时间尺度上三阶非线性中立型动力方程的振动准则（英文）

源于电子工程、机械工程、生态工程和航天工程等领域的许多问题均可用时间尺度上的动力方程来描述,因此,研究这类方程有着重要的理论价值和实际意义.本文利用广义Riccati变换,积分平均和比较原理,研究了一类时间尺度上三阶非线性中立型时滞动力方程的振动性和渐近性,给出了这类方程新的Kamenev型振动准则和Philos型振动准则.本文成果推广了已知文献的多个相应结果并给出了例证.     

时间尺度上具有次线性中立项的三阶 Emden-Fowler 时滞动力方程的振动性

判定时间尺度上时滞动力方程的振动性和渐近性在数学物理、自动控制理论及工程、传染病模型分析和桥梁设计等诸多领域具有重要作用。针对时间尺度上具有次线性中立项的三阶 Emden-Fowler 时滞动力方程的振动性和渐近性开展研究，利用时间尺度上的微积分理论，广义 Riccati 变换和不等式技巧，获得了该方程两个振动定理，改进和推广了已有文献的相应结果，并给出了两个实例验证了新定理的有效性。     

时间尺度上二阶Emden-Fowler型延迟动态方程的振动性

研究了时间尺度上一类二阶非线性中立型阻尼Emden-Fowler型延迟泛函动态方程的振动性,利用时间尺度上的微积分理论和广义的Riccati变换、Yang不等式、H9lder不等式以及一些分析技巧,在两种情形下建立了该方程的几个新的振动准则,所得结果充分反映了阻尼项和中立项在系统振动中的影响作用,所举例子说明,这些准则不仅推广并改进了一些已有的结果,而且具有较好的实用性和可操作性.     

带混合型非线性项的二阶中立型时标动力方程的振动准则（英文）

中立型时标动力方程的振动性在理论上和应用中有着重要的意义.本文研究了一类二阶带混合型非线性项的中立型时标动力方程的振动性.首先,我们定义了中立项系数函数π(t).当π(t0)=∞时,利用广义李卡提变换技巧和均值技巧,建立了二阶中立型动力方程振动的一些新的判据.其次,当π(t0)∞时,通过加强假设条件及应用某些不等式和一些分析技巧,我们也得到了该方程振动的几个判据.我们的工作推广并改进了相关文献关于二阶中立型动力方程振动的结果.最后,作为应用给出两个实例说明所获定理的重要性.     

带混合型非线性项的二阶中立型时标动力方程的振动准则

中立型时标动力方程的振动性在理论上和应用中有着重要的意义.本文研究了一类二阶带混合型非线性项的中立型时标动力方程的振动性.首先,我们定义了中立项系数函数丌(t).当丌(t0)=∞时,利用广义李卡提变换技巧和均值技巧,建立了二阶中立型动力方程振动的一些新的判据.其次,当7r(t0)＜∞时,通过加强假设条件及应用某些不等式和一些分析技巧,我们也得到了该方程振动的几个判据.我们的工作推广并改进了相关文献关于二阶中立型动力方程振动的结果.最后,作为应用给出两个实例说明所获定理的重要性.     

具有正负系数的二阶非线性中立型方程的非振动准则

中立型泛函微分方程的振动性在理论和应用中有着重要意义。本文研究了一类具有正负系数的二阶非线性中立型时滞泛函微分方程的振动性,利用Banach空间的压缩映象原理和一些分析技巧,建立了该方程非振动的一些新的准则,并给出了定理应用的例子。所得结论推广和改进了现有文献中的一系列结果。     

具连续分布滞量的二阶半线性阻尼微分方程的振动准则

本文研究了一类具连续分布滞量的二阶半线性阻尼微分方程的振动性. 通过利用函数不等式技巧、广义Riccati变换和 函数等方法,给出了此类方程所有解振动新的振动准则,所得结果推广和改进了文献的结果。     

二阶拟线性中立型时滞微分方程的振动性

本文主要研究了一类二阶拟线性中立型微分方程的振动性．文中运用广义Riccati变换,积分平均技巧和Hardy-Littlewood-Polya不等式给出了微分方程若干新的振动准则,与其它现有的结果进行比较,所得结果推广和改进了最近一些文献中的关于某些振动性的结果．     

复合材料/混凝土复合梁的动力特性解

本文探讨用于复合材料／混凝土复合梁动力分析的一种等效非经典理论方法，给出了基本方程和一般解以及非经典理论效应系数，求得固有频率与振型等动力特性的解析解，从而为这类新型复合梁的工程计算提供一种较为简便而实用的计算公式。     

关于一阶线性中立型微分方程解的渐近性和振动性

关于线性中立型微分方程的研究越来越引起人们的关注,其原因在于不仅是数学理论本身的需要,而且中立型方程有其强烈的实际背景。例如,在研究高速电子计算机连接开关电路的无损传输线网络中,就提出了这类方程。参见[1-2]。解的渐近性和振动性的研究是中立型方程研究方面之一,目前已出现了一些很好的结果,如[2-6]。本文目的在于改进[2]关     

具连续分布滞量的非线性抛物型偏微分方程的振动准则

考虑一类具连续分布滞量的非线性抛物型偏微分方程的振动性，借助Green定理将多维振动问题转化为关于某一类具连续分布滞量的非线性微分不等式的一维问题，给出了该类方程在Robin，Dirichlet边值条件下所有解振动的若干充分判据。所得结论充分地表明，振动是由时滞量引起的。     

Recent application of caustics on experimental dynamic fracture studies

Combining the caustic method with high‐speed photography is an efficient optical measurement technique to study the dynamic fracture behaviours of homogenous and isotropic material. In the last decade, the main emphasis is extended to study dynamic fracture of anisotropic material and dynamic propagation of multi‐cracks and interface cracks in practical engineering materials. In this paper, the recent advances and applications about the dynamic caustic method in China are reviewed, such as impact response and dynamic fracture of composite materials (fibre composites, functionally gradient materials and nanometre composites), and dynamic interaction and propagation of multi‐cracks and interface cracks. Particularly, some new numerical methods were developed to solve the complicated caustic equations by introducing both the maximum characteristic size and the relevant angles in caustic patterns. Also, some important experimental results in fracture mechanics are described, and the potential research prospects about dynamic caustics are included as well.     

