String wave spraying of liquid

It is established that an impact-excited string partly immersed into a liquid at an angle to its surface produces wave transport and spraying of the liquid. The liquid is sprayed from some regions on the string excited at definite frequencies. A law governing the conditions of liquid spraying is found and explained in terms of the phase difference between transverse and longitudinal waves in various regions of the oscillating string.     

Vibrational movement of a pair of piezoelectric oscillators along a string

The behavior of a pair of synchronously excited piezoelectric oscillators suspended on a horizontal metal string has been studied. It is established that, at certain frequencies of excitation, the oscillators move consistently at a constant velocity along the string and induce oscillations in the form of a standing transverse wave in a part of the string between the points of suspension.     

Steady-state response of the parametrically excited axially moving string constituted by the Boltzmann superposition principle

Summary.  The steady-state transverse vibration of a parametrically excited axially moving string with geometric nonlinearity is investigated in this paper. The Boltzmann superposition principle is employed to characterize the material property of the string. The method of multiple scales is applied directly to the governing equation, which is a nonlinear partial-differential-integral equation. The solvability condition of eliminating the secular terms is established. Closed form solutions for the amplitude and the existence conditions of nontrivial steady-state response of the summation resonance are obtained. Some numerical examples showing effects of the viscoelastic parameter, the amplitude of excitation, the frequency of excitation, and the transport speed are presented. Received February 12, 2002; revised October 25, 2002 Published online: May 8, 2003 The research was supported by the National Natural Science Foundation of China (Project No. 10172056).     

The nature of the movement of a suspended piezoelectric oscillator along a string

A piezoelectric oscillator, suspended with an elastic rod on a string, moves along this string due to the simultaneous excitation of the longitudinal and transverse oscillations in a rod possessing a residual curvature. Devices comprising a piezoelectric oscillator and a beam waveguide have been created and studied. Such systems are prototypes of piezoelectric motors of a new type capable of performing reversible two-way motion.     

轴向往复运动抽油杆柱在弯曲井眼内横向振动的仿真模型

抽油杆柱横向振动的研究是分析油井杆管偏磨现象的基础。该文将定向井抽油杆柱在弯曲井眼内的横向振动问题简化为具有初弯曲的纵横弯曲梁在油管约束下的横向振动问题。除考虑交变轴向载荷对抽油杆柱横向振动的激励外,首次提出弯曲井眼也是轴向往复运动抽油杆柱横向振动的主要激励。综合考虑弯曲井眼对轴向往复运动抽油杆柱横向振动的激励,以及交变轴向载荷对抽油杆柱横向振动的激励,应用弹性碰撞理论描述油管对抽油杆柱横向振动的约束,基于弹性体振动理论建立了具有初弯曲的抽油杆柱在弯曲井眼内的横向振动仿真模型。采用有限差分法与Newmark法实现了对定向井抽油杆柱横向振动的仿真计算。仿真结果表明:仿真结果与现场实际偏磨情况相符,说明在分析抽油杆柱横向振动时,轴向运动导致的弯曲井眼激励是一项不可忽略的因素;算例油井中,杆管偏磨的危险点主要出现在油井的造斜段与抽油杆柱的受压段。该文所建立定向井抽油杆柱横向振动仿真模型可用于指导抽油杆扶正器的优化配置。     

横向风荷载作用下轴向运动弦线自激振动和稳定性分析

研究了横向定常风荷载作用下轴向运动弦线的非线性自激振动问题。将风荷载模型化为平均风速的非线性函数,建立动力学微分方程。采用Galerkin方法,将运动弦线简化为离散的二维系统并进行线性化,分析弦线平衡构型的稳定性,根据Routh-Hurtwitz判据确定了平衡点的稳定域。确定了多参数下Hopf分岔点及产生稳定极限环的条件。使用增量谐波平衡(IHB)法求解了自激振动的周期响应,按照Floquet理论确定了周期解的稳定性。最后,讨论了运动速度和平均风速稳定性的影响,并给出相应的稳定性条件。     

Transverse vibrations of an axially accelerating viscoelastic string with geometric nonlinearity

Two-to-one parametric resonance in transverse vibration of an axially accelerating viscoelastic string with geometric nonlinearity is investigated. The transport speed is assumed to be a constant mean speed with small harmonic variations. The nonlinear partial differential equation that governs transverse vibration of the string is derived from Newton's second law. The method of multiple scales is applied directly to the equation, and the solvability condition of eliminating secular terms is established. Closed-form solutions for the amplitude of the vibration and the existence conditions of nontrivial steady-state response in two-to-one parametric resonance are obtained. Some numerical examples showing effects of the mean transport speed, the amplitude and the frequency of speed variation are presented. Lyapunov's linearized stability theory is employed to analyze the stability of the trivial and nontrivial solutions for two-to-one parametric resonance. Some numerical examples highlighting the effects of the related parameters on the stability conditions are presented.     

