一类非线性离散人口模型的稳定性和振动性

本文讨论了非线性差分方程ｘｎ＋１＝ｘｎ／１－ａ－ｂｘｎ－ｋ＋ｃｘ＾２ｎ－ｋ平衡点的稳定性，并获得了此方程在条件ａ∈（１，∞），ｂ∈（－∞，＋∞）＝Ｒ，ｃ∈（０，∞）下其正解的渐近性质及其关于正平衡点振动的充分条件，且当Ｋ＝０时建立了正平衡点渐近稳定的充分必要性准则。’     

浸没的球面各向同性球壳自由振动的中厚壳理论

采用六模态的中厚壳理论研究了可压缩流体中球面各向同性球壳的自由振动，即在分析中考虑了剪切变形，旋转惯量和横向正应变的影响，引入５个辅助变量可以理到两类振动及其频率方程，对频率方程作了简化并算例进行了相应的探讨。     

小问题

３２５．设系统的运动方程为：　求： （１）此系统自由振动第一谐波的振幅ａ１与其频率ｗ的关系． （２）画出当ｍ＝ｃ＝１,Ｆ０＝π,ｘ（０）＝０．５;ｘ（０）＝０时的时程曲线和相平面图．（来源：密歇尔斯基理论力学习题集,［俄］第３６版,５７．５题）（李银山,太原理工大学应用力学研究所,太原０３００２４） ３２６．古埃及人在四千年前就已懂得了摩擦学的原理,他们曾用滚子和滑板来搬运重物．有一幅浮雕反映了奴隶们搬运一台石雕巨像的情景（约公元前１９００年）．仔细观察可以发现：巨像放在滑板上,由１７２个奴隶拉着…     

光滑拉伸试件中不同初始形状孔洞长大的有限元模拟

本文对具有不同硬化指数（ｎ＝０．０５，ｎ＝０．１，ｎ＝０．２）的幂硬化材料的光滑拉伸试样的拉伸变形过程进行了有限元模拟，通过有限元计算和经Ｂｒｉｄｇｍａｎ修正分别得到了试样变形过程中心部应力三维度随应变的变化情况；在此基础上运用控制体胞宏观应力三维度的方法，对含不同初始形状孔洞的体胞模型进行了有限元分析，计算结果表明：（１）孔洞初始形状和材料硬化特性对试样的拉伸破坏过程有重要影响；（２）Ｂｒｉｄｇ     

横观各向同性热电材料简支矩形板的自由振动

从耦合的三维压电热弹性理论出发分析了横观各向同性热电材料简支矩板的自由振动,证明其存在两类振动,即解耦的第一类振动和耦合的第二类振动,如果板的结构和上下表面边界条件关于中面对称,则第二类振动又可进一步分解为对称振和反对称振动,给出了热电材料简支矩形板自由振动的三维精确解,采用Ｍｏｎｔｅ Ｃａｒｌｏ法克服了超越方程求复根的困难。对于ＰＺＴ－４矩形板给出了数值结果,分析了耦合效应对振动频率的影响,计算     

中面单向受拉（压）的阶梯式矩形薄板的振动

用奇异函数建立ｘ＝０与ｘ＝ａ两对边简支并受面内均布拉（压）力作用、加两边为任意支承、非单一材质的ｎ级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算子给出振型了函数的表达式及常见支承条件下板的方程。文中给出的固有频率表达式表明,面内均布拉（压）力对固有的数值有影响。此处导出的各种情况下的影响函数,对于求解相应民政部下的阶梯式矩形薄板的静力弯曲和稳定性问题,也是适用的。     

流线型轴对称钝体尾迹特性及其声激励控制

在Ｒｅ＝３．０×１０３～１．０×１０５的范围内实验研究了流线型轴对称钝体尾迹特性，并采用声激励手段对尾迹进行控制．研究表明，自然状态下流线型轴对称钝体尾涡无量纲脱落频率在Ｒｅ＝５．０×１０４～１．０×１０５的范围内具有普适性，适当频率的声激励可以减小回流区，该结果对工程减阻具有实际应用价值．实验中脉冲热线的成功应用为复杂流场的测量提供了新的技术手段．     

