated soils

Abstract: A study on dynamic response of transversely isotropic saturated poroelastic media under a circular non-axisymmetrical harmonic source has been presented by Huang Yi et al. using the technique of Fourier expansion and Hankel transform. However, the method may not always be valid. The work is extended to the general case being in the rectangular coordinate. The purpose is to study the 3-d dynamic response of transversely isotropic saturated soils under a general source distributing in arbitrary rectangular zoon on the medium surface. Based on Biot’s theory for fluid-saturated porous media, the 3-d wave motion equations in rectangular coordinate for transversely isotropic saturated poroelastic media were transformed into the two uncoupling governing differential equations of 6-order and 2-order respectively by means of the displacement functions. Then, using the technique of double Fourier transform, the governing differential equations were easily solved. Integral solutions of soil skeleton displacements and pore pressure as well as the total stresses for poroelastic media were obtained. Furthermore, a systematic study on half-space problem in saturated soils was performed. Integral solutions for surface displacements under the general harmonic source distributing on arbitrary surface zone, considering both case of drained surface and undrained surface,were presented.

Theoretical study of three-dimensional numerical manifold method

Abstract: The three-dimensional numerical manifold method(NMM) is studied on the basis of two-dimensional numerical manifold method. The three-dimensional cover displacement function is studied. The mechanical analysis and Hammer integral method of three-dimensional numerical manifold method are put forward. The stiffness matrix of three-dimensional manifold element is derived and the dissection rules are given. The theoretical system and the numerical realizing method of three-dimensional numerical manifold method are systematically studied. As an example, the cantilever with load on the end is calculated, and the results show that the precision and efficiency are agreeable.

Stability analysis of viscoelastic curved pipes conveying fluid

Abstract: Based on the Hamilton's principle for elastic systems of changing mass, a differential equation of motion for viscoelastic curved pipes conveying fluid was derived using variational method, and the complex characteristic equation for the viscoelastic circular pipe conveying fluid was obtained by normalized power series method. The effects of dimensionless delay time on the variation relationship between dimensionless complex frequency of the clamped-clamped viscoelastic circular pipe conveying fluid with the Kelvin-Voigt model and dimensionless flow velocity were analyzed. For greater dimensionless delay time, the behavior of the viscoelastic pipe is that the first, second and third mode does not couple, while the pipe behaves divergent instability in the first and second order mode, then single-mode flutter takes place in the first order mode.

Bifurcation in a two-dimensional neural network model with delay

Abstract: A kind of 2-dimensional neural network model with delay is considered. By analyzing the distribution of the roots of the characteristic equation associated with the model, a bifurcation diagram was drawn in an appropriate parameter plane. It is found that a line is a pitchfork bifurcation curve. Further more, the stability of each fixed point and existence of Hopf bifurcation were obtained. Finally, the direction of the Hopf bifurcation and the stability of the bifurcating periodic solutions were determined by using the normal form method and centre manifold theory.

Nonlinear complex dynamic phenomena of the perturbed metallic bar considering dissipating effect

Abstract: Considering Peierls-Nabarro effect, one-dimensional finite metallic bar subjected with periodic field was researched under Neumann boundary condition. Dynamics of this system was described with displacement by perturbed sine-Gordon type equation. Finite difference scheme with fourth-order central differences in space and second-order central differences in time was used to simulate dynamic responses of this system. For the metallic bar with specified sizes and physical features, effect of amplitude of external driving on dynamic behavior of the bar was investigated under initial “breather” condition. Four kinds of typical dynamic behaviors are shown: x-independent simple harmonic motion; harmonic motion with single wave; quasi-periodic motion with single wave; temporal chaotic motion with single spatial mode. Poincare map and power spectrum are used to determine dynamic features.