深水无隔水管钻柱的临界转速分析

基于实际的工况考虑了钻柱壁厚、水深、张力、钻井液流速等因素对无隔水管钻柱的影响,根据达朗贝尔原理建立了无隔水管钻柱的涡动微分方程模型;在此模型上由分离变量法推导出了钻柱临界转速方程,并与Rayleigh梁-轴模型的临界转速方程进行对比并验证了本方程的正确性。分析结果表明:在不同阶数的情况下,随着水深或壁厚的增加,临界转速降低;随着张力的增加,临界转速提高;流速对临界转速无明显的影响。本文所得结论对于采用无隔水管钻井技术作业具有指导意义。     

旋转Rayleigh梁的自由振动及失稳特性

基于Hamilton原理,采用模态坐标得到了旋转梁在固定参考系及旋转参考系下的时域常微分方程,详细分析了两端简支边界条件下旋转Rayleigh梁自由振动的行波特性及临界转速。讨论了长细比等因素对旋转Rayleigh梁的行波振动频率和临界转速的影响,并给出了不同转速下系统自由振动的典型模态坐标时间曲线。研究发现:旋转Rayleigh梁系统存在一次和二次临界转速,固定参考系中一次临界转速对应于旋转参考系中零特征值失稳点,转速在一次临界转速(低速)附近时系统只发生共振失稳,系统真正的失稳发生在转速超过二次临界转速之后。     

梯度多孔金属材料梁的屈曲和屈曲基础上的振动

为研究梯度多孔金属材料梁的屈曲以及屈曲附近的振动特性,首先建立了随从分布压力下梯度多孔材料梁的动力学控制方程,得到了描述后屈曲的静态控制微分方程和描述屈曲前后振动响应的控制方程。通过打靶法数值求解两组强非线性方程,获得了简支-固支梯度多孔梁的屈曲临界载荷以及屈曲前后振动频率与载荷之间的关系曲线。分析了孔隙率系数和孔隙分布方式对屈曲临界载荷和屈曲前后振动频率的影响。结果表明,随着孔隙率系数e₀的增加,发生屈曲时的临界载荷减小;各阶固有频率也减小。屈曲前,各阶振动频率随载荷增大而减小,屈曲后,除三阶频率外,一阶和二阶频率随载荷增大而增大。     

Rayleigh旋转梁的动力学建模与动态稳定性分析

基于Rayleigh梁理论,通过欧拉角,运用Hamilton原理,建立了柔性自转轴在Euler坐标系下和Lagrange坐标系下的动力学方程,两个方程相比,Euler坐标系下的动力学方程增加了一个离心力项。运用Galerkin方法对两组方程离散,运用Matlab的数值方法求解了系统的频率和模态。由模态分析得出,离心力项会使陀螺系统的模态在一定转速下由反进动转变为正进动模态;由稳定性分析得出,当转速足够大时,离心力项会使陀螺系统发生颤振失稳现象。     

含旋转运动效应裂纹梁横向振动特性的研究

针对开口裂纹作用下旋转运动欧拉-伯努力梁的振动特性进行了研究。文中使用裂纹梁连续等效刚度模型模拟裂纹效应,将含裂纹旋转运动梁视为弯曲刚度沿梁长度方向连续变化的梁,并应用传递矩阵法推导了求解其振动特性的特征方程。考虑不同裂纹深度和位置、不同旋转速度,分析了梁的一阶和二阶固有频率的变化情况。研究结果表明:旋转运动效应和裂纹效应并非独立影响梁的固有频率,两者间具有耦合作用效应;转速提升使由裂纹导致的频率衰减幅度变小,同时裂纹加深使得由速度升高带来的阶频提升更加显著;相比于二阶频率,耦合作用效应对于一阶频率更加显著。     

含轴向运动效应的裂纹梁横向振动频率研究

针对含轴向运动效应开口裂纹梁,借助裂纹梁连续等效刚度模型,将裂纹效应引入轴向运动梁的横向振动方程.应用传递矩阵法推导了求解其振动频率的特征方程,计算得到裂纹和运动参数连续变化情况下梁的一阶和二阶固有频率数值解.对裂纹和轴向运动参数对梁的振动频率的联合影响机理进行了分析,研究表明,对于梁的一阶和二阶固有频率,轴向运动速度和裂纹深度具有耦合作用效应.裂纹加深使得由轴向速度带来的频率衰减加速;同时,速度提升导致由裂纹引起的频率衰减变得更加剧烈.相较于二阶频率,耦合作用效应对于一阶频率表现得更加显著.     

