圆截面弹性细杆的平面振动

基于Kirchhoff理论讨论圆截面弹性细杆的平面振动．以杆中心线的Frenet坐标系为参考系建立动力学方程．杆作平面运动时,其扭转振动与弯曲振动解耦．讨论任意形状杆的扭转振动和轴向受压直杆在无扭转条件下的弯曲振动,证明直杆平衡的静态Lyapunov稳定性与欧拉稳定性条件为动态稳定性的必要条件．考虑轴向力和截面转动惯性效应的影响,导出弯曲振动的固有频率．     

Rotation of a rod system containing inertial fluid flow

This paper considers a rod system for which it is possible to correctly formulate and solve the problem of three-dimensional motion in the physical space of an elastic pipeline area containing inertial incompressible fluid flow. The precession of the axis of an elastic pipeline along which inertial incompressible fluid flows is described, a physical phenomenon which has not been previously studied. With the use of rigid body dynamics, it was theoretically established that a three-dimensional dynamic process is possible in an open (exchanging mass with the environment) elastic-inertial rod system.     

Numerical—Experimental Investigation of the Elastic Deformation of a Polymeric Pipeline under Impact

The paper reports results of numerical—experimental investigation of the hydroelastic process in a polyimide pipeline filled with a fluid. The propagation of small perturbations in the fluid is considered in an acoustic approximation based on wave equations. The equations are integrated using the method of characteristics and a two–layer difference scheme. The elastic problem is solved by the finite element method and the Newmark difference –method. The stress—strain state of the pipeline is defined by a superposition of fast rod modes of motion and slow shell modes of motion. Satisfactory agreement between calculated and experimental data is obtained.     

考虑分布轴向力的细长杆横向振动与失稳分析

为量化梁、杆、柱的自重(下称分布轴向力)对静力失稳和动力横向振动的影响,在《材料力学》和《机械系统动力学》教材的基础上,建立了分布轴向力下的杆柱失稳和横向振动的力学、数学模型.采用有限差分法、伽辽金法和数值积分法获取计算结果.结果表明:考虑分布轴向力的杆柱横向振动固有频率随杆长增加而减小,杆柱失稳时一阶固有频率为0;分...     

Proof-of-concept prototype development of the self-propelled capsule system for pipeline inspection

This paper studies the prototype development for the self-propelled capsule system which is driven by autogenous vibrations and impacts under external resistance forces. This project aims for proof-of-concept of its locomotion in pipeline environment in order to mitigate the technical complexities and difficulties brought by current pressure-driven pipeline inspection technologies. Non-smooth multibody dynamics is applied to describe the motion of the capsule system, and two non-smooth nonlinearities, friction and impact, are considered in modelling. The prototype of the self-propelled capsule system driven by a push-type solenoid with a periodically excited rod has been designed to verify the modelling approach. The prototype contains a microcontroller, a power supply, and a wireless control module, which has been tested in a clear uPVC pipe via remote control. Various control parameters, e.g. impact stiffness, frequency and amplitude of excitation, are studied experimentally, and finally, the fastest progression of the system is obtained.     

Impact of axial compression and torque on strain localization and fracture under complex cyclic loading of Plexiglas rods

Experimental studies of deformation and fracture of rods made of Plexiglas (PMMA) under complex loading (quasi-static and cyclic torsion under axial compression) are performed. The existence of a range of critical values of axial stress, within which the rod is fractured by the torque, is established. The localization of “frozen” highly elastic strains in constrained cyclic torsion is revealed, and the conditions of its occurrence are determined. The effect of axial stress on strain localization and fracture and the influence of cyclic torsion on the loss of stability of a rod under axial compression are shown.     

Numerical and Asymptotic Solution of the Equations of Propagation of Hydroelastic Vibrations in a Curved Pipe

A mathematical model for propagation of hydroelastic waves in a pipe is developed using the equations of motion of a shell and a fluid. A method for deriving two–dimensional equations is proposed, and asymptotic formulas for solutions of these equations are obtained. A model problem is solved numerically, and the results are compared with data obtained by others. The results obtained make it possible to calculate the propagation of pressure waves for an arbitrary (within the framework of the assumptions made) shape of the axial line of the pipe and can be used in designing systems for diagnostics of pipeline performance.     

Soft-impact dynamics of deformable bodies

Systems constituted by impacting beams and rods of non-negligible mass are often encountered in many applications of engineering practice. The impact between two rigid bodies is an intrinsically indeterminate problem due to the arbitrariness of the velocities after the instantaneous impact and implicates an infinite value of the contact force. The arbitrariness of after-impact velocities is solved by releasing the impenetrability condition as an internal constraint of the bodies and by allowing for elastic deformations at contact during an impact of finite duration. In this paper, the latter goal is achieved by interposing a concentrate spring between a beam and a rod at their contact point, simulating the deformability of impacting bodies at the interaction zones. A reliable and convenient method for determining impact forces is also presented. An example of engineering interest is carried out: a flexible beam that impacts on an axially deformable strut. The solution of motion under a harmonic excitation of the beam built-in base is found in terms of transverse and axial displacements of the beam and rod, respectively, by superimposition of a finite number of modal contributions. Numerical investigations are performed in order to examine the influence of the rigidity of the contact spring and of the ratio between the first natural frequencies of the beam and the rod, respectively, on the system response, namely impact velocity, maximum displacement, spring stretching and contact force. Impact velocity diagrams, nonlinear resonance curves and phase portraits are presented to determine regions of periodic motion with impacts and the appearance of chaotic solutions, and parameter ranges where the functionality of the non-structural element is at risk.     

杆件在横向力和轴向压力共同作用下的内力计算

针对杆件在横向力和轴向压力共同作用下的内力计算问题进行了研究．在考虑杆件变形因素的情形下,推导出了杆件在横向力和轴向压力共同作用下的内力和正应力的计算公式,并与材料力学中未考虑杆件变形因素的对应公式进行了比较,说明了二者之间不同之处．     

Spatial Motion of a Rod in a Viscous Fluid Flow

Equations of spatial motion of a curved finitelength rod in a viscous fluid flow are derived. Analytical solutions of problems on the motion of a straight rod under conditions of pure shear, simple shear, and uniaxial extension of the fluid are obtained. Longitudinal stability of the straight rod during its spatial motion is considered. Effective viscosity of a suspension filled by rigid straight rods is evaluated.     

Fluid–structure interaction with viscoelastic supports during waterhammer in a pipeline

Waterhammer modeling with fluid–structure interaction (FSI) in a pipeline with axial viscoelastic supports is the aim of this research. The viscoelastic materials of supports (or the pipe wall) were described using the generalized Kelvin–Voigt model. Hydraulic governing equations were solved by the method of characteristic (MOC) and axial vibration equation of the pipe wall was solved using the finite element method (FEM) in the time domain. For a typical case study, four different types for supporting the pipeline in the axial direction: fully free to move; fixed (rigid support); elastic and viscoelastic supports, subject to a waterhammer are analyzed and the results are scrutinized. The results quantitatively confirm that the use of supports with viscoelastic behavior in the axial direction of the pipeline can significantly reduce axial-pipe vibrations (displacements and stresses). The consequences of this structural damping on the attenuation of the internal fluid pressure are further demonstrated.     

Post-buckling of a cantilever rod with variable cross-sections under combined load

IntroductionSinceEuler[1] ,Lagrange[2 ] ,Love[3 ] etal.investigatedtheslenderrod ,asoneofthebasicstructuralstabilityproblems ,manyattentionshavebeenpaidtothepost_bucklingofelasticrodsforalongtime .Today ,flexiblerodshavebeenwidelyusedasspring ,linkages ,robot’sarms,largeantennasandsoon .Hence ,thestudiesofpost_bucklingofelasticrodshavewideengineeringandapplyingbackgroundsinrecentdays .Basedontheassumptionthattheaxiallineoftherodisinextensible ,Timoshenkoetal.[4] examinedthepost_bucklingofco…     

爆轰驱动异形杆在空气阻力作用下的动力学模拟

针对本文中提出的一种异形杆结构设计方案,建立爆轰驱动异形杆动力学模型,利用ANSYS/LS-DYNA对爆轰驱动异形杆的运动过程进行了数值模拟,获得了爆炸作用结束后产生塑性变形的异形杆模型及初速度。爆炸作用后异形杆在空气流场中运动只产生弹性变形,将杆视为柔性体,运用ADAMS软件对异形杆在空气阻力作用下的运动过程进行了数值模拟。分析结果表明,将异形杆视为柔性体,考虑爆轰作用引起的杆条塑性变形这一数值算法能更准确地描述爆轰驱动异形杆在空气阻力作用下的运动规律。     

舰载飞机起落架突伸时外筒应力陡增分析

分析了某舰载飞机斜板滑跃起飞试飞时,前起落架在机轮出斜板而卸载后,缓冲器外筒轴向应力未减小反而陡增的现象。在介绍缓冲器结构、工作原理和受力数学模型的基础上,建立了缓冲器外筒轴向应力的计算模型;结合对实测数据的分析,揭示了缓冲器外筒应力陡增的原因。结果表明:外筒轴向应力与缓冲器的行程和活塞运动速度相关,起落架出斜板后外筒应力陡增的主要原因是起落架突伸时,活塞杆高速伸出引起油液阻尼力大幅增加及高速伸出的起落架的下部质量在反阻活门关闭瞬间对外筒底面的撞击。     

Simulation of void fraction profile evolution in subcooled nucleate boiling flow in a vertical annulus using a bubble-tracking approach

A three-dimensional bubble-tracking model of subcooled nucleate boiling flow in a vertical channel at low-pressure conditions is proposed with specific application to the case of boiling in an annulus with a central heating rod. Vapour is distributed in the liquid in the form of individually tracked bubbles. The overall behaviour of the liquid–vapour system results from motion, interaction, coalescence and boiling mechanisms prescribed mostly at the level of bubbles. Bubbles are nucleated at nucleation sites randomly distributed over the heated surface. After nucleation, bubbles slide on the heated wall, detach and then migrate into the lower-temperature region away from the heated surface, where they condense. The proposed model was applied to experiments on subcooled boiling from Purdue University (USA). Experimental and calculated void fraction radial profiles at different axial locations are compared.     

Influence of the connecting condition on the dynamic buckling of longitudinal impact for an elastic rod

The stress wave propagation law and dynamic buckling critical velocity are formulated and solved by considering a general axial connecting boundary for a slender elastic straight rod impacted by a rigid body. The influence of connecting stiffness on the critical velocity is investigated with varied impactor mass and buckling time. The influences of rod length and rod mass on the critical velocity are also discussed. It is found that greater connecting stiffness leads to larger stress amplitude, and further results in lower critical velocity. It is particularly noteworthy that when the connecting stiffness is less than a certain value,dynamic buckling only occurs before stress wave reflects off the connecting end. It is also shown that longer rod with larger slenderness ratio is easier to buckle, and the critical velocity for a larger-mass rod is higher than that for a lighter rod with the same geometry.     

Longitudinal waves in one dimensional non-uniform waveguides

Wave approach is used to analyze the longitudinal wave motion in one dimensional non-uniform waveguides. With assumptions of constant wave velocity and no wave conversion, there exist four types of non-uniform rods and corresponding traveling wave solutions are investigated. The obtained results indicate that the kinetic energy is preserved as a constant and the wave amplitude is inversely proportional to square root of the cross-sectional area of the rod. Under certain condition, there exists a cut-off frequency for the rod with variation in geometric or material properties, below which waves do not propagate along the non-uniform rod. For the rod with arbitrary variable cross-section, the conclusions are similar if the wave frequency is high enough. And a series solution of the wave motion is presented.     

Influence of swirl on the stability of a rod in annular leakage flow

The influence of swirl (flow rotation) on the stability of a rod in annular leakage flow is investigated. Under the assumption of laminar flow and plane vibrations (no whirling), it is shown that the swirl acts, in effect, as an elastic foundation with negative foundation stiffness, the magnitude being proportional to the mean circumferential flow rate squared. Consequently, swirl always lowers the critical axial flow speed in case of divergence instability of a rod of finite length. Numerical analysis is needed to predict the effect of swirl in case of flutter instability of a finite rod; this is not performed here. However, for the flutter-like instability of travelling waves in an infinite rod-channel system, it is shown analytically that swirl again always lowers the critical axial flow speed. Finally, it is found that by circumferential flow alone, the travelling waves are extinguished at a certain flow rate, followed by a divergence-like instability.     

Swing-up and positioning control of an inverted wheeled cart pendulum system with chaotic balancing motions

This paper explores the problem of swinging-up an inverted pendulum formed by a rod attached to a wheeled cart with a hanging bob at its opposite end. The system is driven by the wheeled cart platform system, which is formed by a cart, wheels with counterbalance and connecting-rods. The model of the system is initially obtained under the assumption of rolling without slipping of the wheels, which is then verified by computing the reaction forces. The motion of the wheeled cart is initially oscillating, whereas the rod can move freely giving rise to an under-actuated mechanical system. From the harmonic prescribed motion for the wheeled cart, necessary conditions for chaotic rod motion are deduced by means of the Melnikov function. Once the chaotic oscillation has been reached and the rod is close to the upright position, the force over the wheeled cart is commutated to a control law based on the pole-placement plus integrator technique. This procedure allows driving the rod and the wheeled cart system to the upright position and to a prescribed set point respectively. The onset of strange attractors is crucial in the design of the control law, whose performance to obtain rolling without slipping is researched by means of sensitive dependence, power spectral density, Lyapunov exponents and reaction forces. The results of the analytical calculations are verified by full numerical simulations.