圆柱壳的非线性自由振动分析

本文分析了各向同性封闭圆柱壳的非线性自由振动。文中采用经典的非线性弹性力学方法推导了圆柱壳的大振幅运动方程,这些方程的静态形式与冯·卡门的板理论方程具有同样的精度。文中讨论了四种基本振动模态,并且还以数学公式的形式给出了一般的最终结果,一些例子以曲线给出结果,并进行了比较。结果还表明线性振动可以作为非线性振动的一种特例。     

一端弹性支撑的串列双柱和并列双柱在气流中自由端的振幅响应

本文研究了一端弹性支撑的并列双柱和串列双圆柱在气流中自由端的振幅响应，与单圆柱相比，在小间距时，串列双圆柱中前柱的横向振幅受到较强的激励。而在大间距时，振幅受到抑制，特别当Ｌ／Ｄ＝３．５和４．０时，其振幅响应仅为单柱的１／３左右，而对于后柱，则在大间距时，纵向振幅响应有所增大，而且后柱的振幅响应要比前柱的大得多，而并列双圆柱的自由端振幅基本上受到抑制，在Ｔ／Ｄ＞３．０之后，干扰很快减小到接近单个圆     

Coriolis Effect on the Linear Stability of Convection in a Porous Layer Placed Far Away from the Axis of Rotation

The linear stability theory is used to investigate analytically the Coriolis effect on centrifugally driven convection in a rotating porous layer. The problem corresponding to a layer placed far away from the axis of rotation was identified as a distinct case and therefore justifying special attention. The stability of the basic centrifugally driven convection is analysed. The marginal stability criterion is established as a characteristic centrifugal Rayleigh number in terms of the wavenumber and the Taylor number.     

An Analytical Study of Free Convective Boundary-Layer Flow in Porous Media: The Effect of Anisotropic Diffusitivity

The effect of an anisotropic thermal diffusivity tensor on the free convective boundary-layer flow in porous media is studied. Convection is induced by a generally inclined, uniformly heated surface embedded in a fluid-saturated medium. A third-order boundary-layer theory is presented in order to obtain accurate information on the effect of anisotropy on the rate of heat transfer into the porous medium. It is shown that the thickness of the resulting leading order boundary-layer flow depends on the precise nature of the anisotropy. On the other hand, the anisotropic diffusivity does not induce a fluid drift in the spanwise direction, a result which is different from that obtained in our earlier study of the effects of an anisotropic permeability. It is found that the second order temperature field does not contribute to the overall rate of heat transfer. Finally, we show that the third-order correction to the leading-order rate of heat transfer is given in terms of an explicit formula.     

Transformation of a breaking wave at a drop of a channel bottom

This paper gives results of an experimental study of incident and reflected waves of the bore type in the neighborhood of a sharp change in the channel bed level. It is shown that under conditions typical of accidents at ship locks, the wave height can reach 8 m.Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 46, No. 2, pp. 115–121, March–April, 2005.     

Near-Boundary Stress Wave Field in Anisotropic Plates under Impulsive Load

The stress wave field and the behavior of waves near the free boundary in an orthotropic plate and at the interface between two anisotropic media are studied. The results presented were obtained using the dynamic photoelastic method and optically sensitive fibrous models. Experimental data for impulsively loaded plates with various boundary conditions are analyzed     

FREE VIBRATION OF ANISOTROPIC RECTANGULAR PLATES BY GENERAL ANALYTICAL METHOD

According to the differential equation for transverse displacement function of anisotropic rectangular thin plates in free vibration, a general analytical solution is established. This general solution, composed of the composite solutions of trigonometric function and hyperbolic function, can satisfy the problem of arbitrary boundary conditions along four edges. The algebraic polynomial with double sine series solutions can also satisfy the problem of boundary conditions at four corners. Consequently, this general solution can be used to solve the vibration problem of anisotropic rectangular plates with arbitrary boundaries accurately. The integral constants can be determined by boundary conditions of four edges and four corners. Each natural frequency and vibration mode can be solved by the determinate of coefficient matrix from the homogeneous linear algebraic equations equal to zero. For example, a composite symmetric angle ply laminated plate with four edges clamped has been calculated and discussed.     

Numerical solution of Navier–Stokes equations using multiquadric radial basis function networks

A numerical method based on radial basis function networks (RBFNs) for solving steady incompressible viscous flow problems (including Boussinesq materials) is presented in this paper. The method uses a ‘universal approximator’ based on neural network methodology to represent the solutions. The method is easy to implement and does not require any kind of ‘finite element‐type’ discretization of the domain and its boundary. Instead, two sets of random points distributed throughout the domain and on the boundary are required. The first set defines the centres of the RBFNs and the second defines the collocation points. The two sets of points can be different; however, experience shows that if the two sets are the same better results are obtained. In this work the two sets are identical and hence commonly referred to as the set of centres. Planar Poiseuille, driven cavity and natural convection flows are simulated to verify the method. The numerical solutions obtained using only relatively low densities of centres are in good agreement with analytical and benchmark solutions available in the literature. With uniformly distributed centres, the method achieves Reynolds number Re = 100 000 for the Poiseuille flow (assuming that laminar flow can be maintained) using the density of , Re = 400 for the driven cavity flow with a density of and Rayleigh number Ra = 1 000 000 for the natural convection flow with a density of . Copyright © 2001 John Wiley & Sons, Ltd.     

轴对称薄壁结构自由振动的边界元分析

采用双互易法分析薄壁轴对称结构自由振动的特征频率以及特征模态.首先,采用径向基函数插值域积分里的位移,利用双互易法将域积分转化为子午面边界的积分.然后,将边界物理量、基本解和特解展开为傅里叶级数,沿环向积分后得到的边界积分方程可用于轴对称结构带体积力问题和受非对称载荷的动力学分析,其积分域为轴对称结构子午面边界上的线积分,进一步降低了问题的维度和离散的难度.文章详细探讨了源点处于对称轴的特殊情况,根据基本解和特解的退化形式,针对无体积力和有体积力分别给出了处理奇异矩阵的方案.对于薄壁结构,采用双曲正弦变换处理近奇异积分有效提高积分精度.最后将双互易法和双曲正弦变化应用于薄壁轴对称结构带体积力的静力学和自由振动分析.数值结果表明,文章提出的处理奇异矩阵的方法能够有效处理源点处于对称轴的情况;当圆筒厚高比为$10^{-3}$,边界元计算的特征频率的相对误差为$10^{-3}$,且优于有限元的结果.      

Numerical analysis of funnel formation during unsteady fluid outflow from a rotating cylindrical vessel

The main features of the unsteady outflow of a fluid from a cylindrical vessel rotating together with it at a constant angular velocity through a central drain hole in the bottom are studied. The software package STAR-CD tested on the results of experiments with water in the absence of rotation is used. Certain important features of the phenomenon under consideration related with the formation of vortex funnels in the fluid are established. The effect of the main control parameters of the problem, namely, angular velocity, viscosity, initial depth, etc., is analyzed.