应用数学和力学

1983 Vol. 4, No. 1

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Using Tangential Force Method to Detect the Singular Points and to Discriminate Their Stability Conditions of a Movable Mass Point on any Guide Curve Rotating about a Vertical Axis without Friction

Liu Hsien-chih

1983, 4(1): 1-40.

Abstract(1595) PDF(493)

Abstract:
Ever since one has used generally the state plane method to search the singular points and to decide their eq uilibrium state for a mass points sliding on guide ail rotating about a vertical axis with friction disregarded. For the same purpose,this paper presents another method which wight be briefly named "The Tangential Force Method". In contrast with the state plane method,the new method is much simpler both in argumentation and calculation,especially when one resorts to the five criteria in section XIII.Throughout the paper the function for defining the guide rail was introduced,with great endeavor,in the equations newly set up,in order to avoid deducing them each time,i.e.,the useful equations are set up somewhat once for ever.Moreover,the condition of letting the tangential force vanish yields two solutions,the parabolic and the exponential curves of the shape of the guide rails;they are two additional orthogonal curve families although not conjugate harmonics.In the last part of the paper,we present nine examples to show the superiority of this method against the state plane and the potential function methods;seven of the nine examples might be considered as newly introduced in this paper.

A Study on Ship Hull Vibration Using Finite Element Method

Zhong Wan-xie, He Qiong, Xue Hui-yu, Yang Bo

1983, 4(1): 41-51.

Abstract(1814) PDF(571)

Abstract:
When the beam theory was used to calculate ship hull vibration,greater discrepancies were found between theoretical calculations and actual measurements especially at higher modes.Thus the beam model cannot be considered as a practical one for higher-mode calculations. This paper presents the application of two-dimensional finite element model for the calculation of ship vertical vibration. Using the multi-element structural dynamic analysis program DDJ(DL) developed by ourselves,the hull vibration analysis of two ships (vessel A and vessel B) was carried out on the Model-709 Computer made in the People's Republic of China.The results of the calculation,when compared with actual measurements,show that the two-dimensional model is much more efficient than the traditional beam model. The agreement between the calculations and measurements has been improved greatly,and this discrepancy at the 4th-and 5th-modes has decreased to within 5% as compared to that of more than 20% in the traditional model. Furthermore,the model is relatively simple,the coat and time required for the computation is comparatively lower and shorter,and the calculation can be carried out on a medium-siezed computer. Therefore,this model is especially appropriate for analyzing the dynamic characteristics of ships at early design stages.

A Mixed Explicit-Implicit Antidiffusive Method of Navier-Stokes Eguations for Supersonic and Hypersonic Separated Flow

Zhang Han-xin, Lu Lin-sheng, Yu Zen-chu, Ma Zhan-kui

1983, 4(1): 53-67.

Abstract(1681) PDF(539)

Abstract:
In this paper, a mixed explicit-implicit scheme based on an antidiffusive method is used to solve the Navier-Stokes equations for the supersonic and hypersonic separated flows. The computations are performed for laminar and turbulent flows over the two-and three-dimensional compression corners, The obtained results are compared with the results of numerically computing NS equations^[1,3-5] and these results of the experiments^[6,7].The computations show that the numerical scheme in this paper is satisfactory.

On Dynamic Optimization of Timoshenko Beam

Cheng Keng-tung, Ding Hua

1983, 4(1): 69-76.

Abstract(1822) PDF(428)

Abstract:
The present paper discusses the minimum weight design problem for Timoshenko and Euler beams subjected to multi-frequency constraints. Taking the simply-supported symmetric beam as an example,we reveal the abnormal characteristics of optimal Timoshenko beams,i.e.,the frequency corresponding to the first symmetric vibration mode could be higher than the frequency of antisymmetric vibration mode if a very thin and high strip is suitably formed at the middle of the beam,and optimal Timoshenko beams subjected to two different sets of frequency constraints could have the same minimum weight. The above abnormal characteristics demonstrate the need for including maximum cross sectional area constraint in the problem formulation in order to have a well-posed problem.

Propagation of a Long Wave in a Curved Duct(Ⅰ) Basic Analysis of Long Wave Propagation in a Curved Duct with Variable Cross Section

Gu Sheng-shi, Fang Guang-xiong

1983, 4(1): 77-88.

