次亚正定矩阵的行列式不等式

给出了次亚正定矩阵的概念和它的一系列充要条件 ,得出了许多新的结果 ,将 Hadamard,Minkowski,Ostrowski-Taussky,Ky Fan,Openheim等关于对称正定矩阵的著名行列式不等式推广到了一类非对称矩阵上 .     

一类加强不等式的推广

本文给出了 n个正数 x1 ,x2 ,… ,xn 的如下不等式 :∏nk=1( xαk+x-αk )≥ ( Aαn( x) +A-αn ( x) ) n ,每个 xk≤ xα,∏nk=1( xαk+x-αk )≤ ( Aαn( x) +A-αn ( x) ) n ,每个 xk≥ e.其中 α>0 ,xα=[4α2 +1 +2 α]12α ,常数 e=2 .71 81 82 81 8… ,An( x) =1n∑nk=1xk.     

The solitary waves in a gradually varying channel of arbitrary cross-section

In this paper, the solitary waves in an arbitrary cross-section channel which gradually changes in the streamwise have been studied. TheKdV equation with slowly varying coefficients is derived. Thus, we produced the first term of its asymptotic solution, travel speed of soiltary waves and the relation between the amplitude of wave and the geometric size of channel. The results have been applied to the cases of triangular and rectangular channels. For the channel with varying depths and breadths they are fairly consistent with those of Johnson, Shuto and Mile.     

Pinpoint calculation of tooth deflection on spur gear by means of method of complex variables in plane elasticity

This paper ineorporated and developed the method originated by AIDA.TERACCHI. and NAGAMUYA. to which a high value is set presently at home andabroad, in which the stress and deflection of tooth on spurgears are calculated by means ofthe method of complex variables in plane elasticity. In this paper, their approximatesolution was developed to become exact solution. The accuracy of the mapping shape oftooth was increased. It was mentioned that the mapping function was expressed by fivefractional terms. with the mapping error being less than 1%m.A calculating principle wasproposed to find out the displacement of contact point in relation to central line of theadjacent gear tooth affecting the quality of mesh of gears directly.The computer programwas made, and according to the computed results.the figures were given so that thedisplacement of the contact point in the normal direction can be calculated conveniently forengineering calculation.     

On a class of method for solving problems with random boundary notches and/or cracks

As we know, problems with boundary imperfections (notches or cracks) are the more important one in practical fracture analysis. Frequently, these imperfections would appear in the boundaries of the bodies as a randomly distributed group, and under the loading circumstances would grow up to be unstable cracks which induces catastrophic fracture of the bodies. For right evaluation the fracture behavior of the bodies with such boundary imperfections, it demands mathematical solutions for problems with random boundary notches and/or cracks.     

复杂非线性转子-轴承系统动力特性数值分析

研究非线性高维复杂转子－轴承系统的动力特性。针对系统的局部非线性特征,给出了一种降阶及配套动力积分方法。降阶系统仍保持局部非线性特征,非线性响应数值积分所需的迭代只需在局部非线性的维数上执行。对于油膜力无封闭解的实际轴承,采用变分不等方程有限元法求解Reynolds边值问题,使得油膜力及其Jacobian矩阵的计算变得非常简单明了且与具有协调一致的精度。应用上述方法计算分析了一双跨、椭圆轴承－转子系统的不平衡响应,数值结果展现了系统丰富复杂的非线性现象。     

Acoustoelastic effect simulation by time–space finite element formulation based on quadratic interpolation of the acceleration

Acoustoelastic effect describes the change of ultrasound velocity due to the initial stress. Its simulation involves a numerical analysis of nonlinear elastodynamics and requires high accuracy in the time domain. A time–space finite element formulation, derived from the quadratic interpolation of the acceleration within a time segment, is proposed for an accurate simulation of the acoustoelastic effect in the present study. Ten different integration schemes are generated based on this formulation and nine of them are found to be conditionally stable. Among the nine stable schemes, one is found to obtain a spectral radius of one when the normalized step ratio is less than 5.477, indicating no numerical dissipation or numerical divergence. Compared with integration schemes from previous studies, this integration scheme demonstrates better performance in calculation accuracy and energy conservation. A two-stage approach, namely the static stage and the dynamic stage, has been employed in the simulation of the acoustoelastic effect. The former stage is adopted to obtain the initial stress and the latter stage, where the proposed integration scheme is implemented, is adopted to simulate the ultrasound propagation in an initial stress state. The simulation results of the dynamic stage show that the ultrasound velocity increases in a compression stress state and decreases in a tension stress state for aluminum alloy, which is in good agreement with previous experimental studies. Together with the simulation result of the static stage, it is conjectured that the acoustoelastic effect results from the stress-dependent elastic modulus.