具有分数导数型本构关系的粘弹性柱的动力稳定性

研究简支的受轴向周期激励的粘弹性柱动力稳定性,柱的材料满足分数导数型本构关系.建立了描述粘弹性柱动力学行为的弱奇异性Volterra积分-偏微分方程,利用Galerkin方法将其化归为弱奇异性Volterra积分-常微分方程.利用平均化方法的思想给出了粘弹性柱运动稳定状态的存在性条件.给出一种新的计算方法,克服了存储整个响应历史数据的困难,并给出了数值算例,计算结果与解析方法的结论比较吻合.     

Heisenberg群上移动球面法的应用——一类半线性方程的Liouville型定理

作为Heisenberg群上移动球面法的基础,在Heisenberg群上引入了一类CR反演变换.作为应用,讨论了Heisenberg群上的次临界方程,证明任意非负柱对称解均为平凡解.     

一类微分-差分方程组的内禀对称和等价群变换

研究一类微分-差分方程组的对称和等价群变换.采取内禀的无穷小算子方法,给出了方程组的内禀对称和等价群变换.为结合抽象Lie代数结构,给方程完全分类提供了理论基础.     

有限群中素数方幂阶子群的个数

本文利用基础代数中有关稳定子、陪集等理论,给出了有限群G中pk阶子群个数的 一个结果.     

基于模糊二元运算的直觉模糊群

为了使直觉模糊群也具有经典的结构,首先给出经典集合G的一种直觉模糊二元运算,利用这种直觉模糊二元运算定义了直觉模糊群,讨论这种直觉模糊群的一些性质,并给出直觉模糊群的两种等价定义。由于直觉模糊群具有和群一样经典的结构,因此,使直觉模糊代数的深入研究有了充分的理论基础。     

梁-柱体系在椭圆型荷载作用下的精确解和动力屈曲分析

当梁-柱体系两端铰支时,在随时间周期变化的椭圆型轴向压力的作用下,给出了其动力稳定性问题的一个闭合解.采用Fourier正弦级数形式,以及解析地求解由此产生的常微分方程,求得控制方程的解.找到动力屈曲问题精确的解析解是有困难的,然而该体系的物理特性,为精确解的存在提供了充分的依据.另外,还研究了体系的频率响应特性,静力、驱动力和频率比对临界屈曲荷载的影响.     

二阶Volterra系统对平稳正态激励的统计响应的表示定理的数学证明

1974年,Neal根据Kac和Siegert的思想,给出了一个在电子工程、海洋工程、建筑工程、航空工程、自动控制的随机振动中有重要应用的二阶Volterra非线性系统对平稳正态输入的统计响应的表示定理.1984年,Naess对此定理又给出了一个数学证明.经过研究后发现,他们对定理条件的叙述都是模糊的,而且其数学证明都是有问题的.本文重新讨论了这个表示定理,给出了明确的定理条件及严格的数学证明,为它的广泛应用奠定了理论基础.     

非平凡正规子群的阶相同的有限群

本文研究了非平凡正规子群的阶相同的有限群. 给出了非平凡正规子群唯一的可解群的结构. 对非可解群的情况, 我们也给出了它的刻画.     

L~2(R~3)上基于不完全拟Beta函数修波构造

首先研究两类Shearlet群N_((d,s))和H_d(d=1,2,3)的结构,给出N_((d,s))和H_d的同构群,同时给出了N_((d,s))和H_d上的自同构群.接着利用群直积方法,构造高阶群.在此基础上,给出L~2(R~3)上的酉算子与对应Shearlet群和高阶群之间的关系,同时给出了满足Parseval等式时函数f∈L~2(R~3)在群表示意义下的展开式.最后利用两类不完全拟Beta函数给出L~2(R~3)上修波的具体构造.     

4度Cayley图的Hamilton圈分解的新方法与理论证明

给出了＂Hamilton圈侧枝循环＂等四个定理.它揭示了Abel群上4度Cayley图的Hamilton圈分解的特点及规律.同时,提出了Hamilton圈上＂单向通道＂的＂离合＂理论.在此基础上给出了Abel群上4度Cayley图的Hamilton圈分解的新方法-＂离合法＂,此方法具有简明、快捷、分解方案多的特点.另外,Hamilton圈＂单向通道＂的＂离合＂理论还为解决6度Cayley图的Hamilton圈分解奠定了理论基础.     

An inequality model for solving interval dynamic response of structures with uncertain-but-bounded parameters

In this paper, we look into the dynamic response of structures with uncertain-but-bounded parameters. A new inequality model for determining the interval dynamic response is presented. First we propose an interval dynamic response solution theorem. An inequality model which is a mathematics programming problem is suggested by the presented theorem. Using the central difference method, we substitute the differential items of the inequality model by difference items. By solving them, the interval dynamic response can be obtained. Two examples are used to illustrate the feasibility and the efficiency of the model.     

