GDQR求解弹性地基上输流管道的稳定性

用广义微分求积法（GDQR）研究了弹性地基上输流管道的稳定性问题。基于输流管道运动微分方程及边界条件,采用GDQR进行离散化,获得由动力方程组及边界条件合成的特征值矩阵方程。通过对相应特征值方程的具体分析,计算了左端固定、右端弹性支承下输流管道的发散失稳流速和颤振失稳流速,研究了临界失稳流速和稳定区域随两端支撑弹簧刚度、扭转弹簧刚度的变化情况,分析了质量比、双参数模型地基反力系数和剪切模量对输流管道稳定区域图的影响,得到了一些有益的结论。研究结论对于工程实践有一定的指导意义。     

转动惯量和弹性支承对非保守杆稳定性的影响

研究了具有多个弹性支承的弹性简支杆在切向均布随从力作用下的动力特性和稳定性问题。对于杆内出现的弹性支承情形,采用了以分段表示的运动微分方程、弹性支承处的连续性条件和边界条件来描述。在数值求解时,以含有两个弹性支承简支杆为例,采用有限差分法,导出了差分方程的递推格式以及边界条件和连续条件的离散形式,具体分析了弹性支承的弹性系数和支承位置以及转动惯量对非保守杆的振动频率和稳定性的影响。此外,该方法还能求解复杂边界条件下具有多个弹性支承的非保守弹性杆的复特征值问题。     

边界条件对短梁结构有限元分析影响的研究

梁结构在工程设计中有着广泛应用,其支承情况多种多样,往往不能简单地按理想的固支或简支梁来处理.以一种混合边界条件下短梁结构为研究对象,进行了短梁的模态试验,并基于Abaqus有限元软件,分别对端面固定边界约束、一端固定边界约束、弹性+固定边界混合约束条件下短梁结构进行模态分析.结果表明,边界约束条件通过改变系统刚度,导致模态特征改变.不同边界条件下的梁结构约束模态特征具有显著差异.采用混合边界条件的梁结构约束模态频率与试验结果吻合.     

任意跨弹性支承直梁横向自振的一个新解法

本文给出了任意跨弹性支承(包括扭转弹性支承)直梁横向自由振动的一个新解析解法,将弹性支承反力看作是作用于梁上的未知外力,求得了直梁横向受迫振动响应的解析解,由边界条件确定待定的积分常数,利用支承处支承反力与梁位移间的线性关系导出频率方程,频率方程是以阶数等于弹性支承个数的行列式表示的,振型函数则以统一的解析式表示,刚性支承是本文特例。本文具体导出了几种常见边界条件下的频率方程,最后给出了一个算例。     

轴向受压中间支承梁的横向振动和稳定性

研究了一端固支且自由端轴向受压具有中间支承梁的横向振动和稳定性。利用边界条件推导了此种梁频率方程及分段振型函数的解析表达式。根据频率方程讨论了中间支承位置变化对梁固有频率的影响。应用Ritz-Galerkin截断方法,采用梁的前四阶振型对梁的运动微分方程进行离散化处理,讨论了梁在各个中间支承位置处的失稳形式。发现了在梁上存在一个特殊的中间支承位置ξl,当中间支承位置ξbξl时,随着压力p从零开始增加,梁先发生颤振失稳,当中间支承位置ξbξl时,则梁先发生发散失稳,而在中间支承位置ξl处,梁由颤振失稳跳跃到发散失稳。     

基于变分原理的整体道床结构动力有限元分析

根据国内外铁路隧道整体道床的建设经验,针对弹性支承块式整体道床结构,建立轨道-道床底板-底部垫层相互作用的粘弹性地基梁模型。依据弹性梁动力分析的第一类变量广义HAMILTON拟变分原理,推导出了粘弹性地基上弹性地基梁的动力分析方程,建立了相应的有限元解析方法对整体道床结构的动力响应特征与影响因素进行分析。研究成果对优化整体道床结构的设计参数,分析其动力稳定性具有重要意义。     

扭转弹性支承时连续梁的相关函数解法

在对效叉梁系进行弹性分析时，梁与梁之间的相互作用就相互作用就相当于竖向弹性支承和扭转弹性支承的约束作用。文本依据不同梁段位移方程的相关性＾「１」，建立了扭转弹性支承，以及竖向弹性支承的扭转弹性支承共同作用时连续梁位移方程的计算公式。当竖向弹性支承、扭转弹性支承的风度Ｋｉ＝Ｇｉ＝０时，该计算公式为文献「１」的公式（９）。公式适合手算，也适合编程电算。     

