基础阻抗力的一种时域算法

该文提出一种计算基础阻抗力的时域算法。通过引入一个辅助变量并执行逆傅里叶变换,将基础动力刚度的连续时间有理近似实现为时域高阶常微分方程;进一步定义不同时刻的辅助变量为多个不同的辅助变量,将高阶微分方程等价地转化为以状态空间描述的一阶常微分方程组。微分方程组的稳定性和精度等价于连续时间有理近似的稳定性和精度。之后采用四阶龙格-库塔公式数值地求解获得的一阶微分方程组。典型基础振动问题的分析表明了该文方法的有效性。     

径向载荷作用下复合材料圆柱壳的非线性动力屈曲

采用半解析法求解径向阶跃载荷作用下复合材料圆柱壳的非线性动力屈曲。基于一阶剪切变形理论，由Hamilton原理推导出包含横向剪切变形以及几何初缺陷的圆柱壳的非线性动力方程，位移及载荷沿周向采用级数展开，由Galerkin方法得到微分方程组，通过有限差分法求解；根据响应情况，由B—R准则判定屈曲，确定屈曲临界载荷。     

Optical screen for direct projection of integral imaging

We describe a way to display three-dimensional images by integral imaging using an ordinary projector. We first explain a method that uses a large-aperture converging lens, then we explain the proposed method that uses two sets of lens array. Based on the principle of this new approach, front projection as well as rear projection is possible. Only a proper viewing area can be formed on the optical screen by this method, which improves the brightness of images on the screen. The projector itself does not need an additional optical system. We report on the results of an experiment carried out to confirm the validity of the proposed method.     

圆锥壳的渐进分布传递函数解

本文给出一种求解圆锥薄壳线弹性变形的渐进传递函数方法。壳体的三个位移函数首先沿环向展开为Fourier级数,由此得到解耦的偏微分方程,它包括一个空间变量和一个时间变量。对时间变量进行Laplace变换后进一步将其简化为含复参数s的常微分方程,它的系数是坐标的函数。引入小参数ε＝L／r0sinα,用摄动方法得到一组常微分方程,它可以用渐进分布传递函数方法求解。将各子锥段的解进行综合,构造出了由多段锥壳构成的组合壳体的传递函数解。文中给出了数值算例并与有限元的结果进行了比较。     

On the estimation of failure probability having prescribed statistical moments of first passage time

A method of estimating the probability density function and cumulative distribution function when only the ordinary or central moments of the distribution are known is examined. The technique is used in conjunction with previous work which yields the ordinary moments of time to first passage failure to obtain accurate estimates of the failure probability for two representative oscillators. The results are then compared to those obtained by a nearly exact numerical scheme.     

Application of the Newton method to the so-called integral equation method in transonic flow

Summary A suitable approximation of the Newton method and the complete Newton method are applied to the so-called integral equation method in transonic flow. Results of example calcultion are compared. At first the methods are explained using the example of an ordinary differential equation of first order occurring in the field of hypersonic flow with a connection to the method of Picard-Lindelöf.     

Meshless local boundary integral equation method for 2D elastodynamic problems

A new meshless method for solving transient elastodynamic boundary value problems, based on the local boundary integral equation (LBIE) method and the moving least squares approximation (MLS), is proposed in this paper. The LBIE with the MLS is applied to both transient and steady‐state (Laplace transformed) elastodynamics. Applying the MLS approximation for spatially dependent terms in the first approach, the LBIEs are transformed into a system of ordinary differential equations for nodal unknowns. This system of ordinary differential equations is solved by the Houbolt finite difference scheme. In the second formulation, the time variable is eliminated by using the Laplace transformation. Unknown Laplace transforms of displacements and traction vectors are computed from the LBIEs with the MLS approximation. The time‐dependent values are obtained by the Durbin inversion technique. Copyright © 2003 John Wiley & Sons, Ltd.     

The time-dependent Green's function of the transverse vibration of a composite rectangular membrane

A new method for the approximate computation of the time-dependent Green's function for the equations of the transverse vibration of a multi stepped membrane is suggested. This method is based on generalization of the Fourier series expansion method and consists of the following steps. The first step is finding eigenvalues and an orthogonal set of eigenfunctions corresponding to an ordinary differential operator with boundary and matching conditions. The second step is a regularization (approximation) of the Dirac delta function in the form of the Fourier series with a finite number of terms, using the orthogonal set of eigenfunctions. The third step is an approximate computation of the Green's function in the form of the Fourier series with a finite number of terms relative to the orthogonal set of eigenfunctions. The computational experiment confirms the robustness of the method.     