轴向变速粘弹性Rayleigh梁参数共振稳定性

运用近似解析方法和数值方法研究轴向变速运动黏弹性Rayleigh梁的次谐波共振和组合共振的稳定性区域。基于变分原理,考虑梁断面旋转惯性的影响,推导轴向速度有周期波动的微变形梁横向振动的数学模型;采用多尺度方法建立前两阶次谐波共振和组合共振范围内的参数振动的可解性条件;进而确定梁两端简支边界条件下,因共振而产生的失稳区域;通过微分求积方法求解表征细长Rayleigh梁横向振动的运动微分方程。数值算例分析了黏弹性系数和扭转系数对梁振动失稳区域的影响,将数值仿真结果与近似解析方法的结论进行比较。算例表明:近似解析解的精度较高,第一、第二阶主共振的最大误差分别为3.206%、4.213%。     

纤维增强聚合物布加固裂纹木梁的稳定性

梁中横向裂纹等效为无质量内部转动弹簧，假定纤维增强聚合物(FRP)布与梁表面紧密粘贴，建立了考虑轴向压力二阶效应FRP 布加固裂纹梁线性弯曲的控制方程，并得到其显式解析通解．在此基础上，研究了FRP加固简支裂纹木梁的稳定性，通过数值求解方程，分析了纤维增强聚合物(CFRP)布含量、裂纹深度和位置以及数量等因素对CFRP 布加固简支裂纹杉木梁临界载荷的影响，结果表明：CFRP 加固可明显减小裂纹深度和数量等对裂纹杉木梁临界载荷的影响，且裂纹处弯矩较大或裂纹较深时加固效应愈加显著；CFRP 加固裂纹木梁临界载荷随CFRP 布加固层含量的增加而增加，但当CFRP 布含量达到一定值后，进一步增加CFRP 含量对CFRP加固裂纹梁临界载荷提高并不明显．     

近壁面柱体涡激振动的迟滞效应

柱体涡激振动是典型的流固耦合问题,其响应规律标识码在升速流动和远离壁面条件下获得的. 而自然环境流动通常不断经历升速和降速过程,近壁面柱体的涡激振动可呈现与远离标识码体不同的响应特征. 本研究结合大型波流水槽,设计了具有微结构阻尼的柱体涡激振动装置. 基于量纲分析,开展系列水槽标识码验,通过同步测量柱体涡激振动位移时程和绕流流场变化,研究了升降流速作用下柱体涡激振动触发和停振的临界速度(即上临标识码临界速度)变化规律,探究了近壁面柱体涡激振动迟滞效应. 采用自下向上激光扫射的 PIV 流场测量系统,对比分析了固定柱体标识码振动柱体的绕流特征. 实验观测表明,近壁面柱体涡激振动触发的临界速度呈现随壁面间距比减小而逐渐减小的变化趋势;但标识码速条件下的涡激振动停振所对应的下临界速度却明显小于升速时的涡激振动触发所对应的上临界速度. 采用上临界与下临界约标识码差值可定量表征涡激振动迟滞程度,研究发现该值随着柱体间距比减小呈线性增大趋势. 涡激振动迟滞现象通常伴随振幅阶跃标识码阶跃值则随着间距比减小而非线性减小.      

近壁面柱体涡激振动的迟滞效应

柱体涡激振动是典型的流固耦合问题,其响应规律大多是在升速流动和远离壁面条件下获得的.而自然环境流动通常不断经历升速和降速过程,近壁面柱体的涡激振动可呈现与远离壁面柱体不同的响应特征.本研究结合大型波流水槽,设计了具有微结构阻尼的柱体涡激振动装置.基于量纲分析,开展系列水槽模型实验,通过同步测量柱体涡激振动位移时程和绕流流场变化,研究了升降流速作用下柱体涡激振动触发和停振的临界速度(即上临界和下临界速度)变化规律,探究了近壁面柱体涡激振动迟滞效应.采用自下向上激光扫射的PIV流场测量系统,对比分析了固定柱体和涡激振动柱体的绕流特征.实验观测表明,近壁面柱体涡激振动触发的临界速度呈现随壁面间距比减小而逐渐减小的变化趋势;但流动降速条件下的涡激振动停振所对应的下临界速度却明显小于升速时的涡激振动触发所对应的上临界速度.采用上临界与下临界约减速度差值可定量表征涡激振动迟滞程度,研究发现该值随着柱体间距比减小呈线性增大趋势.涡激振动迟滞现象通常伴随振幅阶跃,振幅阶跃值则随着间距比减小而非线性减小.     

