应用数学和力学

1993 Vol. 14, No. 6

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The Impact Torsionai Buckling of Elastic Cylindrical Shells with Arbitrary Form Imperfection

Wang De-yu, Zhang Shan-yuan, Yang Gui-tong

1993, 14(6): 471-477.

Abstract(1701) PDF(446)

Abstract:
A perturbation analysis for the impact torsional buckling of imperfective elastic cylindrical shells subjected to a step torque is given The imperfection is supposed to be small and has arbitrary form. It is shown that only the imperfection which has the shape of static torsional buckling mode could influence the critical step torque. Finally a formula is presented for the critical step torque.

Saint-Venant’s Torsion Problem for a Composite Circular Cylinder with an Internal Edge Crack

Tao Fang-ming, Tang Ren-ji

1993, 14(6): 479-488.

Abstract(1636) PDF(557)

Abstract:
In this paper the writer uses Muskhelishvili single-layer potential function solution and single crack solution for the torsion problem of a circular cylinder to discuss the torsion problem of a composite cylinder with an internal crack, and the problem is reduced to a set of mixed-type integral equation with generalized Cauchy-kernel. Then, by using the integration formula of Gauss-Jacobi, the numerical method is established and several numerical examples are calculated. The torsional rigidity and the stress intensity factors are obtained. The results of these examples fit the results obtained by the previous papers better.

An Iteration Algorithm for Solving Postbuckling Equilibrium Path of Simply-Supported Rectangular Plates under Biaxial Compression

Qiao Zong-chun

1993, 14(6): 489-497.

Abstract(1639) PDF(581)

Abstract:
In this paper, on the basis of von Kármán large deflection equations and its double trigonometric series solution, we present a simple, fast and effective iteration algorithm for solving simply-supported rectangular plate subjected to biaxial compression.

Noether s Theory for Nonholonomic Dynamical Systems Relative to Noninertial Reference Frame

Yu Hui-dan, Zhang Jie-fang, Xu You-shen

1993, 14(6): 499-506.

Abstract(2031) PDF(606)

Abstract:
The new variational principle of Gauss's form of nonlinear nonholonomic nonpotential system relative to non-inertial reference frame is established by constructing generalized inertial potentials. Naether's theorem and Naether's inverse theorem of the system above is presented and proved. Finally, one example is given to illustrate the application.

On a Generalization of Bertrand’s Theorem

Shi Rong-chang, Mei Feng-xiang

1993, 14(6): 507-513.

Abstract(2200) PDF(446)

Abstract:
Bertrand's theorem for the determination of the applied forces to a holonomic system from one of its first integrals, is extended to nonholonomic systems. Some interesting applications of this new result are also given.

Harten Solution for One-Dimensional Unsteady Equation

Chen Shao-jun

1993, 14(6): 515-524.

Abstract(1639) PDF(436)

Abstract:
In order to use the second-order 5-point difference scheme mentioned to compute the solution of one dimension unsteady equations of the direct reflection of the strong plane detonation wave meeting a solid wall barrier, in this paper, we technically construct the difference schemes of the boundary and sub-boundary of the problem, and deduce the auto-analogue analytic solutions of the initial value problem, and at the same time, we present a method for the singular property of the initial value problem, from which we can get a satisfactory computation result of this difficult problem.The difference scheme used in this paper to deal with the discontinuity problems of the shock wave are valuable and worth generalization.

The Mathematical Model of Bubble Group Noise

Huang Jing-chuan

1993, 14(6): 525-528.

Abstract(1996) PDF(481)

Abstract:
In this paper the mathematical model of bubble group noise are introduced under the arbitrary conditions by using the method of Euler. The calculation indicates that the simulation results consist with the measured value.

On Problems of U-Shaped Bellows with Nonlinear Deformation of Large Axisymmetrical Deflection(I)——Counting Variation of Thickness Distribution

Hu Liang

1993, 14(6): 529-534.

Abstract(2024) PDF(435)

Abstract:
On the basis of paper [1], assuming the logarithm of thickness at arbitrary point on a U-shaped bellows meridian is linear with the logarithm of distance between that point and axis of symmetry, perturbation solutions of the corresponding problems of large axisymmetrical deflection are given. The effects of thickness distribution variation, which result from technology factors, on stiffness of bellows are discussed.

Solution for the Oscillation of a Newtonian Fluid in a Co-Axial Viscometer

Li Ping, Yan Zong-yi, Zhuang Feng-yuan

1993, 14(6): 535-541.

Abstract(2191) PDF(622)

Abstract:
When one cup of a co-axial viscometer oscillates, the measured moment on the other(stationary) cup.shown a phase lag, partly due to the inertial effect of the fluid within the gap between the cups. In this paper such an effect is illustrated by a new exact solution of the Navier-Stokes equation, which is derived herein by a scheme of reducing it to a two-point boundary value problem for ODEs. Our numerical results indicate that, as the Womersley number a or the dimensionless gap width increases, the fluid velocity profile within the gap gradually deviates from the linear one and transits to that of the boundary layer type, with the result that the moment decreases in the magnitude and lags behind in the phase. With the advantage of high accuracy and excellent stability, the scheme proposed herein can readily be extended to solve other linear periodic problems.

Boundary Value Problems for Second Order Delay Differential Equations

Li Long-tu, Wang Zhi-cheng, Qian Xiang-zheng

1993, 14(6): 543-549.

Abstract(1563) PDF(439)

Abstract:
In this paper, using a fixed point principle and existence principle given in [1], we study the boundary value problems for second order differential equations. Some new existence results are obtained.

Numerical Simulation of Wing-Body Junction Turbulence Flow

Wang Xi-liang, He Mo-qin

1993, 14(6): 551-557.

Abstract(1424) PDF(512)

Abstract:
Wing-body junction turbulence flow is simulated by using RANS equation and boundary fitted coordinate technique. Three order differential scheme is used in the computation of convection term and two layers turbulence model are employed in the calculation.

Existence of Closed Orbits for a Differential Equation Model Concerning Multi-Molecule Reactions

Zhang Wei-nian

1993, 14(6): 559-566.

Abstract(1761) PDF(626)

Abstract:
In this paper, the existence of closed orbits for the biochemical reaction model dx/dt=1-xⁿy²,dy/dt=a(xⁿy²-y) is discussed, where n is a positive integer and x≥0,y≥0,a>0 We also point out that the equation has no dosed orbits or has stable limit cycles arising from Hopf bifurcations under a certain condition of a.