Modeling of vibrational non-impact motion of mobile-based body

The paper deals with vibrational non-impact displacement of a mobile-based body on an inclined plane. Two cases are considered: when the body is subjected to kinematical excitement, and when the plane is excited in two perpendicular directions. This phenomenon is used in vibratory assembly devices, where vibration excitement compensates interdependent orientation errors of the components subjected to assembly. Transient and periodic regimes of the body motion from static to dynamic equilibrium are investigated. Dependencies of maximum displacement and average creeping displacement speed upon the elastic resistance force, body pressure to the plane force, the ratio of mutually perpendicular vibration amplitudes, and the phase of these vibrations are presented. The possibilities and conditions of automatic components assembling by applying vibration displacement are characterized.     

Vibrational dynamics of a light body in a liquid-filled rotating cylinder

The behavior of a light free cylindrical body in a rapidly rotating horizontal cylinder containing a liquid under vibrational action (the vibration direction is perpendicular to the rotation axis) is investigated. An intense rotation of the body relative to the cavity is detected. Depending on the vibration frequency, the body rotation velocity in the laboratory reference system may be higher or lower than the cavity rotation velocity and in the resonance region they may differ by several times. The mechanism of motion generation is theoretically described. It is shown that the motion is related with the excitation of inertial oscillations of the body: the cause of the motion is an average vibrational force generated due to nonlinear effects in the Stokes boundary layer near the oscillating body. The formation of large-scale axisymmetric vortex structures periodic along the rotation axis, which appear under conditions of inertial oscillation of the body during its motion, both leading and lagging, is detected.     

Effect of vibration on the stability of a plane displacement front in a porous medium

The effect of linearly polarized vibration on the stability of a plane displacement front in a porous medium is studied. The problem of the stability of the motion of a plane displacement front traveling at a constant velocity U under the action of vibration normal to the front is considered. It is shown that under the action of vibration the dynamics of the plane displacement front can be described by the Mathieu equation with a dissipative term. Using the standard averaging method, in the case of high-frequency vibration it is revealed that vibration can only increase the stability of the system. It is found that the vibration stabilizes the plane displacement front with respect to part of the perturbation spectrum.     

Vibrational thermal convection about a uniformly heated cylinder

Vibrational convection under conditions of weightlessness has now been investigated for closed cavities of various geometries (see, for example, [1–3]). However, the question of vibrational convection developing around a heated body in an unconfined fluid remains open. Here, the convection developing under conditions of weightlessness about a uniformly heated infinite cylinder vibrating at high frequencies together with the fluid in a direction perpendicular to the cylinder axis is considered. The nonlinear equations of averaged motion are solved numerically by a finite-difference method. It is shown that at high values of the vibrational Grashof number boundary-layer type flow with a structure consisting of two symmetrical jets perpendicular to the direction of vibration is formed. The flow and heat transfer characteristics are determined.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 23–26, May–June, 1989.The author wishes to thank E. M. Zhukovitskii for supervising the work.     

几何非线性摩擦阻尼隔振系统动力学行为研究

非线性隔振系统由于具有较线性系统更优的隔振性能,因此在工程中应用广泛.本文通过配置与被隔振对象的运动方向相垂直的库伦摩擦阻尼器,构建了几何非线性摩擦阻尼模型.由于引入了几何非线性,因此其摩擦力与位移正相关,这与传统与位移无关摩擦力模型有显著不同.首先,建立了具有几何非线性摩擦阻尼的数学模型以及隔振系统的受迫振动方程;然后,使用谐波平衡法求解了动力学方程,并使用数值仿真方法验证了谐波平衡法求解的准确性;最后,研究了几何非线性摩擦阻尼隔振器的绝对位移传递率和相对位移传递率.研究结果表明,在库伦摩擦阻尼选择适当,非线性摩擦阻尼系统可以在保持高频振动衰减效果的前提下,显著降低系统共振峰,其性能优于传统的恒定摩擦阻尼隔振模型.同时,几何非线性摩擦阻尼系统能够避免传统摩擦阻尼系统中的“锁定”现象,从传递率角度来说,不利于共振峰控制;但从激励环境改变引发隔振系统失效的角度来看,几何非线性摩擦阻尼系统可以拓宽系统对激励幅值的适应范围,避免隔振系统失效.本文的研究结果对此类隔振系统的设计和摩擦阻尼参数的选择具有通用的指导意义.      

