文克尔地基上阶梯式矩形薄板的振动

用奇异函数建立文克尔地基上阶梯式矩形薄板自由振动和强迫振动的微分方程并求得其通解,用Ｗ算子给出振型函数的表达式及常见支承条件下板的频率方程,用广义函数的富里叶展开,讨论板在不同载荷作用下的强迫振动响应     

文克尔地基上阶梯式单向矩形薄板的振动

用奇异函数建立文克尔地基上阶梯式单向矩形薄板自由振动和强迫振动的微分方程并求得其通解，用Ｗ算子给出主振型函数的表达式及常见支承条件下板的频率方程，用广义函数讨论板在不同形式载荷作用下的强迫振动响应·     

快速多极方法的概念性介绍

本文对快速多极方法作一概念性的非严格的描述, 该方法用来评估具有源分布的卷曲核函数.我们分别考虑了非振动核情形以及振动核情形. 对于非振动核情形, 我们概述了由Greengard 和Rokhlin 提出的经典快速多极方法的主要思想. 对于振动核情形, 我们介绍了最近由Engquist 和Ying所发展的定向快速多极方法.     

矩形网格扁壳结构的非线性振动

本文运用作者已建立的矩形网格扁壳的非线性弹性理论,求解了该类结构的非线性振动问题。通过采用横向挠度（网格节点横向位移）和力函数的某种（广义）Fourier级数形式的设定解,由试函数的加权得到解中系数之间的关系和决定时间未知函数的振动方程,然后利用正则摄动法和迦辽金法推导出结构自由振动和谐和激励作用下结构非线性受迫振动的幅频关系,并给出了计算实例。     

带有阻尼项的二阶非线性微分方程的振动性

利用一类Φ(t,s,l)型的新函数,对带有阻尼项的二阶非线性微分方程建立了新的振动准则,推广和改进了已有的一些振动结果.     

二阶脉冲时滞微分方程的振动性

本文研究了二阶脉冲时滞微分方程的振动性,分别运用完全平方技术和引入参数函数,得到了方程振动的两个充分准则.     

轴对称加载的阶梯式压力容器的径向振动

用奇异函数建立轴对称加载的阶梯式压力容器径向自由振动和强迫强振的微分方程并求得其通解,用Ｗ算子给出主振型函数的表达式及常见支承条件下容器的频率方程。     

一类二阶中立型微分方程的振动性

研究了一类具有正负系数和非线性中立项的二阶变时滞的非线性泛函微分方程的振动性,通过引入参数函数和Riccati变换,获得了方程振动的判别准则,这些准则改善了对方程的条件限制,所得结论推广并改进了现有文献中的一系列结果.     

高阶变系数函数方程的非振动解

给出一类高阶非线性函数方程的一些新的非振动准则,并且给出了在差分方程中的若干应用,结果改进和推广了近期文献的某些结果.     

一类二阶中立型泛函微分方程的振动性

讨论了一类二阶中立型微分方程的振动性 ,通过引入参数函数 ,结合完全平方技术 ,给出了该类方程解振动的更为一般形式的判别准则 .     

等腰三角形Mindlin板的自由振动分析

提出了一种新方法来对基于 Mindlin剪切变形理论的等腰三角形板进行自由振动分析 .此方法采用了一种新的基函数并利用 pb-2 Rayleigh-Ritz边界函数得到了一种新型的 Ritz方法 .这种方法的有效性通过收敛性和对比性分析得到了证实 .数值结果表明此方法相当精确有效 .     

Asymmetric free vibration of circular plate in contact with incompressible fluid

Vibration of circular plates in contact with fluid has extensive applications in the industry. This paper derives added mass and frequencies for asymmetric free vibration of coupled system including clamped circular plate in contact with incompressible bounded fluid. Considering small oscillations induced by the plate vibration in the incompressible and inviscid fluid, velocity potential function is used to describe the fluid motion. Derivation uses Kirchoff’s thin plate theory. Two approaches are used to derive the free vibration frequency of the system. The solutions include an analytical solution employing Fourier–Bessel series and a variational formulation applied simultaneously on the plate and fluid. Strong correlation is found between free vibration frequencies of the two solutions. Finally the effect of fluid depth on the added mass and free vibration frequencies of the coupled system is investigated.     

均布载荷作用下波纹扁壳的非线性振动

应用轴对称旋转扁壳的非线性大挠度动力学方程,研究了波纹扁壳在均布载荷作用下的非线性受迫振动问题．采用格林函数方法,将扁壳的非线性偏微分方程组化为非线性积分微分方程组．再使用展开法求出格林函数,即将格林函数展开为特征函数的级数形式,积分微分方程就成为具有退化核的形式,从而容易得到关于时间的非线性常微分方程组．针对单模态振形,得到了谐和激励作用下的幅频响应．作为算例,研究了正弦波纹扁球壳的非线性受迫振动现象．该文的解答可供波纹壳的设计参考．     

