转子系统热膨胀状态下固有横振频率

把转子的惯性力看成作用在轴上的外力,采用新的非线性渐近法研究热膨胀对转子系统固有横振频率的影响.     

多支承矩形厚板固有横振频率的特征方程

采用Laplace变换研究了两对边简支多支承矩形厚板的固有横振,并给出了其振型函数及频率的特征方程。     

有横撑系杆拱桥的侧向稳定承载力

基于能量原理推导了有横撑系杆拱桥侧向弹性稳定承载力的解析计算公式,并通过算例的有限元数值解验证了提出的解析公式的正确性,最后讨论了结构参数对稳定承载力的影响。推导的稳定承载力解析式对系杆拱桥的分析与设计具有实用意义。     

轴压下弹性支承连续叠层梁固有横振

把轴压下弹性支承连续叠层梁按单跨强迫振动梁来处理，给出了其固有横振时的振型函数及频率方程。     

具有中间支承的薄膜固有振动分析

把具有中间支承的薄膜固有振动转化为多个集中载荷作用下的薄膜强迫振动，然后采用Laplace变换求得了具有中间支承薄膜固有振动振型的解析解，并通过实例计算说明了该方法的应用。     

横摇条件下主机隔振对船舶推进轴系横向振动的影响研究

以典型船舶轴系试验台架为研究对象,基于有限元法,建立了该轴系的有限元模型,并通过试验对模型进行了验证,计算分析了主机隔振条件下轴系的固有特性,并从运动形式的角度出发,将横摇运动等效为重力加速度的变化,作为边界条件,对该模型进行瞬态响应分析。计算结果表明:主机隔振会降低整个系统的固有频率,但对轴段的固有特性没有影响;在横摇条件下,联轴器位置的传递力和位移显著增大,并传递至轴段部分,使轴系的振动更加严重。     

Maxwell模型粘弹性矩形厚板固有横向振动

由于各向同性粘弹性体剪应力-角应变的本构关系与应力-应变的本构关系相似,据此可得到Maxwell模型粘弹性矩形厚板固有横振微分方程。并讨论了Maxwell粘弹性矩形厚板的振动特性。     

中心为非固有点的线束对应

在两线束射影对应中，当两线束中心为非固有点时，两线束的射影关系式如何确定？本文给出了适当的解析方法。实践证明：当两线束中心之一为非固有点时，所得曲线为双曲线，抛物线或退化的二次曲线；当两线束中心均为非固有点时，所得曲线是双曲线或退化的二次曲线。     

封面设计的符号空间

符号化空间解析有效揭示了封面设计对书籍内质的反映过程,有助于封面设计构思的多维化,并引发对封面设计新的解构.通过引入符号的组合与聚合概念从横、纵两方面对封面设计的空间意义进行解析,并结合作者的设计实例加以阐明,从而形成封面设计的符号化理解.     

深水半潜式平台Mathieu不稳定问题研究

半潜式平台的垂荡运动相对较大, 当平台的纵摇固有有周期和垂荡固有周期处于一定的倍数关系时, 平台的纵摇/横摇运动可能落入Mathieu不稳定区。该文对半潜式平台Mathieu 方程进行了推导, 获得了各参数的计算公式;根据Mathieu不稳定图谱或数值计算方法, 可判断纵摇/横摇运动的稳定性。选取了一个生存状态下的半潜式平台为算例, 分析了平台发生Mathieu 不稳定问题的条件, 并通过调整关键参数抑制不稳定问题的发生, 从而获得了避免Mathieu不稳定问题的工程措施, 为今后半潜式平台设计提供参考。     

琴弦振动理论在工程中柔索求拉力的应用

琴弦横向振动时，振动固有频率主要与三个因素有关；张紧力；弦密度；弦长。它的逆问题，柔索的张紧力与索的密度、索横向振动的固有经、索的长度有关，应用这个理论可以对大型斜拉桥的索力、体育馆的吊索力以及特大型水坝的起吊闸门的索力等进行检测，并可以识别吊索故障。本文提供理论及应用技术，同时讨论了如何控制误差。     

一般振动系统的多输入状态反馈部分极点配置

本文讨论具有非对称阻尼、刚度矩阵的一般振动系统多输入部分极点配置问题。基于系统的矩阵二阶微分方程而非一阶状态方程形式,采用多输入状态反馈控制,使系统的部分极点得以配置,同时使其它的极点保持不变。对于该配置问题,本文给出了控制增益矩阵的一种显式解,最后用一个算例说明本文方法。     

Integral transform solution of internal flow problems based on Navier–Stokes equations and primitive variables formulation

