Application of the modified method of multiple scales to solving the problem of a thin clamped circular plate of a very large deflection

In this paper,asymptotic behaviour of the solution to the problem of a thin clamped circular plate under uniform normal pressure at very large deflection is restudied by means of the modified method of multiple scales given in[1?].The result presented herein is in good agreement with the one obtained by professor Chien Wei-zang who first proposed the method of composite expansions to solve this problem in[3].However,by contrast,the advantage of the modified method of multiple scales it seems to be relatively simpler than the method used in[3].It is also shown that the restriction of the method of paper[1-2]pointed out in paper[4]is not essential,and several computation errors in[3]are corrected as well.     

Random fixed point theorems for commuting random operators in probabilistic functional analysis

Random fixed point theorems are of fundamental importance in probabilistic functional analysis. In complete separable metric space random fixed point theorems have been discussed by Bharucha-Reidf1/27, Hans[3], Itohf4,5J and the author’s papers[15-20].In this paper we obtain a random fixed point theorem for commuting random operators in probabilistic functional analysis. Our results generalize some important results also extend and unify some results in Jungck[6,7,8]t Das and Naiki[9] as well as Bhoades[10] adn ciric[11].     

利用钻孔法测定残余应力问题

钻孔法是测量残余应力的一个重要方法。本文就有关文献所提供的A、B值进行分析和比较。对试验中由于贴片钻孔所造成的偏差提出了修正公式。此公式使用简便,经验算,误差在10％以内。     

THE FIRST-ORDER APPROXIMATION OF NON-KIRCHHOFF-LOVE THEORY FOR ELASTIC CIRCULAR PLATE WITH FIXED BOUNDARY UNDER UNIFORM SURFACE LOADING (Ⅲ)──NUMERICAL RESULTS

1ShanghaiUniversity;ShanghaiInstituteofAppliedMathematicsandMechanics,Shanghai200072P.R.ChinaIX.NondimensionalEquationsandBoundaryConditionsoftheFirstOrderApproximateTheoryFortheconvenienceofnumericalcomputation,webeginbytransformingthedifferentialequatio…     

Comment on “Precise Control for vibration of rigid-flexible mechanical arm”

The results presented in a paper by Zichen et al. [1] has some flaws. The idea in [1] is to combine assumed modes method using an integration method with optimal control adaptive law for a spatial rigid-flexible mechanical arm as an underactuated mechanical systems (UMS). The nonlinear dynamic equation formulation from reference [6] is incorrectly used in [1]. Furthermore, the control law approach in [1] was to achieve a similar result for a UMS rigid manipulator as the one published by Spong [2] and a proper citation must have been credited.     

纤维束增强复合材料细观统计破坏理论

本文分别用剪滞模型和载荷几何局部分配法则分析了纤维束和束中纤维的载荷集中。在此基础上,利用裂纹临界核模型的统计方法,建立了小纤维束(须考虑纤维束的边界影响)和大纤维束增强复合材料的细观统计破坏准则,并用这两个准则研究了纤维束增强复合材料的断裂强度问题,所算得的强度和裂纹临界长度的合理性表明了这两个准则的正确性。     

无拉力Winkler地基梁静力分析的线性互补法

提出了无拉力Ｗｉｎｋｌｅｒ地基梁弯曲的线性互补法．将地基反力作为未知量而获得了一组地基与梁之间相对竖向位移和反力的线性互补方程．计算结果表明本文解与文［２，３］解吻合良好。     

Bending of a circular cylinder containing a crack

The study of bending of cracked circular cylinders is of more significance. The bending of cylinders containing radical crack or cracks was discussed by refs. [1]–[4] and that of concentrically craked circular cylinders was studied by [5]. Continuing [6] and using complex variable methods in elasticity, this paper deals with the bending problems of a circular cylinder, containing an internal linear crack at any position under an acting force perpendicular to the crack. The general forms of displacements, stresses, and stressintensity factors, expressed in terms of series, are obtained and to this bending problems with small Ah are presented good approximate formulas for the stress-intensity factors whose variations with the center of the crack are analysed. Finally, the twist angle per unit length and the center of bending for the radically cracked circular cylinder, one of whose crack-tips is located at the origin, have been computed and the results are almost the same as that calculated in [1].     