Sliding Contact with Friction at Arbitrary Constant Speeds on a Pre-Stressed Highly Elastic Half-Space

Resisted by Coulomb friction, a rigid indentor slides at a constant arbitrary speed on a generalized neo-Hookean half-space under pre-stress. A dynamic steady-state situation in plane strain is assumed, and is treated as the superposition of contact-triggered infinitesimal deformations upon finite deformations due to pre-stress. Exact solutions are presented for both deformations, and the infinitesimal component exhibits the anisotropy typically induced by pre-stress, and wave speeds that are sensitive to pre-stress. In view of the unilateral constraints of contact, these and other critical speeds define the sliding speed ranges for physically-acceptable solutions. In particular, a Rayleigh speed is the upper bound for subsonic sliding. Solutions are further constrained by the unilateral requirement that contact zone shear must oppose indentor/half-space slip. The generic parabolic indentor is used for illustration, and it is found that traction continuity at the contact zone leading edge is lost for supersonic sliding and at the single sliding speed allowed in the frictionless limit in the trans-sonic range. A range of acceptable pre-stresses is also identified; for pre-stresses that lie out of range, either a negative Poisson effect occurs, or the Rayleigh wave disappears, thereby precluding sliding in the subsonic range. This revised version was published online in August 2006 with corrections to the Cover Date.     

Dispersion and localisation in structured Rayleigh beams

This paper brings a comparative analysis between dynamic models of couple-stress elastic materials and structured Rayleigh beams on a Winkler foundation. Although physical phenomena have different physical origins, the underlying equations appear to be similar, and hence mathematical models have a lot in common. In the present work, our main focus is on the analysis of dispersive waves, band-gaps and localised waveforms in structured Rayleigh beams. The Rayleigh beam theory includes the effects of rotational inertia which are neglected in the Euler–Bernoulli beam theory. This makes the approach applicable to higher frequency regimes. Special attention is given to waves in pre-stressed Rayleigh beams on elastic foundations.     

用材料力学公式计算任意截面短梁正应力时的修正项研究

对材料力学中梁的弯曲应力公式增加一修正项,以反映短梁弯剪翘曲变形对应力分布的影响。提出一种根据短梁横截面边界形状及艾瑞应力函数求解应力修正项的方法,应用弹性力学空间问题的一般理论,通过应力平衡方程、应变相容方程及应力边界条件,建立了关于任意截面短梁的应力修正项及剪应力的基本方程。在所建立的基本方程基础上,导出了矩形截面和圆形截面短梁修正应力的具体计算公式,该修正应力与均布荷载大小及弹性模量与剪切模量之比均成正比,但与截面惯性矩成反比。数值算例表明,本文方法计算的应力与通用有限元软件ANSYS计算的结果吻合良好,从而验证了本文方法及其基本公式的正确性。     

Dynamic stability of pre-twisted beams with non-constant spin rates under axial random forces

This paper investigates the dynamic stability of a pre-twisted cantilever beam spinning along its longitudinal axis with a periodically varying speed and acted upon by an axial random force at the free end. The spin rate of the beam is characterized as a small periodic perturbation superimposed on a constant speed, and the axial force is assumed as the sum of a static force and a weakly stationary random process with a zero mean. Both the periodically varying spin rate and the axial random force may lead to parametric instability of the beam. In this work, the finite element method is applied first to get rid of the dependence on the spatial coordinate. The method of stochastic averaging is then adopted to obtain Ito’s equations for the system response under different resonant frequency combinations. Finally, the first-moment and the second-moment stability conditions of the beam are derived explicitly. Numerical results are presented for a simple harmonic speed perturbation and a Gaussian white noise axial force.     

Bifurcation and chaos of a cable–beam coupled system under simultaneous internal and external resonances

The bifurcation and chaos of a cable–beam coupled system under simultaneous internal and external resonances are investigated. The combined effects of the nonlinear term due to the cable’s geometric and coupled behavior between the modes of the beam and the cable are considered. The nonlinear partial-differential equations are derived by the Hamiltonian principle. The Galerkin method is applied to truncate the governing equation into a set of ordinary differential equations. The bifurcation diagrams in three separate loading cases, namely, excitation acting on the cable, on the beam and simultaneously on the beam and cable, are analyzed with changing forcing amplitude. Based on careful numerical simulations, bifurcations and possible chaotic motions are represented to reveal the combined effects of nonlinearities on the dynamics of the beam and the cable when they act as an overall structure.     