基于预约模式的移动充电车实时需求响应策略研究

预约模式下移动充电车实时需求响应问题是移动充电行业发展过程中的新问题,该问题包含了两类不同特点、存在动态交替影响关系的需求,不仅有时间窗约束、实时响应性要求,也有动态不确定性的特点。针对以上问题特点,本文以最大化整体收益为目标,提出联动的两阶段实时需求响应策略,引用近似动态规划求解决策未来价值,并融入到以下两阶段中:第一阶段基于多阶段随机动态决策模型与禁忌搜索算法生成了可以动态调整的充电服务方案;第二阶段基于第一阶段提出了针对动态需求的实时响应决策流程。最后,对比实验验证了本策略在不同客户规模与动态度下的有效性,并得出管理启示。本研究可以支持制定移动充电车的实时需求响应策略,对类似具有动态特征的需求响应问题具有启发意义。     

基于数值分析的动水效应对连续刚构桥抗震性能影响

为了研究不同水深下,动水效应对连续刚构桥抗震性能的影响,基于一实际工程,利用有限元软件Midas建立全桥模型,采用反应谱数值分析法,并考虑桩土的相互作用,研究了动水效应对连续刚构桥抗震性能的影响.结果表明:考虑动水效应将会减小结构的频率,且高阶频率对动水效应更加敏感;另外,动水效应将会放大结构的地震响应,随着水深的增加,地震响应的增大幅度也越大.当水深达到20m以上时,动水效应将使结构的内力增大约10%,此时在抗震设计中应重点考虑动水效应的影响.     

A beam segment element for dynamic analysis of large aqueducts

Large aqueduct structure is a complex structure that is commonly used in hydraulic engineering, especially in large-scale water conveying projects. The analysis of dynamic response for an aqueduct structure is necessary if the aqueduct is built in an earthquake area. Traditional 3D finite element analysis is time consuming and the existing simplified response method cannot take into account all the effects, such as the bending-torsion coupling effect and the constrained torsion, of the deformations of the thin wall structure of the aqueduct body. For this special structure, a simple and yet accurate model for dynamic analysis is needed. In this paper, a beam segment element is developed and used for the calculation of dynamic response for aqueduct structures. With the frame of the aqueduct being modeled using beam element, the proposed model can calculate the dynamic response of the whole aqueduct structures. Results are compared with that of a general purpose finite element analysis software using 3D finite element model. Good agreement is achieved between the two models. However, the proposed model needs less elements and much less computing time.     

随机结构动力反应和可靠性分析

本研究随机动力荷载作用下随机结构反应有限元分析方法，提出了随机结构动力反应和基于随机抗力可靠性计算公式。     

由Gurtin变分原理求解任意形状板动力响应的半解析法

该半解析法以Gurtin变分原理为基础，在空间域作有限元离散，在时间域取级数．本文研究了任意形状板时域函数的取法，使得各种支承条件，任意形状板的动力响应问题均可由本计算模式得到具有相当精度和效率的解．     

Prediction of the dynamic response of a mini-cantilever beam partially submerged in viscous media using finite element method

In this work, the use of mini cantilever beams for characterization of rheological properties of viscous materials is demonstrated. The dynamic response of a mini cantilever beam partially submerged in air and water is measured experimentally using a duel channel PolyTec scanning vibrometer. The changes in dynamic response of the beam such as resonant frequency, and frequency amplitude are compared as functions of the rheological properties (density and viscosity) of fluid media. Next, finite element analysis (FEA) method is adopted to predict the dynamic response of the same cantilever beam. The numerical prediction is then compared with experimental results already performed to validate the FEA modeling scheme. Once the model is validated, further numerical analysis was conducted to investigate the variation in vibration response with changing fluid properties. Results obtained from this parametric study can be used to measure the rheological properties of any unknown viscous fluid.     

On designing experiments for a dynamic response modeled by regression splines

Dynamic response systems are often found in science, engineering, and medical applications, but the discussion on experimental design for such a system is relatively rare in literature. For an experimenter, designing such experiments requires making decisions on (1) when or where to take response measurements along the dynamic variable and (2) how to choose the combination of experimental factors and their levels. The first consideration is unique for such experiments, especially when the measurement cost is high. In this paper, we present a design approach through the mixed‐effect linear model, which is based on a hierarchical B‐spline function for the dynamic response. We develop several theorems that can assist in finding a statistically efficient sampling plan and propose an algorithm for searching the D‐optimal design of a dynamic response system.     

Vibration of submerged floating tunnels due to moving loads

The concept of submerged floating tunnel (SFT) has become an increasingly attractive idea to cross the straits. The structural solution in this scheme includes buoyancy force on tunnel body plus tension in mooring tethers. This paper investigates the effect of submergence on the dynamic response of SFT due to moving load. The inertial effect of the fluid is accounted for by evaluating the added mass of tunnel using two and three dimensional models. It is found that fluid–structure interaction increases dynamic amplification of the tunnel deflection (in some cases very significantly). The results show that although the 3D model predicts lesser inertial contribution for surrounding fluid, it is not always possible to associate the larger response with the 2D or 3D models. The discrepancy between the results of the two models decreases as the tether stiffness increases. This indicates that the adoption of Morison’s equation for evaluating the fluid loading on the tunnel is a reasonable assumption when the tether stiffness is high. It is also found that by increasing the tether stiffness, it is possible to introduce a major reduction in the dynamic amplification of the response and by this way control the dynamic response of the SFT.     

Non-probabilistic convex models and interval analysis method for dynamic response of a beam with bounded uncertainty

This paper is concerned with the comparison of two non-probabilistic set-theoretical models for dynamic response measures of an infinitely long beam. The beam is on an uncertain foundation and subjected to a moving force with constant speed. The steady state vibration is analyzed with finite element method. The dynamic responses of the beam are approximated to the first-order respect of the uncertainty variables. As a rule, in convex models and interval analysis, the uncertainties are considered to be unknown, but they give out their allowable vector space. Comparing the convex models with interval analysis in mathematical proofs and numerical calculations, it’s shows that under the condition of transform an interval vector to an outer enclosed ellipsoid, the dynamic response of the infinitely long beam predicted by interval analysis is smaller than that by convex models; under the condition of transform a hyperellipsoid to an outer enclosed interval vector, the dynamic response of the infinitely long beam calculated by convex models is smaller than that by interval analysis method.