Hybrid surrogate-model-based multi-fidelity efficient global optimization applied to helicopter blade design

A multi-fidelity optimization technique by an efficient global optimization process using a hybrid surrogate model is investigated for solving real-world design problems. The model constructs the local deviation using the kriging method and the global model using a radial basis function. The expected improvement is computed to decide additional samples that can improve the model. The approach was first investigated by solving mathematical test problems. The results were compared with optimization results from an ordinary kriging method and a co-kriging method, and the proposed method produced the best solution. The proposed method was also applied to aerodynamic design optimization of helicopter blades to obtain the maximum blade efficiency. The optimal shape obtained by the proposed method achieved performance almost equivalent to that obtained using the high-fidelity, evaluation-based single-fidelity optimization. Comparing all three methods, the proposed method required the lowest total number of high-fidelity evaluation runs to obtain a converged solution.     

The mixed-type integral equations for transient elastodynamic plane crack problems

In the present paper, by use of the boundary integral equation method and the techniques of Green fundamental solution and singularity analysis, the dynamic infinite plane crack problem is investigated. For the first time, the problem is reduced to solving a system of mixed-typed integral equations in Laplace transform domain. The equations consist of ordinary boundary integral equations along the outer boundary and Cauchy singular integral equations along the crack line. The equations obtained are strictly proved to be equivalent with the dual integral equations obtained by Sih in the special case of dynamic Griffith crack problem. The mixed-type integral equations can be solved by combining the numerical method of singular integral equation with the ordinary boundary element method. Further use the numerical method for Laplace transform, several typical examples are calculated and their dynamic stress intensity factors are obtained. The results show that the method proposed is successful and can be used to solve more complicated problems.     

Bending Analysis of Classical Symmetric Laminated Composite Plates by the Strip Element Method

A new formulation of strip element method based on classical laminated plate theory is derived for the bending analysis of laminated composite plates. In this method, an infinite-length plate is first considered and is discretized into a set of strip elements in the width direction. The principle of minimum potential energy is applied to obtain the ordinary differential equations, which are functions of only the coordinate in the length direction. These differential equations can then be solved analytically. The boundary conditions on the length coordinate direction are finally used to determine the deflection distribution in the plate. The strip element solutions are presented for a rectangular laminated composite plate with various boundary conditions and load cases. The solutions are compared with those of the Rayleigh-Ritz method, and very good agreement is obtained.     

A generalized forward gradient procedure for rate sensitive constitutive equations

Many forward gradient schemes have been proposed for the time-integration of the stiff constitutive equations of rate sensitive solids. It is shown here that one of these methods can be interpreted as a hybrid ordinary differential equation integrator which combines explicit and semi-implicit Runge-Kutta methods. This observation permits development of higher order schemes, illustrated here by one of second order. An embedded first order estimate provides a reliable step-size control. The method is applied to an overstress model and to an internal variable model, and is used in a finite element analysis of hydrostatic bulging of sheet metal.     

Response spectral density determination for nonlinear systems endowed with fractional derivatives and subject to colored noise

A computationally efficient method for determining the response of non-linear stochastic dynamic systems endowed with fractional derivative elements subject to stochastic excitation is presented. The method relies on a spectral representation both for the system excitation and its response. Specifically, first the ordinary non-linear differential equation of motion is transferred into a set of non-linear algebra equations by employing the harmonic balance method. Next, the response Fourier coefficients are determined by solving these non-linear equations. Finally, repeated use of the proposed procedure yields the response power spectral density. Pertinent numerical examples, including a fractional Duffing and a bilinear oscillator, demonstrate the accuracy of the proposed method.     

High resolution speckle interferometry using virtual speckle pattern produced by information of deformation process

A high resolution new fringe analysis method for ESPI with only one camera is proposed by using features of speckle interferometry in a deformation process of a measured object. The profile of intensity of each speckle of the speckle patterns in the deformation process is analyzed by the Hilbert transform. A virtual speckle pattern for creating a carrier fringe image is produced artificially by using the information of profiles of intensities of speckles. The deformation map of the measured object can be detected by the virtual speckle pattern in an operation based on the spatial fringe analysis method. Experimental results show that the difference between the results by the new and the ordinary methods is 0.1 rad as standard deviation. From the results, it is confirmed that the high resolution measurement can be performed by this method the same as compared to the ordinary measurement method which needs to employ three speckle patterns.     