锻压操作机夹持长棒料随动过程动态受力分析

研究了锻压操作机夹持长棒料锻件锻压随动过程中夹钳的受力状态。利用拉格朗日方程及有限元方法建立了包含操作机及其锻件的总体动力学方程。操作机系统建立为端部悬挂质量弹簧的Euler-Bernoulli梁模型,随动过程中因为梁上节点位移激励引起操作机系统的瞬态振动。计算结果与LS-DYNA显式有限元模型结果进行了比对,吻合良好。结果表明,对于长棒料锻件,液压机锻压的位置对操作机的动态受力有着十分显著的影响。     

Thermal Vibrational Convection in Rotating Cavities

The average vibrational motion of a nonisothermal fluid in a uniformly rotating cavity is described theoretically. Equations are obtained using the averaging technique in the high-frequency vibration approximation. It is found that the rotation significantly affects both the intensity of the average flows and the structure of the pulsatory velocity field generating resonance amplification of the fluid vibrations ar certain ratios of the rotation frequency and the force field oscillation frequency. This makes rotation an important controlling factor ensuring a strong averaged effect under relatively weak vibrational action. The problem of excitation of vibrational convection in a plane rotating layer is considered on the basis of the equations obtained when the vibration frequency substantially exceeds the rotation frequency.     

A light cylinder under horizontal vibration in a cavity filled with a fluid

The behavior of a light cylindrical body of circular cross-section under horizontal vibration in a rectangular cavity filled with a fluid is experimentally investigated. At critical vibration intensity the body is repelled from the upper side of the cavity and takes up a stable suspended position, in which the gravity field is balanced by the vibrational repulsive force, executing longitudinal oscillations. As the vibrations are intensified, the gap between the cylinder and the wall widens. A new form of instability, namely, the excitation of the tangential motion of the body along the vibration axis, is found to exist on the supercritical range. The cylinder is at a finite distance from the upper side of the cavity and the tangential motion is due to the loss of symmetry of the oscillating motion. The transition of the cylinder to the suspended state and its return to the wall, as well as the excitation of the average longitudinal motion and its cessation, occur thresholdwise and have a hysteresis. The body dynamics are studied as a function of the dimensionless vibration frequency.     

Application of active piezoelectric patches in controlling the dynamic response of a thin rectangular plate under a moving mass

The governing differential equation of motion for an undamped thin rectangular plate with a number of bonded piezoelectric patches on its surface and arbitrary boundary conditions is derived using Hamilton’s principle. A moving mass traveling on an arbitrary trajectory acts as an external excitation for the system. The effect of the moving mass inertia is considered using all the out-of-plane translational acceleration components. The method of eigenfunction expansion is used to transform the equation of motion into a number of coupled ordinary differential equations. A classical closed-loop optimal control algorithm is employed to suppress the dynamic response of the system, determining the required voltage of each piezoactuator at any time interval. In a numerical example for a simply supported square plate under two different loading paths, the effect of the mass velocity and mass weight of the moving load on the dynamic behavior of the uncontrolled system is investigated. The results show that, depending on the path of the moving mass, the inertia effect is very important, causing different behaviors of the system. In addition, the number of vibrational modes involved in determining the dynamic response of the system is crucial. The inertia effect is more important for an orbiting mass loading case compared to the case in which the moving mass is traversing the plate on a straight line. A number of equally spaced piezo patches are used on the lower surface of the plate to control the displacement of the center point of the plate. The implemented control mechanism proves to be very efficient in suppressing the near resonant dynamic response of the system, requiring fairly low levels of voltage for each patch. Increasing the area of the employed piezo patches would reduce the required maximum voltage for controlling the response of the system.     

