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1957年  第1卷  第4期

庆祝《力学学报》创刊55周年专栏
远程星际航行
1957, 1(4): 351-360. doi: 10.6052/0459-1879-1957-4-1957-024
表面曲率对边界层的影响与边界层外缘附近的连结问题
1957, 1(4): 361-375. doi: 10.6052/0459-1879-1957-4-1957-025
正交各向异性的固定边矩形板
1957, 1(4): 379-390. doi: 10.6052/0459-1879-1957-4-1957-026
伟大十月社会主义革命前及苏维埃时期力学在莫斯科大学的发展
1957, 1(4): 391-415. doi: 10.6052/0459-1879-1957-4-1957-027
论文
THE EFFECTS OF SURFACE CURVATURE ON LAMINAR BOUNDARY-LAYER FLOW
In at least one case where the potential flow in the neighborhood of the outer edge of the boundary-layer varies rapidly, the boundary-layer theory has not been well understood. The interest in this problem led the author to the study of the laminar flow of a viscous incompressible fluid over a curved surface whose curvature, as has been found previously, displays rather large effects on the nature of boundary-layer flow. The specific point to be investigated here is the question as to how to join the boundary-layer with the potential flow. On the basis of the fact that the viscous effects decay exponentially in the lateral direction, it has been intuitively suggested that, in the neighborhood of the outer edge of the boundary-layer, the velocity in the main stream direction ui should asymptotically approach that in the main stream. Namely,where x and y are the coordinates shown in Fig. 1. Rc( = 1/ε2}, K and R denoteReynolds number, the curvature of the surface and a large constant respectively.By an order-of-magnitude analysis, Murphy obtained the following differential equation of the motion in a boundary-layer over a particular curved surface with curvature K = A/εα~1/2 ,along which the surface pressure gradient is zero. where A and f are respectively a small constant and the stream function; ηis definedas y/(2εx~1/2), and f is a function of nnnnnn only.In the case of zero pressure gradient, Murphy gave an approximate representation, of the potential flow as follows:which, by virtue of (1), loads toThe no-slip condition ad the wall yields:Herotofore the problem may be further simplified to a steaightforward numerical com-pulation. Since A is very small, assume a solution of ( 2 ) of this formBy expanding both sides of (8) into power serics of A, there result the following joining conditions:when η≤1From the no-slip condition at wall it followsSituilarly the differential equations for various orders may bo deduced from (2) and(5): The first equation of ( 7 ) appears in the case of the flat plate problem is well-known Blasius solution. It can be shown at the present stage that the solution of (7 ) and conditions given in ( 6) are consistent. Substituting ( 6 ) in ( 7 ) and neglecting terms of order e-η3 it indicates that expressions in ( 6 ) are the solutions of ( 7 ) in the region of large η. Consequently there is no difficulty in satisfying the joining conditions. With the joining conditions given in ( 6) and no-slip conditions, the equation of (7) can be easily solved numerically. For small 17, the following solutions are found: order A0order A1 whereorder A2 wherewhere a=1.32824, C1 and C2 are numerically found to be-5.767 and -2.3 respectively. It is noticed that Murphy's solution misses the part C1h1, and that a is not a constant, but a function of A. Similarly, the solutions of higher order can be obtained. In Fig. 3 the tangential velocities are calculated to order of A2, In conclusion, the following points may be noted:1. the boundary layer flow joins the potential flow asymptotically, that is, with an order of o(e-η3).2. the curvature has little effect on boundary layer, the effect on shearing stress τ0 is where μis the measure of viscosity.3. the curvature has larger effect on the velocity profile in the neighbourhood of the outer edge of the layer. The velocity for convex surface is greater than for a flat-plate, whereas for concave surface it is smaller. In the region of small η, the velocities may be approximately represented by the power series given above; however,in the region of large η, the velocity profiles can bo approximated by 1/(1+2Aη).
1957, 1(4): 375-378. doi: 10.6052/0459-1879-1957-4-1957-030
衍射问题的一个简化计算法
张厚玫
其中r为距离,k=2π/波长,c为波的傳播速度,t为时間,i=-1~(1/2).则可根据基尔霍夫公式把求任一点P的扰动的問題化为一个求面积分的問題。后来玛吉(Maggi),柯特勸(Kottler)等人又証明可把这面积分化为一个线积分,于是P点的扰动u为:
1957, 1(4): 416-422. doi: 10.6052/0459-1879-1957-4-1957-028
力学学报 第一卷作者索引
四画至七画平板上压制筋条的塑性流动固题具有加强圆孔的畏条的应力分析··.·················,·········……(弱)..........……,.············……(265)仁全培王王B.B.戈瞥别夫:律大十月砒会主义革命前及苏雅埃时期力学在莫斯科大学的癸展·····························································……=.( 391)?.
1957, 1(4): 423-426. doi: 10.6052/0459-1879-1957-4-1957-029
力学学报第一卷1957年
栗一驯戏们的日标。…………·。………………………………………………………………()均匀备向同性湍流在后期亵变时的涡性桔措—……··回…··回…··周培源、蔡树棠(3)透平机械畏叶片气体动力学阀题……、··,……·,…………………………吴仲华(川翼狱而杜体的弯曲周胚…………………·。……,………………………··林同贼( 49)狮性体动力学中的倒易定理及它的一些应用……………………,……··胡海昌(6)材刺·的应?..
1957, 1(4): 428-431. doi: 10.6052/0459-1879-1957-4-1957-032
力学学报1957年第一卷分类目录
翼截面柱体的弯曲問題………………………………………………林同驥1 49彈性体动力学中的倒易定理及它的一些应用………………………胡海昌1 63簡支于四角頂的矩形板的支座反力…………………………………胡海昌1 138关于苏联学者在壳体理論某些問題的工作(特別在扁壳理論方面)……………………X.M.穆士达利林华宝譯2 152关于彈性体固有频率的兩个变分原理………………………………胡??2 169考虑剪应变的彈性薄壁杆件的振动理....
1957, 1(4): 432-435. doi: 10.6052/0459-1879-1957-4-1957-031