桥梁结构边界条件变异对固有振动特性的影响分析

针对实际桥梁结构复杂的边界条件，分析其对结构固有振动特性的影响因素。采用解析的方法分析简支梁在纵向不同程度的约束效应，以及简支梁、连续梁支承处不同刚度弹性扭转约束对结构自振特性的影响，并提出利用有限元分析来考虑复杂结构的边界条件变异影响的方法。最后以重庆轻轨PC梁以及一中承式拱桥的实测及计算固有频率结果验证了实际边界条件变化对固有频率的显著影响。     

考虑底板与池壁相互作用和池壁剪切变形影响的圆形水池动力特性计算

考虑圆形水池池壁剪切变形的影响、底板对池壁的径向约束作用和转动约束作用,将圆形水池底板与池壁的相互作用简化成端部受切向弹性约束和转动弹性约束下的弹性地基Timoshenko梁,基于Timoshenko梁振动的修正理论,导出了底部环向简支、顶部分别为自由、铰支和固支三种边界条件下的振动频率超越方程;根据池壁和弹性地基梁微分方程的类比性,阐述了利用ANSYS建立圆形水池振动模态分析的有限元方法。利用二分法对底板环形简支的圆形水池的振动频率进行了计算,分析了顶部不同边界条件、池高、池的半径和底板对池壁弯曲约束刚度对池壁振动频率的影响。得到了圆形水池轴对称振动可采用弹簧-质量模型进行基频估算、该文所建立的分析方法只能分析圆形水池的轴对称振动模态、圆形水池底板与池壁相互作用对基频影响不明显、壁厚的剪切变形和转动惯量对高阶振动影响大等结论。     

Winkler地基上修正Timoshenko梁振动分析

利用Bernoulli-Euler梁理论建立的弹性地基梁模型应用广泛,但其在高阶频率及深梁计算中误差较大,利用修正的Timoshenko梁理论建立新的弹性地基梁振动微分方程,由于其在Timoshenko梁的基础上考虑了剪切变形所引起的转动惯量,因而具有更好的精确度。利用ANAYS beam54梁单元进行振动模态的有限元计算,所求结果与理论基本无误差,从而验证了该理论的正确性。基于修正Timoshenko梁振动理论推导出了弹性地基梁双端自由-自由、简支-简支、简支-自由、固支-固支等多种边界条件下的频率超越方程及模态函数。分析了弹性地基梁在不同理论下不同约束条件及不同高跨比情况下的计算结果,从而论证了该理论计算弹性地基梁的适用性。分析了不同弹性地基梁理论下波速、群速度与波数的关系。得到了约束条件和梁长对振动模态及地基刚度对振动频率有重要影响等结论。     

基于n阶GBT热-机载荷作用下FGM梁的振动特性和稳定性分析

研究了热-机载荷耦合作用下弹性地基FGM梁的振动特性与稳定性。考虑到材料的物性依赖于温度变化且组分沿梁厚按幂律分布。首先,基于一种扩展的n阶广义剪切变形梁理论(n-th GBT),应用Hamilton原理,统一建立了系统自由振动及屈曲问题力学模型的控制方程,采用一种改进型广义微分求积法(MGDQ)获得FGM梁静动态响应的数值解。其次,通过算例验证GBT的有效性并给出阶次n的理想取值,在丰富梁理论的同时,也可验证或改进其他各种剪切变形梁理论。最后,讨论并分析了升温、边界条件、初始轴向机械载荷、梯度指标、地基刚度、跨厚比等诸多参数对FGM梁振动特性和稳定性的影响。     

Influences of elastic foundations and boundary conditions on the buckling of laminated shell structures subjected to combined loads

This article presents to study the stability of laminated orthotropic cylindrical and truncated conical shells resting on elastic foundations and subjected to combined loads with the clamped and simply supported boundary conditions. Here, axial tensile loads separately applied to the small and large bases of a laminated truncated conical shell, respectively. The basic relations, the modified Donnell type stability and compatibility equations have been obtained for laminated orthotropic truncated conical shells on the Pasternak type elastic foundation. Applying Galerkin method, the critical combined loads of laminated orthotropic conical shells on the Pasternak type elastic foundation with different boundary conditions are obtained. The appropriate formulas for single-layer and laminated cylindrical shells on the Pasternak type elastic foundation made of orthotropic and isotropic materials are found as special cases. Finally, influences of the boundary conditions, the elastic foundation, the number and ordering of the layers and variations of the shell characteristics on the critical combined loads are investigated. The results are compared with their counterparts in the literature.     

