近似平衡多项式加速度动力显式算法

利用已知初始时刻的信息，建立一种可以取到任意阶高精度的多项式加速度单步隐式算法。在该隐式方法中，待采解方程纽系数矩阵中质量阵的系数远远大于阻尼阵和剐度阵的系数，略去非对角阻尼阵和非对角刚度阵对方程组的影响，得到一种近似平衡多项式加速度动力显式计算方法。此方法的精度主要由加速度多项式插值的项数、步长、质量阵的每件数、质量刚度比（质量阵和刚度阵的范数之比）决定。在此基础上给出了这种算法的通式，进行了精度分析，结果表明：如果时间步长h足够短，n次加速度近似平衡动力显式算法的精度可以达到O（hn＋1）。算例采用5次加速度近似平衡显式算法，计算结果的精确性证明了本算法的可行性。     

平方非线性振动系统1／2亚谐解的分析

采用二次近似的平均法，利用maple和matlab编制程序，对一类具有平方非线性的受迫振动系统进行了研究。得到该类系统主共振和1／2亚谐共振时的性态，研究发现对于二次非线性的系统只有采用二次近似才能得到较好的结果，并将该结果与数值积分的结果比较，发现所用的设解形式及二次近似均能较好的反映平方非线性项的影响。另外，研究还发现只有在一定的参数范围内才存在1／2亚谐解。本文的研究方法对分析非对称振动系统有一定参考价值。     

基于机器学习对三角堰流量系数的预测研究

为了准确高效得出三角堰泄流系数的大小，本研究基于广义神经网络、最小二乘支持向量机和遗传规划对三角堰流量系数进行智能建模．将无量纲参数堰顶角、弗劳德数、堰顶长与堰高之比、堰顶长与堰顶水深之比作为模型输入参数，流量系数作为模型输出参数．研究表明，最小二乘支持向量机性能优于广义神经网络和遗传规划．在测试阶段，均方根误差为0.000 73，散射指数为0.001 02，决定系数为0.999 59，最大误差为1.7 %．该模型精度较高，预测值较准确，具有较强的工程适用性．本研究通过对三角堰流量系数进行智能建模，采用机器学习对非线性物理关系进行高精度拟合，准确高效得出三角堰流量系数的大小，可为水利水电工程设计人员和我国灌区精确量水用水提供一种新的方法和思路．     

冲击温度的近似计算方法

将冲击温度的计算归纳为三种近似方法，并对这三种方法进行了概述，同时还给出了一些材料参数的估算方法．在利用等熵线计算冲击温度时，从冲击绝热线出发推导了一个半解析的等熵方程．计算了铁的冲击温度，并与实验测量值作了比较．结果表明，利用三项式物态方程并考虑熔化相变潜能的影响后算得的冲击温度与测量值符合得比较好，另外，本文还对影响冲击温度计算值的若干因素进行了分析．     

轴对称冲击有限元一致质量矩阵迭代解

给出高速冲击动力有限元一致质量矩阵解的迭代过程，即把集总质量矩阵解作为初值进行有限次迭代得到满足工程需要的一致质量矩阵近似解．实际算例说明，一致质量近似解较集总质量解改善了对应力波传播过程的分析，而且在高速冲击计算中能给出与实验接近的计算结果．     

基础埋置深度对土壤——多层结构动力相互作用的影响

本文利用Baranov-Novak关于埋置基础水平与摆动耦合振动的结果及Veletsos与Verbic关于粘弹性地基振动的结果,给出了与埋置基础等效的无埋置基础的动力刚度系数及阻尼系数,并以钢筋混凝土框架结构为例来说明基础埋置深度对土壤——多层结构动力相互作用的影响。计算结果表明,结构体系第一振型的弹性位移及阻尼比并不总是随埋深比的增加而单调变化;在一定的范围内,结构体系基础有埋深时的基频与无埋深时的基频之比与埋深比之间有着近似的线性关系;结构体系的地震位移响应基本上是由第一振型控制的。     