高聚物折射率的测量

本文提出两种测量高聚物折射率的简单方法，其一是基于洛仑兹－洛仑茨公式导出混合物质折射率公式，并由此发展成一种折射率的测量方法；其二是用溶液制膜法将高聚物制成薄膜，从而实现折射率的测量．两种测量都可用阿贝折射仪完成．     

覆冰四分裂输电线舞动研究

建立四分裂覆冰输电线的面内垂直和扭转两个方向的连续体耦合非线性动力学偏微分方程,利用Galerkin方法将偏微分方程转换为常微分方程.选初始攻角和面内结构阻尼为参数,应用中心流形理论并借助符号运算软件Mathematica程序,得到系统在分岔点处中心流形上的约化方程,并应用规范形理论对约化方程进行化简,得到系统极坐标下的Hopf分岔方程,研究了参数连续变化对系统稳定性及舞动幅值的影响.对系统进行数值分析得到了系统的运动相图和时程曲线,结果表明系统收敛于稳定的极限环.     

The Golden-Ten equations of motion

Golden Ten is an observation game which is played with a small ball rolling down in a large bowl. This paper describes the motion of the ball in the bowl by means of deterministic mechanical model, which leads to a set of ordinary second-order differential equations. A first impression of the solution is obtained through a numerical approximation, based on some preliminary estimates. Part of the solution is computed exactly, yielding a simple estimation procedure for the coefficient of air friction, which is one of the two main parameters controlling the system (the other parameter is the angle of inclination). An asymptotic solution method eventually leads to an approximate explicit solution, describing the motion of the ball as an elliptical spiral. One of the conclusions is a simple prediction strategy.     

Homotopy analysis of MHD boundary layer flow of an upper-convected Maxwell fluid

The problem of a magnetohydrodynamic (MHD) boundary layer flow of an upper-convected Maxwell (UCM) fluid is considered for the analytical solution using homotopy analysis method (HAM). The non-linear partial differential equations are transformed to an ordinary differential equation first taking boundary layer approximations into account and then using the similarity transformations. The analytical solution is presented in the form of an infinite series. The recurrence formulae for finding the coefficients are presented and the convergence is established. The effects of the Deborah number and MHD parameter is discussed on the velocity profiles and the skin friction coefficients. It is found that the results are in excellent agreement with the existing results in the literature for the case of hydrodynamic flow.     

On the contact of an inflated spherical membrane-fluid structure with a rigid conical indenter

The large deformations of a spherical membrane inflated by an incompressible fluid in contact with a frictionless rigid conical indenter are analyzed. The objective is to study the stress distribution and the fluid pressure in this membrane-fluid structure in response to contact with the conical indenter. The membrane is assumed to be homogeneous, elastic, and isotropic while the enclosed fluid is taken to be incompressible. The equilibrium equations of the membrane-fluid structure are expressed as a set of two first-order ordinary differential equations for the part of the membrane in contact with an indenter and four first-order ordinary differential equations for the part not in contact. A neo-Hookean material model is used to describe the material property of the membrane. The nonlinear system of ordinary differential equations is solved numerically using the shooting method.     

Non‐reflecting artificial boundaries for transient scalar wave propagation in a two‐dimensional infinite homogeneous layer

This paper presents an exact non‐reflecting boundary condition for dealing with transient scalar wave propagation problems in a two‐dimensional infinite homogeneous layer. In order to model the complicated geometry and material properties in the near field, two vertical artificial boundaries are considered in the infinite layer so as to truncate the infinite domain into a finite domain. This treatment requires the appropriate boundary conditions, which are often referred to as the artificial boundary conditions, to be applied on the truncated boundaries. Since the infinite extension direction is different for these two truncated vertical boundaries, namely one extends toward x →∞ and another extends toward x→‐ ∞, the non‐reflecting boundary condition needs to be derived on these two boundaries. Applying the variable separation method to the wave equation results in a reduction in spatial variables by one. The reduced wave equation, which is a time‐dependent partial differential equation with only one spatial variable, can be further changed into a linear first‐order ordinary differential equation by using both the operator splitting method and the modal radiation function concept simultaneously. As a result, the non‐reflecting artificial boundary condition can be obtained by solving the ordinary differential equation whose stability is ensured. Some numerical examples have demonstrated that the non‐reflecting boundary condition is of high accuracy in dealing with scalar wave propagation problems in infinite and semi‐infinite media. Copyright © 2003 John Wiley & Sons, Ltd.