On Hashin–Shtrikman-type bounds for nonlinear conductors

For linear composite conductors, it is known that the celebrated Hashin–Shtrikman bounds can be recovered by the translation method. We investigate whether the same conclusion extends to nonlinear composites in two dimensions. To that purpose, we consider two-phase composites with perfectly conducting inclusions. In that case, explicit expressions of the various bounds considered can be obtained. The bounds provided by the translation method are compared with the nonlinear Hashin–Shtrikman-type bounds delivered by the Talbot–Willis (1985) [2] and the Ponte Castañeda (1991) [3] procedures.     

具有中心圆孔的[0°/90°]_s复合材料层合板的边界元法分析

本文在文[1]的基础上,采用子结构法建立了多层复合板的边界元方法,对具有中心园孔[0°/90°]_s的层合板的层间应力作了计算,同有限元法的结果进行了比较,结果表明,应用边界元法处理这类问题,单元划分少,节约了计算机时,而且有较高的计算精度。     

横观各向同性轴对称问题的加权残数法及其工程应用

利用文[1,5]的理论,本文提出用两个调和函数的方法求解横观各向同性的轴对称问题,将它引入加权残数法,推得了一系列简洁的边界型最小二乘配法公式,就结构工程和岩土工程的两个例题作了计算,得到了有用的结论。本文的方法比列赫尼茨基的重调和函数法更为简便。     

THE APPLICATION OF MULTI－SCALE PERTURBATION METHOD TO THE STABILITY ANALYSIS OF PLANE COUETTE FLOW

ＴＨＥＡＰＰＬＩＣＡＴＩＯＮＯＦＭＵＬＴＩ－ＳＣＡＬＥＰＥＲＴＵＲＢＡＴＩＯＮＭＥＴＨＯＤＴＯＴＨＥＳＴＡＢＩＬＩＴＹＡＮＡＬＹＳＩＳＯＦＰＬＡＮＥＣＯＵＥＴＴＥＦＬＯＷＺｈｏｕＺｈｅ－ｗｅｉ（周哲玮）（ＳｈａｎｇｈａｉＵｎｉｖｅｒｓｉｌｙ;Ｓｈａｇ...     

SH Waves in(1-x)Pb(Mg_(1/3)Nb_(2/3))O_(3-x)PbTiO_3 Piezoelectric Layered Structures Loaded with Viscous Liquid

The velocity dispersion and attenuation of shear horizontal(SH) waves in a layered piezoelectric structure loaded with viscous liquid is studied,where the(1- x)Pb(Mg_(1/3)Nb_(2/3))O_(3-x)PbTiO_3[PMN-xPT]single crystal is chosen as the piezoelectric layer.The PMN-xPT is being polarized along[011]_c and[001]_c so that the macroscopic symmetries are mm 2 and 4 mm,respectively.For the nonconductive liquid,the electrically open and shorted conditions at the interface between the liquid and the piezoelectric layer are considered.The phase velocity equations are derived analytically.The effects of the electrically boundary condition,the viscous coefficient and mass density of liquid as well as the thickness of the PMN-xPT layer on the phase velocity and attenuation are graphically illustrated.The results show that the phase velocity for the[011]_c polarized PMN-0.29 PT is much smaller than that for the[001]_c polarized PMN-0.33 PT,and the effects of viscous coefficient and piezoelectric layer thickness on the phase velocity for the[011]_c case are stronger than that for the[001]_c case.In addition,the electrical boundary conditions have an obvious influence on the propagation behaviors.These results can be useful for the designs and applications of acoustic wave devices and liquid biosensors.     

Finite Difference Method for the Acoustic Radiation of an Elastic Plate Excited by a Turbulent Boundary Layer: A Spectral Domain Solution