碳纳米管增强复合材料圆锥薄壳非线性自由振动

考虑碳纳米管复合材料作为功能梯度材料的不均匀性,基于连续介质理论以及哈密尔顿变分原理,建立了功能梯度碳纳米管增强复合材料开口圆锥薄壳结构的非线性运动偏微分控制方程,然后利用Galerkin法,将非线性偏微分控制方程转化为常微分控制方程,进而采用谐波平衡法求解了开口圆锥壳的非线性自由振动问题,并探讨了圆锥薄壳几何参数、碳纳米管参数对结构非线性自由振动的影响．数值研究表明结构的无量纲非线性自由振动频率与线性自由振动频率的比值随圆锥薄壳长厚比的增大而变小、并随圆锥角的增大而变大．     

阶梯形闭口薄壁杆的约束扭转振动

用奇异函数建立非单一材质的ｎ级阶梯形闭口薄壁杆约束扭转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杆的频率方程。     

在哈密顿体系下分析非线性动力学问题

首先将ｎ维未知向量ｑ的二阶非线性力系统Ｍｑ＋Ｇｑ＋Ｋｑ＝Ｆ（ｑ,ｑ,ｔ）转化为与其等价的２ｎ维未知向量ｖ的一阶微分方程ｖ＝Ｈｖ＋ｆ（ｖ,ｔ）,其中非线性部分ｊｉ（ｖ,ｔ）＝０（ｉ＝１,．．．ｎ）,ｆｉ（ｖ,ｔ）＝Ｆｉ－ｎ（ｑ,ｑ,ｔ）（ｉ＝ｎ＋１,．．．２ｎ）;然后给出一种求解ｖ的逐步积分公式,从而将精细积分法进一步推广应用到非线性动力学问题。算例表明本方法的计算量较小且结果合理可靠。     

Free vibration analysis of a hung clamped-free cylindrical shell partially submerged in fluid

The free flexural vibration of a hung clamped-free cylindrical shell partially submerged in a fluid is investigated. The fluid is assumed to be inviscid and irrotational. The cylindrical shell is modelled by using the Rayleigh-Ritz method based on Sanders’ shell theory. The kinetic energy of the fluid is derived by solving the boundary-value problem related to the fluid motion. The natural vibration characteristics of the partially submerged cylindrical shell are discussed with respect to the added virtual mass approach. In this study, the nondimensionalized added virtual mass incremental factor for the partially submerged finite shell is derived. This factor can be readily used to estimate the change in the natural frequency of the shell due to the presence of a fluid.     

Harmonic vibrations and waves in a cylindrical helically anisotropic shell

A Kirchhoff-Love type applied theory is used to study the specific characteristics of harmonic waves and vibrations of a helically anisotropic shell. Special attention is paid to axisymmetric and bending vibrations. In both cases, the dispersion equations are constructed and a qualitative and numerical analysis of their roots and the corresponding elementary solutions is performed. It is shown that the skew anisotropy in the axisymmetric case generates a relation between the longitudinal and torsional vibrations which is mathematically described by the amplitude coefficients of homogeneous waves. In the case of a shell with rigidly fixed end surfaces, the dependence of the first two natural frequencies on the shell length and the helical line slope α, i.e., the geometric parameter of helical anisotropy, is studied. A boundary value problem in which longitudinal vibrations are generated on one of the end surfaces and the other end is free of forces and moments is considered to analyze the degree of transformation of longitudinal vibrations into longitudinally torsional vibrations. In the case of bending vibrations, two problems for a half-infinite shell are studied as well. In the first problem, the waves are excited kinematically by generating harmonic vibrations of the shell end surface in the plane of the axial cross-section, and it is shown that the axis generally moves in some closed trajectories far from the end surface. In the second problem, the reflection of a homogeneous wave incident on the shell end is examined. It is shown that the “boundary resonance” phenomenon can arise in some cases.     