橡胶支座基础隔震建筑地震作用实用计算方法

在分析国内外橡胶支座基础隔震建筑地震作用计算方法的基础上,提出了计算橡胶支座基础隔震建筑地震作用的实用计算方法。该文建议的方法考虑了地运动参数和结构参数等多种因素与结构动力特征的相互关系,计算结果与时程分析的结果比较接近,能够满足工程设计的要求。     

TWO SIMPLE FAST INTEGRATION METHODS FOR LARGE-SCALE DYNAMIC PROBLEMS IN ENGINEERING

A new simple explicit two-step method and a new family of predictor–corrector integration algorithms are developed for use in the solution of numerical responses of dynamic problems. The proposed integration methods avoid solving simultaneous linear algebraic equations in each time step, which is valid for arbitrary damping matrix and diagonal mass matrix frequently encountered in practical engineering dynamic systems. Accordingly, computational speeds of the new methods applied to large system analysis can be far higher than those of other popular methods. Accuracy, stability and numerical dissipation are investigated. Linear and nonlinear examples for verification and applications of the new methods to large-scale dynamic problems in railway engineering are given. The proposed methods can be used as fast and economical calculation tools for solving large-scale nonlinear dynamic problems in engineering.     

柔性动边界梁的弹塑性动力响应分析

实际工程中的梁结构并不是采用理想的刚性支承,而通常具有柔性动边界。该文建立了柔性动边界梁的计算模型,模型考虑了梁端有弹性支承、阻尼支承以及刚性块等情况,并利用有限差分方法对运动方程进行离散,研究分析了在动载作用下柔性动边界梁的弹塑性动力响应。研究表明:动边界对梁的变形和受力有很大的影响,与刚性支承相比,竖向弹性支承能够降低梁的振动频率,并且使梁的内力和相对位移幅值减小,从而提高结构的抗力,但提高抗力的效果与载荷作用时间的长短以及振动衰减的程度相关。     

A novel six degrees-of-freedom parallel manipulator for aircraft fuselage assemble and its trajectory planning

Parallel manipulators have been successfully used for pose adjustment. However, aircraft fuselages are heavy and have complex shapes, so the existing parallel manipulators are not suitable for aircraft fuselages. For the first time, this paper presents a novel six degrees of freedom parallel manipulator for aircraft fuselages. Compared with other parallel manipulators, the presented parallel manipulator is suitable for large round parts. The Jacobi matrix of the presented parallel manipulator is derived, which is expressed by roll, pitch, and yaw. Using the derived Jacobi matrix, inverse kinematics of the presented parallel manipulator is investigated systemically. Combining Newton’s second law with Euler equations, dynamic equations of the manipulator are derived. Using the derived dynamic equations, inverse dynamics of the manipulator are also investigated systemically. For improving safety and efficiency of fuselage pose adjustment, a new trajectory planning algorithm is proposed which is based on the minimum mean force. Simulation experiment results demonstrated the ability of the trajectory planning algorithm to achieve stable movement comparable to the time-optimal trajectory planning algorithm. At the conclusion of this paper, practical applications of the presented parallel manipulator are shown.     

How to adaptively resolve evolutionary singularities in differential equations with symmetry

Many time-dependent partial differential equations have solutions which evolve to have features with small length scales. Examples are blow-up singularities and interfaces. To compute such features accurately it is essential to use some form of adaptive method which resolves fine length and time scales without being prohibitively expensive to implement. In this paper we will describe an r-adaptive method (based on moving mesh partial differential equations) which moves mesh points into regions where the solution is developing singular behaviour. The method exploits natural symmetries which are often present in partial differential equations describing physical phenomena. These symmetries give an insight into the scalings (of solution, space and time) associated with a developing singularity, and guide the adaptive procedure. In this paper the theory behind these methods will be developed and then applied to a number of physical problems which have (blow-up type) singularities linked to symmetries of the underlying PDEs. The paper is meant to be a practical guide towards solving such problems adaptively and contains an example of a Matlab code for resolving the singular behaviour of the semi-linear heat equation.     

Fitting ordinary differential equations to short time course data

Ordinary differential equations (ODEs) are widely used to model many systems in physics, chemistry, engineering and biology. Often one wants to compare such equations with observed time course data, and use this to estimate parameters. Surprisingly, practical algorithms for doing this are relatively poorly developed, particularly in comparison with the sophistication of numerical methods for solving both initial and boundary value problems for differential equations, and for locating and analysing bifurcations. A lack of good numerical fitting methods is particularly problematic in the context of systems biology where only a handful of time points may be available. In this paper, we present a survey of existing algorithms and describe the main approaches. We also introduce and evaluate a new efficient technique for estimating ODEs linear in parameters particularly suited to situations where noise levels are high and the number of data points is low. It employs a spline-based collocation scheme and alternates linear least squares minimization steps with repeated estimates of the noise-free values of the variables. This is reminiscent of expectation-maximization methods widely used for problems with nuisance parameters or missing data.