正交各向异性地基平面问题动力响应研究

以位移分量为基本未知量,在直角坐标系下建立正交各向异性地基的平面应变问题动力偏微分方程．采用Laplace-Fourier变换和逆变换方法,引入初始条件和边界条件,推导了任意形式表面动荷载作用下正交各向异性地基平面问题在时域内动力反应的积分形式解．基于理论解,编制了相应的计算程序,并对正交各向异性土
体表面作用线性移动谐振荷载进行了算例分析,研究了土体参数、荷载移动速度、荷载频率不同而导致的土体表面各点竖向位移幅值的变化规律,以及荷载速度对竖向应力分量的影响规律．数值分析结果表明：土体的各向异性、荷载频率和移动速度对表面位移幅值有较大影响,土体阻尼比对于荷载中心点附近的位移幅值影响较小;荷载移动速度对于竖向应力分量有较大影响,这对工程实践具有重要指导意义．     

The circular disk straddling the interface of a two-phase flow

The motion is determined for a thin circular disk straddling the plane interface of an immiscible two phase creeping flow and moving parallel or perpendicular to the interface. Expressions are derived for the drag coefficient on the disk.     

高速铁路碎石道砟振动的离散元模拟

道砟振动对其磨损、破碎和道床累积变形有显著影响,为揭示高速车辆移动荷载作用下道砟动态响应特性,建立有砟道床离散元模型,开展车辆-轨道耦合动力学计算得到离散元模型输入荷载,模拟分析高速车辆以不同速度通过时有砟道床的振动响应,并与车辆-轨道耦合动力学计算结果进行对比分析。结果表明,轨枕、道砟和道床块振动位移波形相似,位移幅值沿道床深度方向减小,道床块振动位移与轨枕底面以下0.3m处道砟的振动位移相当;轨枕、道床块振动速度与加速度随行车速度提高而增大;受道砟颗粒间复杂相互作用的影响,道砟振动加速度会出现突变。道床离散元模型能合理反映道砟颗粒的振动响应特性,道床块模型体现了道床层在有砟轨道结构中的动力传递与减振特性,两种道床模型的计算结果具有一定的相似性。     

Thermostressed state of a piezoelectric bodywith a plane crack under symmetric thermal load

The paper addresses a thermoelectroelastic problem for a piezoelectric body with an arbitrarily shaped plane crack in a plane perpendicular to the polarization axis under a symmetric thermal load. A relationship between the intensity factors for stress (SIF) and electric displacement (EDIF) in an infinite piezoceramic body with a crack under a thermal load and the SIF for a purely elastic body with a crack of the same shape under a mechanical load is established. This makes it possible to find the SIF and EDIF for an electroelastic material from the elastic solution without the need to solve specific problems of thermoelasticity. The SIF and EDIF for a piezoceramic body with an elliptic crack and linear distribution of temperature over the crack surface are found as an example __________ Translated from Prikladnaya Mekhanika, Vol. 44, No. 3, pp. 96–108, March 2008.     

Sand-Fluid Interface under Vibration

The average dynamics of the interface between a pure fluid and a granular medium with fluid-filled pores in a closed vibrating cavity are investigated experimentally. Three types of vibration, namely, linear and circular translational in a horizontal plane and rotational about a vertical axis, are considered. In all cases, the excitation of a dynamic relief on the surface of the granular medium, preceded by fluidization of the sand, is observed. For more complicated vibration types, additional average effects are manifested, such as the generation of an average granular-medium motion relative to the cavity under circular vibration and the displacement of the fluidized granular medium toward the rotation axis under rotational vibration. In the cases considered, the regularities of the average dynamics of the fluidized granular medium are found. It is shown that the phenomena in a granular-medium-fluid system can be analyzed using the two-fluid theoretical model.     

Free vibration analysis of open thin deep shells with variable radii of curvature

In the present paper, free vibration of a thin open curved shell with parabolic curvature was studied. This shell has a curvature with variable radius in one direction. The equations of motion of this shell were inferred by first order shell theory. According to perpendicular nature of loading on shell of marine structures, the assumptions of Donnell–Mushtari–Vlasov can be used with an acceptable level of accuracy and the in-plane displacement along shell straight direction “x” can be neglected as compared to the displacement in two other directions. The natural frequencies and mode shapes related to the first five vibrational modes were extracted using semi-analytical methods including power series method, Galerkin method and beam function method. The results of the semi-analytical methods were validated against those obtained by using the finite element method. Out of the studied semi-analytical methods, Galerkin method was found to have an appropriate convergence in both natural frequency and mode shape. Adopting eight terms of the response series, Galerkin method has an appropriate convergence compared with the results of finite element.     