加权最小二乘无网格法

在最小二乘法和移动最小二乘近似的基础上提出了加权最小二乘无网格法．该方法除节点外又引入了一些辅助点，控制方程在所有节点和辅助点处的残差用最小二乘法予以消除，边界条件用罚函数法引入．另外对移动最小二乘近似进行了改进，并给出了最小二乘法中泛函的简化格式，因而提高了计算效率．与配点法相比，新方法精度高，稳定性好，并且系数矩阵是对称正定矩阵．与Galerkin法相比，该方法不需要进行高斯积分，因而计算量小．算例表明该方法具有效率高、精度高和稳定性好等优点，并且易于实现．     

平面理性四节点及五节点四边形有限元

推导了平面四点及五点理性元公式，具有完全二次解的插值近似，完全通过分片试验，不发生零能模式，不发生剪切自锁。数例表明本文理性元的优越性。     

近似评价函数确定运动极限及其在形状优化中的应用

针对二维连续体形状优化过程中解析灵敏度求解困难的情况,利用响应面方法将目标函数和约束函数近似显式化,建立序列二次规划模型。为了保证优化模型的可靠性,结合试验设计方法,以较少的结构分析代价构造约束响应面,从而能够快而稳定地收敛,本文重点研究并建立了二次近似评价函数用以计算自适应运动极限的策略。算例说明这种策略是有效而稳定的。     

固体二次冲击雨贡纽线的一个表示式

根据文献[1],本文导出了固体材料二次冲击雨贡纽线的一个表示式。在二次冲击雨贡纽线写为D2=C+Au2+Bu22形式时,给出了系数C,A和B的函数关系式。文中根据所导出的公式,并在对主雨贡纽线取为D1=Co+1形式的条件下,对铅、铀两种材料的二次雨贡纽点作了数值计算,所得结果与Neal的实验结果是符合的。     

A three dimensional approach to model steel wire ropes used in high energy absorber apparatus

The modeling method and dynamical characteristics of steel wire ropes has been researched for several decades. In the past, steel wire ropes were usually modeled as a two dimensional system, which was only suitable for the planar motion. Also, no kink-wave propagation was considered when steel wire ropes were used in relatively low speed engineering application areas. By contrast, a three dimensional approach to model steel wire ropes used in high energy absorber apparatus is presented in this paper. Three dimensional contacts between steel wire ropes and other objects and kink-wave propagation in steel wire ropes are taken into consideration when applying the new approach to model steel wire ropes. Compared to the two dimensional model of steel wire ropes, the proposed model regards steel wire ropes as a multi-body system consisting of identical cylindrical elements with 6 degrees of freedom connected by space constraints. Impact forces generated by three dimensional contacts between steel wire ropes and other objects are calculated and theories of elastic wave propagation are applied to analyze the kink-wave propagation when steel wire ropes are loaded with a sudden perpendicular impact by a high speed moving object. In addition, mathematical model of steel wire ropes is established and numerical simulation of the three dimensional model of steel wire ropes is implemented. By comparing the simulation results with the experimental data available, the model of steel wire ropes proposed in this paper is demonstrated to be valid and correct. Therefore, the proposed modeling method can be treated as a new approach in the research field of modeling steel wire ropes. The dynamical characteristics of the steel wire ropes based on this new modeling approach are addressed simultaneously and plots of the dynamics of steel wire ropes cannot only be regarded as a basis for the further comparative studies, but also can provide some significant and interesting results.     