Stabilization of a nonlinear Kirchhoff equation by boundary feedback control

This paper is concerned with stabilization of an axially moving Kirchhoff string by boundary feedback control. We derive a nonlinear system describing transverse oscillation of the string using Hamilton??s principle and prove exponential stabilization of the system by the direct Lyapunov method. The result shows that oscillation of a nonlinear axially moving Kirchhoff string can be suppressed by a new type of boundary feedback control.     

粘弹性流体法向力作用下的抽油杆柱横向振动仿真

聚合物抽油机井抽油杆柱在粘弹性流体井筒内偏心运动时,抽油杆柱受到交变粘弹性流体法向力的作用。该文指出了交变粘弹性流体法向力是抽油杆柱横向振动的激励。考虑抽油杆柱所受粘弹性流体法向力与抽油杆柱横向振动位移的耦合关系,建立了受粘弹性流体法向力作用的抽油杆柱在油管内横向振动仿真的力学和数学模型。采用有限差分法和Newmark法实现了对抽油杆柱在油管内横向振动的仿真计算。分析了抽油杆柱在初始偏心和粘弹性流体法向力激励下的横向振动规律。仿真结果表明:抽油杆柱的任何初始偏心都会导致在全井范围内发生杆管碰撞现象;抽油杆柱下冲程杆管碰撞更为剧烈,且泵端附近碰撞力最大;由于粘弹性流体法向力的存在,杆柱与油管壁的接触碰撞更加频繁,加剧了杆管偏磨。所建立的粘弹性流体法向力作用下的抽油杆柱横向振动仿真模型对于聚驱井杆管偏磨分析、扶正器的优化配置具有指导作用。     

Theory of the thermoelastic generation of mechanical vibrations in internally stressed solids by laser radiation

An investigation was made of the behavior of transient deformations in solids with internal stresses exposed to time-modulated laser radiation. The nonlinear theory of thermoelasticity is used to propose a model for the excitation of mechanical stresses which takes account of the stress dependence of the thermoelastic coupling parameter. An expression is derived for the electric signal recorded by a piezoelement when mechanical vibrations are generated in a uniformly deformed sample. The results are compared with existing experimental data and show qualitative agreement. Pis’ma Zh. Tekh. Fiz. 24, 82–88 (July 12, 1998)     

Application of a second-order Godunov-type finite difference scheme to a nonlinear elastodynamic problem

A second-order Godunov-type finite difference scheme is applied to the governing equations of finite amplitude plane motion of a hyperelastic string. The governing equations, expressed in conservation form, are a hyperbolic system of four first-order partial differential equations. Numerical results are presented for a string subjected to a transverse impact at its midpoint, and the string is modelled by a strain energy function which is realistic for simple tension. Similarity solutions, valid for times before reflections occur, are in excellent agreement with the results from the finite difference scheme and provide a partial check on the validity of the scheme. Numerical results, which include the effects of reflections and interactions of waves, are shown graphically.     

Numerical analysis of the radiated fields of ultrasonic transducers

A finite element model is implemented for simulating the radiated fields of both planar and curved transducers in acoustic media. The approach is based on general finite element analysis developed for solving the governing equations of elastic wave propagation. The distributions of the wave fields are presented for both the nearfield and farfield regions of the transducer. Three excitation pulses with the same center frequency but different bandwidths are examined and the accuracy is indicated by a comparison of the simulation results for the axial and transverse fields with the analytical results for continuous wave excitation.     

Piezoelectric fiber optic phase modulator with a reduced level of spurious polarization modulation

It is experimentally demonstrated that a tenfold decrease in the level of spurious polarization modulation can be achieved in a fiber optic phase modulator comprising two fiber sections featuring the polarization mode conversion, arranged on the same piezoelement.     

A superposition method of reflected wave for moving string vibration with nonclassical boundary

A reflected wave superposition method is proposed for an axially traveling string with classical and nonclassical boundaries, based on the reflection of the propagating wave on both sides of the string, combining its initial conditions and the continuity conditions in order to obtain the expressions for the reflected wave. The reflection process, in three phases, is deduced and a determinate expression for the transverse vibration is obtained. The correctness and superiority of the proposed method is verified by comparison with the Newmark-β method for an axially moving string with a fixed and a spring-dashpot boundary.     