Load motion along a beam on a viscoelastic half-space

An expression is derived for equivalent foundation of a viscoelastic half-space interacting with an Euler–Bernoulli beam. It is shown that this equivalent viscoelastic foundation depends on frequencies and wave numbers of the waves in the beam. The real and imaginary part of it substantially varies for phase velocities in between the Rayleigh and shear waves velocities. Radiation of elastic waves occurs for velocities larger than some velocity in that interval. The steady-state beam displacements due to a uniformly moving constant load are calculated for different velocities. The maximum displacement under the load takes place for a velocity of order of the Rayleigh waves velocity.     

非对称混杂边界轴向运动Timoshenko梁橫向振动分析

研究两端带有扭转弹簧且弹簧系数均可任意变化的非对称混杂边界下的轴向运动Timoshenko梁的横向振动.利用非对称混杂边界条件推导对应任意弹簧系数的系统超越方程以及特征函数.运用数值方法计算系统的固有频率及其相应的模态函数,并研究确定梁的刚度、轴向速度以及边界处扭转弹簧的刚度的影响.通过数值算例,比较7imoshenko梁、瑞利梁、剪切梁和欧拉梁的固有频率随轴向速度的变化,分析转动惯量和剪切变形的影响.     

旋转楔形-回形梁的高次动力学建模和末端变形分析

对四种不同结构中心刚体-柔性Euler Bernoulli梁系统进行刚柔耦合动力学分析．其中以等截面梁、变截面梁、等截面回形梁、变截面回形梁为对象,研究楔形梁及回形梁对系统的末端变形位移影响．变截面梁的宽高尺寸沿着轴向线性变化．梁的变形包含了轴向、横向、耦合变形项（横向弯曲引起的纵向缩短）．采用假设模态法和第二类Lagrange方程建立系统的动力学方程,并用C++编写软件进行动力学仿真．研究表明：在相同条件下,梁的截面尺寸及空心部分对梁末端变形位移影响十分明显,且当梁在较大变形情况下,该高次耦合模型依然能得到正确的结果,因此在针对实际结构建模时,建立符合实际截面的模型至关重要．     

Determination of hourglass coefficients in the theory of a Cosserat point for nonlinear elastic beams

The theory of a Cosserat point has recently been used [Int. J. Solids Struct. 38 (2001) 4395] to formulate the numerical solution of problems of nonlinear elastic beams. In that theory the constitutive equations for inhomogeneous elastic deformations included undetermined constants associated with hourglass modes which can occur due to nonuniform cross-sectional extension and nonuniform torsion. The objective of this paper is to determine these hourglass coefficients by matching exact solutions of pure bending and pure torsion applied in different directions on each of the surfaces of the element. It is shown that the resulting constitutive equations in the Cosserat theory do not exhibit unphysical stiffness increases due to thinness of the beam, mesh refinement or incompressibility that are present in the associated Bubnov–Galerkin formulation. Also, example problems of a bar hanging under its own weight and a bar attached to a spinning rigid hub are analyzed.     

Secular Equations for Rayleigh and Stoneley Waves in?Exponentially Graded Elastic Materials of General Anisotropy under the Influence of Gravity

The Stroh formalism is employed to study Rayleigh and Stoneley waves in exponentially graded elastic materials of general anisotropy under the influence of gravity. The 6×6 fundamental matrix N is no longer real. Nevertheless the coefficients of the sextic equation for the Stroh eigenvalue p are real. The orthogonality and closure relations are derived. Also derived are three Barnett-Lothe tensors. They are not necessarily real. Secular equations for Rayleigh and Stoneley wave speeds are presented. Explicit secular equations are obtained when the materials are orthotropic. In the literature, the secular equations for Stoneley waves in orthotropic materials are obtained without using the Stroh formalism. As a result, it requires computation of a 4×4 determinant. The secular equation presented here requires computation of a 2×2 determinant, and hence is fully explicit. A Rayleigh or Stoneley wave exists in the exponentially graded material under the influence of gravity if the wave can propagate in the homogeneous material without the influence of gravity. As the wave number k????, the Rayleigh or Stoneley wave speed approaches the speed for the homogeneous material.