爆破振动作用下顺层岩质边坡稳定性分析

基于对顺层岩质边坡的受力分析,在极限平衡理论的基础上,应用Mohr-Column准则,按照Bishop关于边坡稳定性安全系数的定义,推导出在爆破振动作用下顺层岩质边坡稳定性安全系数的计算方法。通过算例分析,证实了计算方法的可行性,说明了爆破振动拟静力系数同顺层边坡安全系数的关系。研究结果表明,垂直向下、水平指向坡外的爆破振动荷载以及两者的联合爆破荷载对边坡稳定性安全系数的影响最大;爆破荷载拟静力系数从0起每增加0.05,爆破振动水平指向坡外和垂直向下时,层裂长度为12.76 m的顺层边坡安全系数分别减少7.801%～10.665%、1.366%～1.978%,无层裂的顺层边坡安全系数分别减少7.61%～10.546%、1.473%～2.289%。同时,爆破振动产生的层裂长度、边坡长度以及联合爆破荷载的方向对边坡稳定性也有影响。     

Multiscale permutation mutual information quantify the information interaction for traffic time series

Pendulums and similar systems, such as links of chains, bodies hanging on ropes, kinematic chains forming working parts of manipulators, and robotic devices, are frequently used in industrial applications. They often cooperate in tubes or working spaces limited by walls or other rigid obstacles. This was the inspiration to carry out this study on the influence of impacts on the behaviour of a chain-like system represented by a double pendulum moving between two vertical walls. The simulations were performed for a specified extent of excitation frequencies. The results indicate a number of bifurcations that change the character of the induced motion to regular, quasi-periodic, and chaotic in the individual frequency subintervals.

     

Some dynamic properties of axially loaded wire ropes

Results are presented on the transverse damping, the transverse fundamental natural frequency as well as the longitudinal fundamental natural frequency for axially loaded wire ropes. Twelve different wire ropes are tested. During the test, a mass is centrally attached to the rope. The results indicate an increasing transverse damping with an increasing axial load. This damping is primarily attributed to a Coulomb damping. Although core material and construction influence the transverse damping of the wire rope, no relationships are found when comparing this damping with the structural strength, the number of wires used in the rope, the alloy composition or the heat treatment of the rope materials. The transverse and longitudinal fundamental natural frequencies of the axially loaded wire ropes with a mass centrally attached has been satisfactorily modeled.     

Analytical procedure for modelling recursively and wire by wire stranded ropes subjected to traction and torsion loads

The aim of this article is to introduce a new theoretical procedure for modelling wire ropes subjected simultaneously to tensile and torsional loads. The procedure is based upon the beam assumption and takes account wire by wire of the double helical wires on the basis of general thin rod theory developed by [Love, A., 1944. Mathematical Theory of Elasticity. Dover Publications, New York]. The proposed kinematics are based on the assumption that wires are un-lubricated and therefore that no relative sliding between adjacent wires happens.     

Propagation of plane P-waves at interface between elastic solid and unsaturated poroelastic medium

A linear viscoporoelastic model is developed to describe the problem of reflection and transmission of an obliquely incident plane P-wave at the interface between an elastic solid and an unsaturated poroelastic medium, in which the solid matrix is filled with two weakly coupled fluids (liquid and gas). The expressions for the amplitude reflection coefficients and the amplitude transmission coefficients are derived by using the potential method. The present derivation is subsequently applied to study the energy conversions among the incident, reflected, and transmitted wave modes. It is found that the reflection and transmission coefficients in the forms of amplitude ratios and energy ratios are functions of the incident angle, the liquid saturation, the frequency of the incident wave, and the elastic constants of the upper and lower media. Numerical results are presented graphically. The effects of the incident angle, the frequency, and the liquid saturation on the amplitude and the energy reflection and transmission coefficients are discussed. It is verified that in the transmission process, there is no energy dissipation at the interface.     

Computations of hydrodynamic coefficients, displacement-amplitude ratios and forces for a floating cylinder due to wave diffraction and radiation

Computations of the hydrodynamic coefficients, displacement-amplitude ratios and loadings on floating vertical circular cylinder due to diffraction and radiation are presented here. The boundary value problem (BVP) is solved in terms of diffraction potential and three potentials due to radiation, two translational motions about x-axis (surge) and about z-axis (heave), one rotational motion about y-axis (pitch). The analytical expressions for the hydrodynamic coefficients, displacement-amplitude ratios and loadings for this case were obtained previously by Bhatta and Rahman [1]. In this paper, we present the computational aspects of those analytical results for different depth to radius and draft to radius ratios. JMSL (Java Mathematical and Statistical Library) is used to compute special functions and solve complex matrix equations.     