Abstract(1673) PDF(489)

Abstract:
The propagation of a long wave in a three-dimensional curved duct with variable cross section is studied in this paper. It is shown that a three-dimensional Helmholtz equation can be decomposed into a two-dimensional Laplace (or Poisson) equation and a one-dimensional Webster equation by the curvilinear orthogonal coordinate system,non-dimensionization of reduced wave equation and regular perturbation with small parameter ka,where k is the wave number and a is the characteristic radius of the duct. The influences of the duct's geometric parameters (thearea variation of the cross section,the curvature and torsion of the central line) on the asymptotic expansion of the solution are analysed. It is concluded that the effects of the variation of the cross sectional area first appear in the first term of the asymptotic expansion,and when the cross section shape has certain symmetric properties,the effects of the curvature and torsion of the central line first appear in the third and the fourth terms,respectively. An example of long wave propagation in a curved circular duct is also given at the end of this paper.

A Theorem on Potential of Isotropic Symmetric Second-Order Tensor Function

Cheng Yuan-sheng

1983, 4(1): 89-92.

Abstract(1877) PDF(530)

Abstract:
In this paper we propose and prove the following theorem:If the second-order tensor H is an isotropic function of a symmetric second-order,tensor T,and there exists a potential function for H,then there will certainly exist a potential function for T,too.

Some Problems Associated with the Disturbed Matrix Lyapunov Equation for Linear Time-lnvarint Discrete Systems

Huang Lin, Zhu Wei-ling

1983, 4(1): 93-101.

Abstract(1818) PDF(506)

Abstract:
Both the Lyapvnov stability and Popov's hypex-stability of discrete linear time-invariant system in case of system parameter disturbance are discussed in this paper. The allowable disturbance ranges are given so that the maintenance of the Lyapunov stability and the Popov's hyperstability of a discrete linear system is guaranteed. The results find their significance in the MRAC.

The Large Deflection Problem of Circular Thin Plate with Variable Thickness under Uniformly Distributed Loads

Wang Xin-zhi

1983, 4(1): 103-112.

Abstract(1760) PDF(568)

Abstract:
In this paper,to begin with,the large deflection equation of variable thickness circular plates is given. By using small parameter method and revised iteration jointly a cubic approximate solution is obtained. A characteristic is also given for comparison with linear theory.

One Type of Solutions of Conduction of Nervous Pulses and the Stability of Action Potential

Tang Wen-liang

1983, 4(1): 113-121.

Abstract(1672) PDF(525)

Abstract:
This paper reports a type of laws which governs action potential of nervous impulses,and it is discussed by general form-nonlinear dispersive process. We find that the nervous wave is a slowly varying amplitude solitary wave in the small dispersive case. He prove that the solitary wave is not generated in the ordinary dispersion,but a travelling wave with varying amplitudes may be obtained. The stability of various possible action potentials and bifurcation in overdamped case are also discussed in this paper.

The Perturbation Finite Element Method for Solving Problems with Nonlinear Materials

Xie Zhi-cheng, Wang Rei-wu, Yang Xue-zhong, Chien Zhen-dong

1983, 4(1): 123-134.

Abstract(1777) PDF(703)

Abstract:
The perturbation method is one of the effective methods for solving problems in nonlinear continuum mechanics. It has been developed on the basis of the linear analytical solutions for the o-riginal problems. If a simple analytical solution cannot be obtained,we would encounter difficulties in applying this method to solving certain complicated nonlinear problems. The finite element method appears to be in its turn a very useful means for solving nonlinear problems,but generally it takes too much time in computation. In. the present paper a mixed approach,namely,the perturbation finite element method,is introduced,which incorporates the advantages of the two above-mentioned methods and enables us to solve more complicated nonlinear problems with great saving in computing time.Problems in the elastoplastic region have been discussed and a numerical solution for a plate with a central hole under tension is given in this paper.

Discussion on “Longitudinal Free Vibration of Inhomogeneous Elastic Straight Strut with a Variable Cross Section”

Bai Zhen-e, Liu Hsien-chih

1983, 4(1): 135-136.

Abstract(1836) PDF(442)

Abstract: