支承弹簧对输液曲管固有频率和极限流速的影响

基于Hamilton变分原理,导出具有弹性支撑的1/4圆形输液曲管的变分—积分方程。采用多个函数组合的方法,选取满足边界条件的试函数,利用Galerkin直接法求出系统的固有频率和极限流速的近似解析公式。数值结果表明,弹簧对固有频率和极限流速都有显著影响。根据数值结果,用最小二乘法给出固有频率和极限流速与弹簧刚度的关系公式。     

两端固支输流管道流固耦合振动的稳定性分析

根据Hamilton变分原理,建立了两端固支管道流固耦合振动的控制方程,用幂级数近似管道的振型函数,求得了方程的解析解,推导了管道固有频率、临界流速、临界压力的计算方法。最后,应用本文推导的计算方法,对一段典型飞机发动机输油管道进行了计算分析,研究了前两阶固有频率,临界流速、临界压力与流体压力、流速、管道固支长度之间的关系。     

两端支承输流管道的稳定性和临界流速分析

推导两端支承梁弯曲振动的频率方程和振型函数的解析表达式。利用频率方程讨论两端扭转弹簧刚度变化对梁的前两阶弯曲振动特征值的影响。以两端支承梁的振型函数为假设振型导出两端支承输流管道在定常流作用下临界速度的解析表达式,为今后分析这类系统的动态响应提供理论依据。利用临界流速公式系统地分析和讨论扭转刚度、重力系数和轴向预紧力对管道临界流速的影响特性。研究结果表明,量纲一扭转弹簧刚度在0到50区间内变化时对临界流速的影响较大,但大于50时影响明显减弱。当重力系数和轴向预紧力增大时,临界流速也随着增大。一般而言,两端扭转弹簧刚度越大也会增大相应的临界流速值。     

输流管道在支承激励下的动态特性分析

根据Hamilton原理推导出了两端简支输流管道在支承简谐激励下的控制方程,提出了一种求解该方程的方法-伽辽金-模态法.讨论了阻尼、流速、压力和简支长度对管道前两阶固有频率的影响,并分析了流速和压力对管道最大相对位移的影响情况.通过笔者给出的求解管道失稳临界值的方法,求出了管系的临界流速、临界压力和临界简支长度.结果表...     

拉索平面内自由振动影响因素分析

考虑抗弯刚度、垂度和几何非线性的影响，建立了拉索非线性自由振动方程，针对考虑与否垂度和几何非线性，分别建立了线性无垂度和有垂度理论、非线性无垂度和有垂度理论，用谐波平衡法求得拉索振动固有频率的近似解析解。其结果与龙格-库塔积分法得到的结果较为一致。此外，还给出了抗弯刚度、垂度和几何非线性对拉索振动固有频率影响的定量判定。     

机电集成超环面传动系统强非线性振动研究

考虑机电集成超环面传动系统中行星轮与蜗杆、定子间电磁啮合非线性,建立了系统带平方项的强非线性振动微分方程组;采用多尺度法求出了系统非线性振动时域响应的二次近似解析解,作出了系统自由振动时域响应近似解析解与数值解对比曲线;研究了系统外加激励频率接近派生系统固有频率及其2倍、1/2倍时系统的主共振、亚谐波和超谐波共振响应。研究结果表明:多尺度法所得系统近似解析解具有较高的精确度;系统存在较多的共振频域区间,传动系统工作中外加激励应当尽量避免这些频率范围。     

一端固定一端简支输流管道流固耦合振动分析

根据Hamilton原理,建立了一端固定、一端简支输液管道的流固耦合振动控制方程,采用直接解法解出了管道自由振动的固有频率、临界压力和临界流速的表达式。对某采油树管道进行了流固耦合振动计算,分析了流体的流速和压力对管道固有频率的影响,得到了固有频率、临界压力和临界流速与管道长度、流体压力和流速之间的关系曲线。     

旋转柔性悬臂梁的固有频率分析

在精确描述柔性梁非线性变形基础上,利用Lagrange方程推导出考虑动力刚化项的一次近似刚柔耦合动力学方程。忽略柔性梁纵向变形的影响,给出一次近似简化模型,引入无量纲变量,对简化模型作无量纲化处理,首先分析模态截断数对固有频率的影响,其次研究一次近似简化模型和零次近似简化模型的振动特性。研究发现,梁固有频率与模态截断数有关,合理的模态截断数应随无量纲角速度的增大而适当增加;一次近似简化模型的固有频率随无量纲角速度和系统径长比的增大而增大,零次近似简化模型的固有频率随无量纲角速度增大而减小;一次近似简化模型下梁横向弯曲振动不存在物理意义上的共振失稳现象。现有典型文献的相关结论值得商榷。     

基于各向正交异性薄板模型的钢丝绳芯输送带弯曲振动特性分析

基于各向正交异性薄板的小挠度理论,首先建立了钢丝绳芯橡胶输送带上下分支横向自由振动模型,采用经典解法建立了下分支输送带SFSF边界模型、上分支槽型输送带底部SCSC、侧帮SFSC边界模型的解析解,其次采用胡拜尔(Huber)近似推导公式计算了钢丝绳芯输送带的主刚度,最后采用数值分析法对输送机的上、下分支输送带的前6阶固有频率、振型,以及固有频率随张力的变化规律进行了分析。结果表明:上、下分支输送带的固有频率随着带张力的增加而增加,且张力对下分支输送带的频率影响最大,对上分支输送带底边的固有频率影响较小,研究结果为输送带的弯曲振动响应及避免共振设计提供了依据。     

求解非均质变截面轴扭转振动固有频率的混合状态方法

本文给出了均质等截面轴扭转振动的混合状态方程及其解。对于非均质变截面轴，可以把它划分为很多微段，然后，利用段与段之间的连续条件推出一个传递公式，最后，利用边界条件可将固有频率求出。     

悬臂输送管道流-固耦合动力学系统的直接解法

根据变分原理导出了输送管道(流—固耦合问题)自由振动的变分方程,采用直接解法求出了输送管道自由振动的固有频率和极限流速。     

Transfer matrix modelling for the 3-dimensional vibration analysis of piping system containing fluid flow

For three dimensional vibration analysis of piping system containing fluid flow, a transfer matrix formulation is presented. The fluid velocity and pressure were considered, that coupled to longitudinal and flexural vibrations. Transfer matrices were derived from direct solutions of the differential equations of motion of pipe conveying fluids, and the variations of natural frequency with flow velocities for straight and curved pipes were investigated. The results were confirmed to the corrections of known data. The scheme of this study can be easily applied to the related fields, using small size personal computers with core memory about 200kbytes.     

Dynamic analysis of Coriolis flow meter using Timoshenko beam element

Coriolis mass flow meter (CFM) is used to measure the rate of mass flow through a pipe conveying fluid. In the present work, the Coriolis effect produced in the pipe due to a lateral excitation is modeled using the finite element (FE) method in MATLAB©. The coupled equation of motion for the fluid and pipe is converted to FE equations by applying Galerkin technique. The pipe conveying fluid is excited at its fundamental natural frequency. The time lag observed between symmetrically located measurement points which are equidistant from the point of excitation, is utilized to predict the mass flow rate. The results predicted by the present code is validated using the experimental, and numerical results published in the literature. The main contribution is the development of a FE model, using three node Timoshenko beam element to analyse the dynamics of fluid conveying pipes subjected to external excitation. The direction of the Coriolis force is perpendicular to the plane containing the velocity of flow vector and angular velocity vector of the pipe. Hence a three dimensional FE model is essential. This model can include curved geometry, damping, velocity and gyroscopic effects for three dimensional flexible tubes. The reduced integration used for overcoming shear locking in two node elements, will result in the formation of spurious modes leading to an incorrect prediction of natural frequencies and velocity. These modes will not occur while using three node elements. Influence of spatial as well as temporal discretisation on the time lag and frequency are also discussed. The sensitivity analysis shows that the time lag varies linearly with the mass flow rate.     

Experimental determination of time lag due to phase shift on a flexible pipe conveying fluid

A finite element model of a flexible tube conveying fluid is developed in MATLAB^© based on the principle of virtual work, using a three-node isoparametric beam element. Finite element equations are formulated by applying Galerkin technique on the coupled equations of pipe conveying fluid. The present element developed is capable to model three-dimensional flexible tubes by including curved geometry, effects of damping, velocity and gyroscopic effects. The external excitation applied at the middle of the tube in the lateral direction produced a time lag between the lateral responses, which were measured at two equidistant points from the excitation point. This is due to the Coriolis effect, and the same is simulated using the developed code. An experiment, supported with a robust error analysis, is also conducted on a straight polyurethane tube conveying water, subjected to a sinusoidal excitation at the center between the clamped supports. The measured time responses are compared with the numerical values predicted by the code. The time lags for both cases are obtained from the temporal shift along the time axis, between the zero crossing points of the time–response curves. The results obtained agreed well. The code can be used to predict the time lag, which is correlated to the mass flow rate. The proposed method will help to design Coriolis mass flow meters for existing pipelines, without altering the system.     

动力流体传输曲管振动特性有限元分析

针对悬臂的动力流体传输曲管,建立了它的振动方程和有限元分析模型。并通过对AN-SYS软件的二次开发,自定义了单元,以求解带有陀螺矩阵的曲管振动方程;同时考察了输液曲管的稳定性,求出了输液曲管发生颤振失稳时的临界流速。实例计算结果表明自定义的单元是正确的,具有很高的计算精度。用该自定义单元分析输液曲管的振动特性具有一定的实际意义。     

On the vibrations of three-dimensional angled piping systems conveying fluid

The vibrations of three dimensional angled pipe systems conveying fluid are studied by using the finite element method. Extended Hamilton's principle is applied to derive the equations of motion. The characteristics matries consisting of inertia, stiffness, and Coriolis terms are derived by variational method, in which the effects of the internal flow velocity and pressure are considered. The change of dynamic characteristics of the piping system due to the variation of flow velocity, pressure and the geometry of the system is investigated. As a result, it can be found that the natural frequency of the system decreases generally as the flow velocity and pressure increase and that the tendency is more significant as the geometry of the system is similar to the straight pipe.     

两端简支输液管道流固耦合振动分析

根据Hamilton原理推导出流固耦合自由振动变分方程，采用直接解法求解自由振动的固有频率、临界流速和临界压力的解析解表达式。讨论了流速、压力和简支长度的变化对管道固有频率的影响，分析了简支长度和压力的变化对临界流速的影响。     

Dynamic response of rotating flexible cantilever pipe conveying fluid with tip mass

In this study the vibration system is consisted of a rotating cantilever pipe conveying fluid and a tip mass. The equation of motion is derived by using the Lagrange's equation. Also, the equation of motion is derived applying a modeling method that employs hybrid deformation variables. The influences of the rotating angular velocity and the velocity of fluid flow on the dynamic behavior of a cantilever pipe are studied by the numerical method. The effects of a tip mass on the dynamic behavior of a rotating cantilever pipe are also studied. The influences of a tip mass, the velocity of fluid, the angular velocity of a cantilever pipe and the coupling of these factors on the dynamic behavior of a cantilever pipe are analytically clarified. The natural frequencies of a cantilever pipe conveying fluid are proportional to the angular velocity of the pipe and a tip mass in both axial direction and lateral direction.     

Frequency response analysis of cylindrical shells conveying fluid using finite element method

A finite element vibration analysis of thin-watled cylindrical shells conveying fluid with uniform velocity is presented The dynamic behavior of thin-walled shell is based on the Sanders’ theory and the fluid in cyhndrical shell is considered as inviscid and incompressible so that it satisfies the Laplace’s equation A beam-like shell element is used to reduce the number of degrees-of-freedom by restricting to the circumferential modes of cylindrical shell An estimation of frequency response function of the pipe considering of the coupled effects of the internal fluid is presented A dynamic coupling condition of the interface between the fluid and the structure is used The effective thickness of fluid according to circumferential modes is also discussed The influence of fluid velocity on the frequency response function is illustrated and discussed The results by this method are compared with published lesults and those by commercial tools     

Generalized thermodiffusion for an unbounded body with a spherical cavity subjected to periodic loading

In this paper, a general solution to the field equations of generalized thermodiffusion in an infinite thermoelastic body with a spherical cavity has been obtained in the context of the theory of generalized thermoelastic diffusion. The bounding surface of the sphere is subjected to periodic loading and the temperature and chemical potential are assumed to be zero on the curved surface. The generalized theory of thermoelasticity is applied to account for finite velocity of heat propagation. The closed form solutions for distributions of displacement, temperature and stresses are obtained. The solutions valid in the case of small frequency are deduced and the results are compared with the corresponding results obtained in other generalized thermoelasticity theories. Numerical results applicable to a copper-like material are also presented graphically and the nature of variations of the physical quantities with radial coordinate and with frequency of vibration is analyzed.