应用数学和力学

1998 Vol. 19, No. 7

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The Influence of Cardiovascular Dynamic Coupling on the Blood Pulse Wave Propagation in Human Body

Wang Yingxiao, Wu Wangyi, Wen Gongbi

1998, 19(7): 565-576.

Abstract(2083) PDF(790)

Abstract:
For the first time.the pressure and flow pulse wave propagation phenomenon isstudied in this paper on the basis of the cardiovascular dynamic coupling.E(t)-R modelis adopted for left ventricle and T-Y tube model for systemic arteries.Furthermore,impulse response method and Fourier analysis method are employed.After reasonablecardiovascular parameters and their value have been selected,the pressure and flowwaveforms are obtained at any poing along the systemic arteries.The results fitmeasured data well.In addition,the influences of cardiovascular parameters on pulsewave propagation are studied.The work is useful in practice.

Three Dimensional Elasticity Solution for Vibration Problem of Thick Plate

Xu Xu, He Fubao

1998, 19(7): 577-585.

Abstract(2144) PDF(936)

Abstract:
In this paper,based upon the basic equations of three dimensional theory of elastodynamics,the governing differential equations of thick pla ie have been formulated.The dynamic response of stress and displacement of thick plate subjected to the transversed forced are obtained.It is shown that the vibrational characters of thick plate consist of three modes:thickness shear mode,symmetric mode and anti-symmetric mode.The characteristic equations of simply supported thick plate are derived and the comparison of the free vibration frequencics based on the classic theory,middle thickness plate theory and three dimensional elasticity theory are given.

Steady State Motions of Shallow Arch under Periodic Force with 1:2 Internal Resonance on the Plane of Physical Parameters

Bi Qinsheng, Chen Yushu

1998, 19(7): 587-596.

Abstract(2201) PDF(611)

Abstract:
The bifurcation dynamics of shallow arch which possesses initial deflection underperiodic excitation for the case of 1:2 internal resonance is studied in this paper.The whole parametric plane is divided into several different regions according to the types of motions; then the distribution of steady state motions of shallow arch on foe plane of physical parameters is obtained.Combining with numerical method,the dynamics ofthe system in different regions.especially in foe Hopf bifurcation region.is studied indetail.The rule of the mode interaction and the route to choos of the system is alsoanalysed at the end.

Proximal Point Algorithm with Errors for Generalized Strongly Nonlinear Quasivariational Inclusions

Ding Xieping

1998, 19(7): 597-602.

Abstract(1991) PDF(668)

Abstract:
In this paper,a class of generalized strongly nonlinear quasivariational in clusions are studied.By using the properties of the resolvent opera for associated with amaximal monotone mapping in Hilbert space,an existence theorem of solutions forgene ralized strongly nonlinear quasi variational inclusion is established and a new proximal point algorithm with errors is suggested for finding approximate solutions which strongly converge to the exact solution of the generalized strongly nonlinearquasivariational inclusion.As special cases,some known results in this field are also discussed.

A New Approach to Backlund Transformations of Nonlinear Evolution Equations

Fan Engui, Zhang Hongqing

1998, 19(7): 603-608.

Abstract(1962) PDF(864)

Abstract:
In this paper.a new approach to Backlund transformations of nonlinear evolution equations is presented.The results obtained by this procedure are completely the sameas that by Painleve truncating expansion.

Flow of a Train of Deformable Fluid Particles in a Tube

Chen Jinnan, Charles Maldarelli

1998, 19(7): 609-618.

Abstract(2089) PDF(455)

Abstract:
In the article,the boundary integral technique is used to solve the hydrodynamic movement of a train of deformable fluid particles in a tube.When a fluid particle is ina tube,the total normal stress difference is not constant and more.this force tends todistend and elongate the particle.We find that the difference between the velocity of a deformable fluid particle and a sphere(with the same radius) increases as the distance between the particles decreases,and that the increase in velocity with L'/a' is greaterthe capillary number,and this increase becomes less pronounced as radius decreases.

The Orthogonal Polynomials and the Pade’ Approximation

Faiz Ahmad

1998, 19(7): 619-623.

Abstract(2699) PDF(1785)

Abstract:
The diagonal Pade' approximates for exp(x).tan x and tanh x are obtained in a simple manner by using the property of Legendre polynomials that on [-1,1] P_n(x) is orthogonal to every polynomial of lower degree.Gauss's quadrature formula is used tofined the denomiators of some functions.

Magnetoelastic Bending and Stability of Soft Ferromagnetic Rectangular Plates

Zhou Youhe, Wang Xingzhe, Zheng Xiaojing

1998, 19(7): 625-630.

Abstract(2035) PDF(529)

Abstract:
In this paper,the phenomenon of magnetoelastic bending is theoretically simulated for soft ferromagnetic rectangular thin plates in applied magnetic fields.A numerical program of 3d FEM is established to capture the nonlinear coupling intercationbetween magnetic fields and bending deflection.Afler the nonlinear characteristic of the bending deflection and the magnetic(field) force is quantitatively displayed,wediscuss the critical magnetic field and the effect of the incident angle of obliquely applied magnetic field on the critical field to the phenomenon of magnetoelastic instablitlity.

Numerical Analysis and Construction of Limiter of High Resolution Difference Scheme

Zhang Mengping, Liu Ruxun

1998, 19(7): 631-640.

Abstract(1910) PDF(660)

Abstract:
In the paper,based on the theory of the remainder effects of difference schemes,some typical limiters are analysed and compared.For different limiters,the different strength of numerical dissipation and dispersion of schemes is the reason why theschemes show obvious different characteristics.After analysing and comparing thenumerical dissipation and dispersion of various schemes,a new kind of limiter isproposed.The new scheme has high resolution in sharp discontinuities,and avoids the "distortion" due to the stronger numerical dispersion in the relatively more smooth region.Numerical experiments show that the scheme has good properties.

Invariant Sub-Manifolds and Modes of Nonlinear Autonomous Systems

Zhao Guojing, Wei Jianguo

1998, 19(7): 641-647.

Abstract(1986) PDF(1112)

Abstract:
A definition of the modes of a nonlinear autonomous system was developed.The existence conditions and orbits' nature of modes are given by using the geometry theory of invariant manifolds that include stable manifold theorem,center maifold theorm and sub-center manifold theorem.The Taylor series exyansion was used inorder to approach the sub-manifolds of the modes and obtain the motions of the mods on the manifolds.Two examples were given to demonstrate the applications.

Inertial Manifolds for Nonautonomous InfiniteDimensional Dynamical Systems

Wang Zongxing, Fan Xianling, Zhu Zhengyou

1998, 19(7): 649-657.

Abstract(2086) PDF(836)

Abstract:
In this paper,the long time behavior of nonautonomous infinite dimensional dynamical systems is discussed.Under the spectral gap condition.It is proved that there exist inertial manifolds for a class of nonautonomous evolution equations.