浸没的球面各向同性球壳的自由振动

本文引入三个们移函数并用球面调和函数展开，可将球面各向同性弹性力学的基本方程转化成一个独立的二阶常微分方程和另一个耦合的二阶常微分方程组，采用液动压力表示流体与壳的相互作用，可以把无限大不可压缩流体中任意厚度球面各向同性球壳的自由振动频率计算归结为一个代数循征值问题，文中计算了若干种情况下球壳的频率，在各向同性情形与有关文献作了比较。     

On Free Nonlinear Vibrations of Fluid-Filled Cylindrical Shells with Multiple Natural Frequencies

Nonlinear free vibrations of a cylindrical shell fully filled with a perfect incompressible fluid are studied. The case is examined where two natural frequencies of the shell are close __________ Published in Prikladnaya Mekhanika, Vol. 41, No. 10, pp. 127–138, October 2005     

Transient response of a moving spherical shell in an acoustic medium

A ring-stiffened spherical shell is submerged in an acoustic medium. The shell is thin and elastic. The acoustic medium is inviscid, irrotational and compressible. The center of mass of the shell is subjected to a translational acceleration which is an arbitrary function of time. The absolute displacements of the shell are expressed in terms of the relative displacements and the displacement of the base of the shell, base being defined as the rigid ring placed at the equator. The motion of the acoustic medium is governed by the wave equation. The transient response of the shell is investigated numerically. The results are compared with the results of the in-vacuo response. The effects of the plane wave approximation and the base velocity on the transient response of the shell are studied. The numerical results show that the plane wave approximation accurately predicts the response of the shell in the acoustic medium for short times after excitation. The displacements of the shell in fluid are larger than those in vacuo. But when the base of the shell is restrained from translating, the displacements in fluid are smaller than those in vacuo. Therefore, base translation has a very significant effect on the transient response of the shells submerged in an acoustic medium.     

Vibrations of a circular cylinder submerged in a fluid with a non-homogeneous upper boundary

Results of solving a linear problem on steady vibrations of a horizontal cylinder submerged in a fluid, whose upper boundary is partially closed by a solid lid, whereas the rest of the surface is free, are presented. Multipole and eigenfunction expansion methods are used. Reciprocity relations are derived. Added-mass and damping coefficients and the wave amplitudes on the free surface of the fluid are calculated.     

Natural frequencies of submerged piezoceramic hollow spheres

An exact 3D analysis of free vibration of a piezoceramic hollow sphere submerged in a compressible fluid is presented in this paper. A separation method is adopted to simplify the basic equations for spherically isotropic piezoelasticity. It is shown that there are two independent classes of vibration. The first one is independent of the fluid medium as well as the electric field, while the second is associated with both the fluid parameter and the piezoelectric effect. Exact frequency equations are derived and numerical results are obtained. The project supported by the National Natural Science Foundation of China (No. 19872060)     

On modelling and linear vibrations of arbitrarily sagged inclined cables in a quiescent viscous fluid

A theory of free linear vibrations of arbitrarily sagged inclined cables in a viscous fluid is presented in the framework of the heavy fluid loading concept. The static equilibrium shape of the cable is found by using the model of inextensible catenary and the validity ranges of this approximation are assessed. The dynamics of the viscous fluid is described by the linearised Navier–Stokes equations and their solution is pursued analytically by formulating the fluid field variables via potential functions. The vibration problem of a submerged cable is solved by Galerkin's method and the modal added mass and modal viscous damping coefficients are calculated. As a prerequisite for this analysis, the free vibrations of a cable in vacuum are addressed and a very good agreement with known results is observed. The physical interpretation of the dependence of modal added mass and modal damping coefficients on the ‘design variables’ for a fluid-loaded cable is given and the possible extensions of the suggested theory to capture weakly nonlinear effects are highlighted.     

Axisymmetric oscillations of two spherical shells in a compressible fluid

To find the interaction between spherical shells at the frequency of their free oscillations in a fluid, we examine the problem of axisymmetric oscillations of two identical spherical shells under the assumption that the shell centers of curvature do not coincide. The solution is found for the cases of a compressible and an incompressible fluid by the series method with reduction to an infinite system of linear equations. A mathematical justification of the method used is presented.