A finite difference method is developed to study, on a two-dimensional model, the acoustic pressure radiated when a thin elastic plate, clamped at its boundaries, is excited by a turbulent boundary layer. Consider a homogeneous thin elastic plate clamped at its boundaries and extended to infinity by a plane, perfectly rigid, baffle. This plate closes a rectangular cavity. Both the cavity and the outside domain contain a perfect fluid. The fluid in the cavity is at rest. The fluid in the outside domain moves in the direction parallel to the system plate/baffle with a constant speed. A turbulent boundary layer develops at the interface baffle/plate. The wall pressure fluctuations in this boundary layer generates a vibration of the plate and an acoustic radiation in the two fluid domains. Modeling the wall pressure fluctuations spectrum in a turbulent boundary layer developed over a vibrating surface is a very complex and unresolved task. Ducan and Sirkis [1] proposed a model for the two-way interactions between a membrane and a turbulent flow of fluid. The excitation of the membrane is modeled by a potential flow randomly perturbed. This potential flow is modified by the displacement of the membrane. Howe [2] proposed a model for the turbulent wall pressure fluctuations power spectrum over an elastomeric material. The model presented in this article is based on a hypothesis of one-way interaction between the flow and the structure: the flow generates wall pressure fluctuations which are at the origin of the vibration of the plate, but the vibration of the plate does not modify the characteristics of the flow. A finite difference scheme that incorporates the vibration of the plate and the acoustic pressure inside the fluid cavity has been developed and coupled with a boundary element method that ensures the outside domain coupling. In this paper, we focus on the resolution of the coupled vibration/interior acoustic problem. We compare the results obtained with three numerical methods: (a) a finite difference representation for both the plate displacement and the acoustic pressure inside the cavity; (b) a coupled method involving a finite difference representation for the displacement of the plate and a boundary element method for the interior acoustic pressure; (c) a boundary element method for both the vibration of the plate and the interior acoustic pressure. A comparison of the numerical results obtained with two models of turbulent wall pressure fluctuations spectrums - the Corcos model [3] and the Chase model [4] - is proposed. A difference of 20 dB is found in the vibro-acoustic response of the structure. In [3], this difference is explained by calculating a wavenumber transfer function of the plate. In [6], coupled beam-cavity modes for similar geometry are calculated by the finite difference method. This revised version was published online in July 2006 with corrections to the Cover Date.     

BUCKLING AND POST-BUCKLING OF ANNULAR PLATES UNDER xNON-AXISYMMETRIC PLANE EDGE FORCES

On the basis of both the general theory[1,2]and the finite element method[4]ofperforated thin plates with large deflection,the buckling and post-buckling of annular platesunder non-axisymmetric plane edge forces are studied.     

General digital picture processing and texture analysis for photoelasticity

In this paper, a general digital picture processing and texture analysis for photoelasticity is developed. Overcoming some defects of references [2] and [3], it presents an effective method to analyse fringe patterns of the photoelasticity. By means of the trigonometric function relationship between the light intensity I and the image fringe order N, the equations of the fringe order N on brightness Z are deduced, and the mechanical parameters are thus obtained. We established a system of sigital picture processing and texture analysis for photoelasticity, which is called OYC-1 system. Finally, this system is checked with an example. It is found that the differences between measured results and the theoretical values are within 2.3 percent.This paper is supported by the science funds of the Academia Sinica.     

On Mode Interactions for a Weakly Nonlinear Beam Equation

In this paper an initial-boundary value problem for a weakly nonlinear beam equation with a Rayleigh perturbation will be studied. It will be shown that the calculations to find internal resonances in this case are much more complicated than and differ substantially from the calculations for the weakly nonlinear wave equation with a Rayleigh perturbation as for instance presented in [3] or [7]. The initial-boundary value problem can be regarded as a simple model describing wind-induced oscillations of flexible structures like suspension bridges or iced overhead transmission lines. Using a two-timescales perturbation method approximations for solutions of this initial-boundary value problem will be constructed.     

A new approximate analytical solution of the ideal potential flow around a circular cylinder between two parallel flat plates

In ref. [1], Lin obtained an approximate analytical solution of the ideal potential flow around a circular cylinder between two parallel flat flates.In this paper, the author shows that one may obtain the result coinciding with that obtained in ref. [1] by making use of the Shvez's method^[2]. Morever, we can obtain a more accurate result than that obtained in ref. [1], if we make use of the improved Shvez's method^[2]. Some calculating examples are presented.     

结构的多机并行分析Ⅱ——PPCG法的实现

以多Transputer系统为应用的硬件环境,本文讨论文[1]中提出的PPCG1法和PPCG2法的实现问题,给出了用3L并行Fortran语言编写PPCG法应用程序的实现方法。特别讨论了与通讯有关的计算,给出了有关的并行Fortran程序段。最后用算例说明了PPCG1和PPCG2法的有效性。     

Reissner型板中应力强度因子的近似方程和近似解法

本文在文献[1],[2]的基础上对Reissner型板进行分析,发现与经典板理论类似的近似方程用于求解Reissner型板的断裂问题是有效的,并用能量法解得受弯边裂纹和中心裂纹板的应力强度因子。将结果与文献[3]比较表明,用本文的近似方法求解应力强度因子方法简便且精度较高。