Spanwise correlations in the wake of a circular cylinder and a trapezoid placed inside a circular pipe

The spanwise correlation of a circular cylinder and a trapezoidal bluff body placed inside a circular pipe in fully developed turbulent regime is studied using hotwire anemometer. The present configuration possesses complex fluid structure interaction owing to the following features: high blockage effect; low aspect ratio of the body; upstream turbulence and interaction of axisymmetric flow with a two dimensional bluff body. The spatial correlation of such configuration is seldom reported in the literature. Results are presented for Reynolds number of Re_D=1×10⁵. Three different blockage ratios (0.14, 0.19 and 0.28) are considered in the present study. Correlation coefficient is observed to improve with increase in blockage ratio. Compared to a circular cylinder, a trapezoidal bluff body possesses high correlation length. The near wall effects tend to increase the phase drift, which is reflected in low correlation coefficients close to the pipe wall. The results show that the simultaneous effect of curvature, low aspect ratio and upstream turbulence reduces the correlation coefficients significantly as compared to unconfined and confined (parallel channel) flows. The low frequency modulations with a circular cylinder are higher for lower blockage ratios. The three-dimensionality of vortex shedding for trapezoid with a blockage ratio of 0.28 was observed to be lower compared to circular cylinder and all other blockage ratios. Low frequency modulations were found to be responsible for weak vortex shedding from a circular cylinder compared to a trapezoidal bluff body. The vortex shedding is observed to be nearly two dimensional in case of a trapezoidal bluff body of blockage ratio 0.28.     

Reflection and refraction of plane quasi-longitudinal waves at an interface of two piezoelectric media under initial stresses

This paper is devoted to study a problem of reflection and refraction of quasi-longitudinal waves under initial stresses at an interface of two anisotropic piezoelectric media with different properties. One of the two media is aluminum nitride, which is considered the down piezoelectric medium and the above medium is chosen as PZT-5H ceramics. The two piezoelectric media welded are assumed to be anisotropic of a type of a transversely isotropic crystals (hexagonal crystal structure, class 6 mm). The equations of motion and constitutive relations for the piezoelectric media have been written. Suitable boundary conditions are used to obtain the reflection and refraction coefficients. For an incidence of quasi-longitudinal plane waves, four independent-type amplitude ratios of elastic displacement components for plane waves, called quasi-longitudinal (qP) and quasi-shear vertical (qSV) waves, are shown to exist. Also, it is observed that there exist four dependent amplitude ratios of electric potential, which are proportional to the previous four types. Finally, it is found that the coefficients of reflection and refraction are functions of angle of incidence, elastic constants, piezoelectric potential parameters and the initial stresses. Numerical computations and the results obtained are depicted graphically. In the end, a particular case has been reduced from the present study. This investigation is considered important because the initial stresses in such practical problems are inevitable and may result in frequency shift, a change in the velocity of surface waves and controlling the selectivity of a filter compensation of the devices.     

考虑内力分项贡献度的框架构件重要性评价

提出了一种水平和竖向荷载共同作用下的框架结构构件重要性评价方法。首先,基于线弹性材料假设,利用应变能方程和节点-外荷载关系计算梁柱构件的轴力、剪力和弯矩;然后,定义构件内力分项计算值与抗力分项值之比为构件分项重要性系数,用于体现构件抗力利用水平;再组合各内力分项系数,针对不同外荷载形式定义构件综合重要性系数,用于体现构件对框架体系整体承载力的贡献;最后,通过两榀框架算例验证了方法的可行性,可为框架的结构优化设计和连续性倒塌分析提供定量依据。