受压旋转钻柱非线性动力学与分叉研究

在水平井钻井过程中,钻柱由于受压很容易发生横向振动,引发钻柱失效、井眼扩径等严重事故。该文将受压柔性旋转钻柱简化为柔性旋转梁,将钻柱受到的复杂载荷简化到柔性旋转梁系统中,基于vonKarman理论建立了柔性钻柱的动力学方程,再利用Galerkin法离散偏微分方程,得到了钻柱的非线性控制方程,并且利用多尺度法得到了平均方程。运用非线性动力学的方法分析柔性旋转梁在共振情况下的复杂动力学响应,得出系统中钻柱旋转角速度对非线性动力学响应的变化规律。研究结果可为水平井钻井过程中减少钻柱失效、提高钻速和降低钻井成本提供参考。     

Dynamical stripe correlations in Cuprate superconductors

Based on the recent observation of the stripe instability in Cuprate superconductors, we present the hypothesis that the normal state finds its origin in a particular kind of stripe-quantum fluid. The charged domain walls are interpreted as strings on a lattice and the quantum fluctuation of an individual string is driven by a proliferation of kinks. The kink dynamics gives rise to meandering fluctuations of the string as a whole. We identify a special string vacuum characterized by a proliferation of charged kinks. This state carries a Luttinger-liquid like electronic excitation spectrum.     

时变长度轴向移动绳横向受迫振动数值分析

分别建立移动集中载荷和移动分布式载荷作用下时变长度轴向移动绳系统的物理模型,基于Leibniz 法和Hamilton 原理推导具有时变参数的横向受迫振动方程,Galerkin法将其离散处理为一系列非线性常微分方程组,改进的四阶Runge-Kutta用于求解不同Galerkin截断阶数的非线性常微分方程组,同时分析基于有限元法求解系统运动方程及Newmark-β数值计算的移动集中载荷下变长度轴向移动绳系统横向振动特性。两种方法数值分析吻合性及收敛性表明建立变长绳移系统模型可靠性及求解时变参数系统方法有效性,同时变长度轴向移动绳系统在不同情况下采用恰当的Galerkin截断阶数能到达更好收敛性及保证计算精度。     

On the application of generalized integral transform technique to wind‐induced vibrations on overhead conductors

The aim of the present paper is to describe the application of the generalized integral transform technique (GITT) for the theoretical analysis of wind‐induced vibrations on overhead conductors. In the mathematical model adopted, the complicated helicoidal geometry of the conductor is simplified by treating it as a homogeneous taut string simple supported at both ends. Solving the governing partial differential equation through the GITT approach, one derives purely analytical or analytical–numerical solutions for the conductor transverse displacement as a function of both position and time. In order to highlight the potential and flexibility of the GITT approach to account for realistic features of the phenomenon, three particular cases of practical interest are analyzed in detail, for which benchmark results are provided: (i) the damped‐free vibrations of the conductor; (ii) the harmonic‐forced vibrations of the conductor without and with Stockbridge dampers; and (iii) the forced vibrations of the conductor under a non‐linear wind excitation. The current results may be combined with previous analytical predictions to compute the conductor amplitudes and bending strains at critical locations. Although this work is focused on a taut string model for the conductor, the approach described herein may be easily extendable to the beam model. Copyright © 2008 John Wiley & Sons, Ltd.     

Gas Flow in a Plane Channel with Oscillating Walls

Gas oscillations occurring in a plane channel in excitation of elastic walls which is symmetric relative to the longitudinal axis are investigated by the methods of numerical modeling. The spatial localization of transverse and longitudinal waves has been revealed and the character of resonance oscillations of the gas in the vicinity of the excitation region for different velocities of the flow has been established.     

抽油杆柱纵向振动共振条件的质疑与力学模型的修正

在研究抽油杆柱纵向振动特性时，将抽油杆柱简化为上端固定于随悬点运动的基础之上、下端受液体负荷激励的力学模型。研究了单级抽油杆柱纵向自由振动的固有频率以及抽油杆柱对各种激励的稳态响应。建立了单级杆柱第i阶固有频率pi和基频p0之间的关系，即pi=(2i-1)p0，指出了单级抽油杆柱产生共振的条件是激励频率等于基频的奇数倍，证明了APIRPllL有杆抽油系统的设计计算推荐方法中关于激励频率等于偶数倍基频时，单级杆柱将产生共振的结论是错误的，并指出了导致这一错误结论的原因是所采用的力学模型是错误的。通过对抽油杆柱动态特性的计算机仿真，进一步证明了本文结论的正确性。