The generalized integral transform technique (GITT) is employed in the solution of incompressible laminar channel flows as formulated by the steady‐state Navier–Stokes and continuity equations under the primitive variables mathematical representation. A hybrid numerical–analytical solution is developed based on eigenfunction expansions in one space co‐ordinate and error‐controlled numerical solution of the resulting system of coupled ordinary differential equations in the remaining space direction. The approach is illustrated for developing flow between parallel‐plates with uniform and irrotational inlet flow condition. The conventional Poisson‐type equation for the pressure field with appropriate boundary conditions is also transformed and simultaneously solved with the momentum equation along the longitudinal direction, by considering eigenvalue problems for each of the two potentials, defined in the transversal direction. The transversal velocity component is then explicitly determined from the continuity equation. Numerical results of the longitudinal velocity component and friction factor fields are reported to illustrate the convergence behaviour and user prescribed error control inherent to the proposed hybrid approach. Critical comparisons with previous contributions on the same method that made use of the streamfunction‐only formulation are also provided. Copyright © 2006 John Wiley & Sons, Ltd.     

Droplet-shaped waves: causal finite-support analogs of X-shaped waves

A model of steady-state X-shaped wave generation by a superluminal (supersonic) pointlike source infinitely moving along a straight line is extended to a more realistic causal scenario of a source pulse launched at time zero and propagating rectilinearly at a constant superluminal speed. In the case of an infinitely short (delta) pulse, the new model yields an analytical solution, corresponding to the propagation-invariant X-shaped wave clipped by a droplet-shaped support, which perpetually expands along the propagation and transversal directions, thus tending the droplet-shaped wave to the X-shaped one.     

Modal vibrations of an infinite cylinder in an acoustic halfspace

Acoustic radiation from an infinite cylindrical surface vibrating with an arbitrary, time-harmonic surface velocity distribution while positioned near the rigid/compliant boundary of a semi-infinite ideal compressible fluid medium is determined in an exact fashion using the classical method of separation of variables. The formulation utilizes the appropriate wave-field expansions and the method of images along with the pertinent translational addition theorem to develop a closed-form solution in form of infinite series. The analytical results are illustrated with numerical examples in which the cylindrical source, vibrating in the monopole and dipole-like modes, is positioned near the rigid/compliant boundary of a water-filled acoustic halfspace. Subsequently, the basic acoustic field quantities such as the modal acoustic radiation impedance load, radiated far-field pressure and the radiation intensity distribution are evaluated for representative values of the parameters characterizing the system.     

三交叉弦结构非线性自由振动频率特性分析

依据哈密顿原理获得了三交叉弦结构非线性自由振动的运动方程,并应用摄动法推导了自振频率下的一阶摄动解。相较于传统的单根弦线非线性振动运动方程多采用单三角级数,三交叉弦结构首次采用三重三角级数解法并成功获取一阶摄动解。通过分析表明,非线性自振频率的解析解除了具有典型的非线性特性,还体现了各个子结构参数变化对整体结构自振频率的影响,即存在子结构间的耦合特性。结果表明,整个结构与局部子结构在子结构自身因参数发生改变时,变化幅度之间不是线性关系,且整体结构小于子结构自身因参数改变的变化幅度。     

自然弯扭梁的耦合振动特性分析

以自然弯扭梁理论为基础对具有一般横截面形状空间曲梁的耦合振动特性进行了研究。 在该梁的运动控制方程中,位移函数和广义翘曲坐标均被定义在形心轴上,且在分析中包括了转动惯量、横向剪切变形以及和扭转有关的翘曲对振动的影响。通过对数学计算软件MATHEMATICA的精确运用可以得到该梁振型的解析表达式,精确的固有频率则可用搜索的方法来确定。为了证明理论的有效性,对两端固支椭圆截面曲梁的固有频率和振型进行了求解,并把数值计算结果同使用PATRAN梁单元的有限元结果进行了比较。     

Submatrix Constrained Inverse Eigenvalue Problem involving Generalised Centrohermitian Matrices in Vibrating Structural Model Correction

Generalised centrohermitian and skew-centrohermitian matrices arise in a variety of applications in different fields. Based on the vibrating structure equation $M$$\ddot{x}$+$(D+G)$$\dot{x}$+$Kx$=$f(t)$ where $M$, $D$, $G$, $K$ are given matrices with appropriate sizes and x is a column vector, we design a new vibrating structure mode. This mode can be discretised as the left and right inverse eigenvalue problem of a certain structured matrix. When the structured matrix is generalised centrohermitian, we discuss its left and right inverse eigenvalue problem with a submatrix constraint, and then get necessary and sufficient conditions such that the problem is solvable. A general representation of the solutions is presented, and an analytical expression for the solution of the optimal approximation problem in the Frobenius norm is obtained. Finally, the corresponding algorithm to compute the unique optimal approximate solution is presented, and we provide an illustrative numerical example.     

变密度环形薄膜的轴对称振动修正摄动解

采用修正摄动法研究了变密度环形薄膜的轴对称横向固有振动，并求得了确定其横向振动固有频率的特征方程，把该方法所得到的修正摄动解与有关文献所得结果进行比较，可知此修正摄动解不但计算简便，而且精度可与经典的打靶法与微分求积法的精度相当。