On the response of a timoshenko beam under initial stress to a moving load

When an axial compressive force is present, the wavelength of the propagating free waves in a beam rapidly decreases. The conventional Euler-Bernoulli beam equations are often not adequate for determining dynamic behavior of the moving load on a beam supported on an elastic foundation when initial axial stress is present. Equations derived by Sun for the Timoshenko beam with initial axial stress (based on Trefftz's theory), form the basis of this investigation. Analytical solutions are presented for deformations of the beam both with and without damping. Expressions of the critical velocity as a function of initial axial stress and foundation modulus parameters, are obtained for the Timoshenko beam. Critical velocities of the Timoshenko beam, with and without axial stress, are compared with that obtained using Euler-Bernoulli beam formulation. Some significant agreements and disagreements in the behaviors of the two systems are described.     

非均匀热载荷作用下功能梯度梁的非线性静态响应

由于功能梯度材料结构沿厚度方向的非均匀材料特性,使得夹紧和简支条件的功能梯度梁有着相当不同的行为特征。该文给出了热载荷作用下,功能梯度梁非线性静态响应的精确解。基于非线性经典梁理论和物理中面的概念导出了功能梯度梁的非线性控制方程。将两个方程化简为一个四阶积分-微分方程。对于两端夹紧的功能梯度梁,其方程和相应的边界条件构成微分特征值问题;但对于两端简支的功能梯度梁,由于非齐次边界条件,将不会得到一个特征值问题。导致了夹紧与简支的功能梯度梁有着完全不同的行为特征。直接求解该积分-微分方程,得到了梁过屈曲和弯曲变形的闭合形式解。利用这个解可以分析梁的屈曲、过屈曲和非线性弯曲等非线性变形现象。最后,利用数值结果研究了材料梯度性质和热载荷对功能梯度梁非线性静态响应的影响。     

Exact solution for stability analysis of moderately thick functionally graded sector plates on elastic foundation

In this article, an exact analytical solution for buckling analysis of moderately thick functionally graded (FG) sector plates resting on Winkler elastic foundation is presented. The equilibrium equations are derived according to the first order shear deformation plate theory. Because of the coupling between the bending and stretching equilibrium equations of FG plates, these plates have deflection under in-plane loads lower than the critical buckling load acting on the mid-plane. The conditions under which FG plates remain flat in the pre-buckling configuration are investigated and the stability equations are obtained based on the flat plate assumption in the pre-buckling state. The stability equations are simplified into decoupled equations and solved analytically for plates having simply supported boundary condition on the straight edges. The critical buckling load is obtained and the effects of geometrical parameters and power law index on the stability of functionally graded sector plates are studded. The results for the critical buckling load of moderately thick functionally graded sector plates resting on elastic foundation are reported for the first time.     

Magneto-thermo-mechanical dynamic buckling analysis of a FG-CNTs-reinforced curved microbeam with different boundary conditions using strain gradient theory

In this article, dynamic buckling analysis of an embedded curved microbeam reinforced by functionally graded carbon nanotubes is carried out. The structure is subjected to thermal, magnetic and harmonic mechanical loads. Timoshenko beam theory is employed to simulate the structure. Furthermore, the temperature-dependent surrounding elastic foundation is modeled by normal springs and a shear layer. Using strain gradient theory, the small scale effects are taken into account. The extended rule of mixture is employed to estimate the equivalent properties of the composite material. The governing equations and different boundary conditions are derived based on the energy method and Hamilton’s principle. Dynamic stability regions of the system are obtained using differential quadrature method. The aim of this paper is to investigate the influence of different parameters such as small scale effect, boundary conditions, elastic foundation, volume fraction and distribution types of carbon nanotubes, magnetic field, temperature and central angle of the curved microbeam on the dynamic stability region of the system. The results indicate that by increasing the volume fraction of CNTs, the frequency of the system increases and thus the dynamic stability region occurs at higher frequencies.     

Vibration analysis of FGM truncated and complete conical shells resting on elastic foundations under various boundary conditions

This article deals with vibration analysis of clamped (C?CC) and freely supported (Fs?CFs), truncated and complete conical shells on elastic foundations with continuously graded volume fraction. The functionally graded material (FGM) properties are assumed to vary continuously through the thickness of the conical shell. First, the basic relations, i.e., the dynamic stability and compatibility equations, of FGM truncated conical shells on the Pasternak-type elastic foundation are obtained. The displacement and Airy stress function are sought depending on a new parameter ??. The parameter ?? depends on the geometry of the shell and the loading and boundary conditions. By applying the Galerkin method to the foregoing equations, the dimensionless frequency parameters of FGM conical shells on the Pasternak-type elastic foundation for two boundary conditions are obtained. Furthermore, the parameter ?? which is included in the formulae is obtained from the minimization of the dimensionless frequency parameters. Finally, the effects of the stiffness of the foundation, boundary conditions, variations of the conical shell characteristics, and composition profiles on the values of the dimensionless frequency parameters are studied. The results are validated through comparison of obtained values with those in the literature.