Hygrothermal effects on the postbuckling of shear deformable laminated plates

The influence of hygrothermal effects on the postbuckling of shear deformable laminated plates subjected to a uniaxial compression is investigated using a micro-to-macro-mechanical analytical model. The material properties of the composite are affected by the variation of temperature and moisture, and are based on a micro-mechanical model of a laminate. The governing equations of a laminated plate are based on Reddy's higher-order shear deformation plate theory that includes hygrothermal effects. The initial geometric imperfection of the plate is taken into account. Two cases of the in-plane boundary conditions are considered. A perturbation technique is employed to determine buckling loads and postbuckling equilibrium paths. The numerical illustrations concern the postbuckling behavior of perfect and imperfect, antisymmetric angle-ply and symmetric cross-ply laminated plates under different sets of environmental conditions. The influences played by temperature rise, the degree of moisture concentration, the character of in-plane boundary conditions, transverse shear deformation, plate aspect ratio, total number of plies, fiber orientation, fiber volume fraction and initial geometric imperfections are studied.     

移相干涉仪环境微扰的外差检测及信号处理

对环境微振动干扰进行补偿可减小移相干涉测量的误差,其中振动量的检测是实现振动补偿的前提。以声光调制器作为光学移频器,在移相式平面干涉仪中组合成外差干涉测振系统,可以实现光程差微小变化(范围为0到1/2波长)的实时检测。在外差信号处理中采用单片RF/IF相位测量芯片直接对两路40MHz模拟信号进行比相,简化了通常使用的数字测相方法,其精确测相的典型非线性值小于1度。用该系统实际测量了周期性振动和地面冲击振动对干涉仪的影响,获得了干涉仪所受微振动的幅度和相位。     

弹性四连杆机构动力学的近似分析及低阶谐振现象的研究

用摄动理论对弹性四连杆机构的运动学关系进行了近似处理,用欧拉－贝努力理论建立了弹性动力学方程,从而对四连杆的低阶谐振现象给予解析分析。在一定边界条件下与有限元分析结果进行了对比,结果表明在曲柄长度与连杆长度相比较小的情况下,对四杆的一阶近似是有效的。     

Asymptotic analysis in fracture: An update

The wide applicability of asymptotics and singular perturbations in fracture is illustrated by reference to three examples: small scale yielding and its extensions which show the influence of constraint, crack bridging of a brittle matrix reinforced by fibres in the long crack limit, and the three-dimensional dynamic perturbation of a propagating crack. Possibilities for further research are indicated. This revised version was published online in July 2006 with corrections to the Cover Date.     

一维随机粗糙面的电磁散射研究

本文主要用小扰动近似方法(SPM)对一维随机粗糙面的电磁散射做了一些数值计算,并讨论了相关长度l,高度均方根h对基片微粗糙表面后向散射系数的影响。     

Homotopy analysis method for heat radiation equations

Here, the homotopy analysis method (HAM), one of the newest analytical methods which is powerful and easy-to-use, is applied to solve heat transfer problems with high nonlinearity order. Also, the results are compared with the perturbation and numerical Runge–Kutta methods and homotopy perturbation method (HPM). Here, homotopy analysis method is used to solve an unsteady nonlinear convective–radiative equation containing two small parameters of ?₁ and ?₂. The homotopy analysis method contains the auxiliary parameter h¯, which provides us with a simple way to adjust and control the convergence region of solution series.     

Higher-Order Properties of the ‘Exchange Rate Dynamics Redux’ Model

In the ‘exchange rate dynamics redux’ model of Obstfeld and Rogoff (1995, Journal of Political Economy, 103(3), 624–660), the short-run and the long-run changes in the net foreign asset are the same. This equivalence is consistent with the first-order linear approximation of the model; but is inconsistent with the long-run consumption smoothing behavior. This paper extends the “redux” model by approximating the changes in the net foreign asset with the second-order perturbation method. This higher-order approximation illustrates that the equivalence does not hold and the difference between the short-run and the long-run changes is of the second order.      

Perturbation LDA: Learning the difference between the class empirical mean and its expectation

Fisher's linear discriminant analysis (LDA) is popular for dimension reduction and extraction of discriminant features in many pattern recognition applications, especially biometric learning. In deriving the Fisher's LDA formulation, there is an assumption that the class empirical mean is equal to its expectation. However, this assumption may not be valid in practice. In this paper, from the “perturbation” perspective, we develop a new algorithm, called perturbation LDA (P-LDA), in which perturbation random vectors are introduced to learn the effect of the difference between the class empirical mean and its expectation in Fisher criterion. This perturbation learning in Fisher criterion would yield new forms of within-class and between-class covariance matrices integrated with some perturbation factors. Moreover, a method is proposed for estimation of the covariance matrices of perturbation random vectors for practical implementation. The proposed P-LDA is evaluated on both synthetic data sets and real face image data sets. Experimental results show that P-LDA outperforms the popular Fisher's LDA-based algorithms in the undersampled case.     

On the background and biresonant components of the random response of single degree-of-freedom systems under non-Gaussian random loading

The variance of the response of a single degree-of-freedom system subjected to a low frequency excitation is usually decomposed into its background and resonant contributions. In this paper we aim at the formulation of such a decomposition for the third statistical moment, which should in principle sidestep the heavy double integration of the bispectrum of the response. In large finite element models, the estimation of the bispectrum of the loading for a given frequency (ω₁,ω₂), which is a necessary stage towards estimation of the response, is the most expensive computational task. We therefore formulate the problem with the underlying constraint that the number of estimations of the bispectrum of the force be kept as small as possible. Invoking the perturbation theory in the context of the computation of integrals, we propose to decompose the third moment into background and biresonant components with expressions that are not trivially adapted from the decomposition of the variance. Thanks to the proposed method, the double integration of the bispectrum is avoided and represents accurately the response of lightly to moderately damped structures under a low-frequency loading. The formal expression for the biresonant component still requires an integration that should preferably be avoided. In the second part of the paper, we then investigate the practical implementation of the proposed formula and study the possible application of local, global or hybrid numerical approximations of that remaining integral, so as to further increase the computational efficiency. Finally two numerical experiments illustrate the prospect of the proposed method: the third statistical moment of the response is accurately computed with less than 20 estimates of the bispectrum of the loading, whereas an advanced numerical procedure for the double integration would require a mesh of probably more than (a) thousand(s) points.     

Theoretical and numerical analysis of convective heat transfer in the rotating helical pipes

In terms of the tensor analysis technique, the relative N-S equations and the energy equation in a rotating helical coordinate system are presented in this paper. Convective heat transfer in the rotating helical pipes with circular cross-section is investigated employing theoretical and numerical method. A perturbation solution up to the secondary order is obtained for a small Dean number. Variations of the temperature distribution with the force ratio (the ratio of the Coriolis force to the centrifugal force), the curvature and the torsion are discussed in detail. Present studies also show the natures of the Nusselt number, as well as the effects of the force ratio, the curvature, and the torsion. This study explores many new characteristics of convective heat transfer in the rotating helical pipes and covers wide ranges of parameters.