膜与不可压缩有界流体接触时的自由振动

圆形膜与流体接触时的振动被广泛应用于工业中．推导了圆形膜在与不可压缩有界流体接触时,非对称自由振动的自振频率．鉴于膜在不可压缩、非粘性流体中振动引起的小振幅,采用速度势函数来描述流体场．使用两种方法来推导系统的自由振动频率．它们包括变分法及一种近似解法——Rayleigh商法．在用两种方法求得的自由振动频率值之间具有良好的相关性．最后,研究了流体的深度、质量密度以及径向张力对耦合系统自由振动频率的影响．     

Transient vibration of an infinite string bearing a concentrated mass and supported by elastic-viscous suspensions

The transient transverse vibration of a string, bearing a concentrated mass and supported by elastic-viscous suspensions a constant distance apart, is investigated. The vibration is excited either by an instantaneous impulsive force or a constant force suddenly applied to the concentrated mass. In the first case a formal Fourier transformation of the Dirac impulse function is employed. In the second case the action of the constant force is regarded as a succession of actions of instantaneous pulses.     

各向异性矩形板自由振动的一般解析解法

根据各向异性矩形薄板自由振动横向位移函数的微分方程建立了一般性的解析解．该一般解包括三角函数和双曲线函数组成的解,它能满足4个边为任意边界条件的问题．还有代数多项式和双正弦级数解,它能满足4个角的边界条件问题．因此,这一解析解可用于精确地求解具有任意边界条件的各向异性矩形卞的振动问题．解中的积分常数可由4边和4角的边界条件来确定．由此得出的齐次线性代数方程系数矩阵行列式等于零可以求得各阶固有频率及其振型,以四边平夹的对称角铺设复合材料迭层板为例进行了计算和讨论．     

Structural damage detection strategy using correlation functions under inconsistent excitation

Structural damage detection using vibration response signals is appealing in recent years since it does not require the identification of the modal parameters or building the structures' finite element model, among which the correlation-function-based damage detection methodologies is a novel topic [1]. Beginning with the introduction of the correlation function theory, this paper proposes a new damage detection strategy using the auto correlation function values of vibration response signals of the structure. The maximum value of the auto correlation functions of the vibration responses from different measurement points are used to form the damage index to locate the damage. Differences of the damage index are used to make the damage location more clearly. As in real world applications, structures may undergo different external excitations [2]. Different external excitations are input into the intact and damaged structure. The results from numerical simulation of stiffness reduction detection of a 12-story frame structure show that the proposed strategy can locate the damage correctly and has a very good anti-noise ability under inconsistent external excitations. As only the vibration responses before and after damage are used in this damage detection strategy, it can be a useful tool for structural health monitoring. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

轴向变速运动粘弹性弦线横向振动的复模态Galerkin方法

在考虑初始张力和轴向速度简谐涨落的情况下,利用含预应力三维变形体的运动方程,建立了轴向变速运动弦线横向振动的非线性控制方程,材料的粘弹性行为由Kelvin模型描述．利用匀速运动线性弦线的模态函数构造了变速运动非线性弦线复模态Galerkin方法的基底函数,并借助构造出来的基底函数研究了复模态Galerkin方法在轴向变速运动粘弹性弦线非线性振动分析中的应用．数值结果表明,复模态Galerkin方法相比实模态Galerkin方法对变系数陀螺系统有较高的收敛速度．     

Free vibrations of composite laminated doubly-curved shells and panels of revolution with general elastic restraints

A unified numerical analysis model is presented to solve the free vibration of composite laminated doubly-curved shells and panels of revolution with general elastic restraints by using the Fourier–Ritz method. The first-order shear deformation theory is adopted to conduct the analysis. The admissible function is acquired by using a modified Fourier series approach in which several auxiliary functions are added to a standard cosine Fourier series to eliminate all potential discontinuities of the displacement function and its derivatives at the edges. Furthermore, the general elastic restraint and kinematic compatibility and physical compatibility conditions are imitated by the boundary and coupling spring technique respectively when the composite laminated doubly-curved panels degenerate to the complete shells of revolution. Then, the desired results are solved by the variational operation. Large quantities of numerical examples are calculated about the free vibration of cross-ply and angle-ply composite laminated doubly-curved panels and shells with different geometric and material parameters. Through the sufficient conclusions obtained from the comparison, it can be seen that highly accurate solutions can be yielded with a little computational effort. To understand the influence of different boundary conditions, lamination schemes, material and geometrical parameters on the vibration characteristics, a series of parametric studies are carried out. Lastly, results for vibration of the composite laminated doubly-curved panels and shells subject to various kinds of boundary conditions and with different geometrical and material parameters are also presented firstly, which can provide the benchmark data for other studies conducted in the future.     

Some unexpected results in vibration of non-homogeneous beams on elastic foundation

A special class of inverse vibration problems is studied in this investigation. We pose the following problem: Find the spatial distribution of the material density and the elastic stiffness of an inhomgeneous beam on elastic formulation so that the vibration mode shape constitutes a preselected function, namely the static deflection of the associated homogeneous beam under some simple loading conditions. Four sets of boundary conditions are considered, in context of polynomial representation of the material density and stiffness. It turns out unexpectedly, that irrespective of the boundary condition, the natural frequency is given by the same analytical formula.