车-轨-桥耦合动力系统影响参数分析

为了考虑高速列车、板式无砟轨道和桥梁相互作用的特点,需将列车模拟为质量-弹簧-阻尼多刚体相互约束的系统,通过列车车轮与钢轨的接触关系,建立车-轨-桥耦合系统的运动方程。重点分析了双线列车以不同工况通过高速铁路桥梁时,列车行驶状态(速度和加速度)、列车悬挂系数和钢轨-轨道-桥梁连接参数分别对车-轨-桥耦合系统的动力学性能影响。结果表明,(1)列车的加速度和速度的变化对耦合系统有不同程度的影响,随着列车行驶速度与加速度在一定范围内增加,车体自身结构的位移振动响应逐渐减小,而钢轨和桥梁结构的位移振动响应则不断增加;(2)列车悬挂参数的改变对列车自身结构影响较大,而对钢轨和桥梁结构影响很小;(3)车体一系刚度系数增大会引起列车系统结构振动响应变大,但车体二系刚度系数的增加却抑制了车体结构的振动响应;(4)除了钢轨的最大加速度随着连续刚度系数增加呈线性递减外,列车、钢轨和桥梁的振动响应不易受钢轨与桥梁间连接参数的影响。     

Nonlinear dynamics of an elastic rod with frictional impact

A model is presented for the impact with friction of a flexible body in translation and rotation. This model consists of a system of nonlinear differential equations which considers the multiple collisions as well as frictional effects at the contacting end, and allows one to predict the rigid and elastic body motion after the impact. The kinetic energy is derived by utilizing a generalized velocity field theory for elastic solids. The model uses a dry coefficient of friction and a nonlinear contact force. We introduce a finite number of vibrational modes to take into account the vibrational behavior of the body during impact. The vibrations, the multiple collisions, and the angle of incidence angle, are found to be important factors for the kinematics of frictional impact. Analytical and experimental results were compared to establish the accuracy of the model.     

Dynamics of a satellite carrying a point mass moving about it

We study the dynamics of a complex system consisting of a solid and a mass point moving according to a prescribed law along a curve rigidly fixed to the body. The motion occurs in a central Newtonian gravitational field. It is assumed that the orbit of the system center of mass is an ellipse of arbitrary eccentricity.We obtain equations that describe the motion of the carrier (satellite) about its center of mass. In the case of a circular orbit, we present conditions that should be imposed on the law of the relative motion of the mass point carried by the satellite so that the latter preserves a constant attitude with respect to the orbital coordinate system. In the case of a dynamically symmetric satellite, we consider the problem of existence of stationary and nearly stationary rotations for the case in which the carried point moves along the satellite symmetry axis.We consider several problems of dynamics of the satellite plane motion about its center of mass in an elliptic orbit of arbitrary eccentricity. In particular, we present the law of motion of the carried point in the case without eccentricity oscillations and study the stability of the satellite permanent attitude with respect to the orbital coordinate system.     

Two-degree-of-freedom vortex-induced vibrations of a circular cylinder at Re=3900

The vortex-induced vibrations of an elastically mounted circular cylinder are investigated on the basis of direct numerical simulations. The body is free to move in the in-line and cross-flow directions. The natural frequencies of the oscillator are the same in both directions. The Reynolds number, based on the free stream velocity and cylinder diameter, is set to 3900 and kept constant in all simulations. The behavior of the coupled flow-structure system is analyzed over a wide range of the reduced velocity (inverse of the natural frequency) encompassing the lock-in range, i.e. where body motion and flow unsteadiness are synchronized. The statistics of the structural responses and forces are in agreement with prior experimental results. Large-amplitude vibrations develop in both directions. The in-line and cross-flow oscillations are close to harmonic; they exhibit a frequency ratio of 2 and a variable phase difference across the lock-in range. Distinct trends are noted in the force-displacement phasing mechanisms in the two directions: a phase difference jump associated with a sign change of the effective added mass and a vibration frequency crossing the natural frequency is observed in the cross-flow direction, while no phase difference jump occurs in the in-line direction. Higher harmonic components arise in the force spectra; their contributions become predominant when the cylinder oscillates close to the natural frequency. The force higher harmonics are found to impact the transfer of energy between the flow and the moving body, in particular, by causing the emergence of new harmonics in the energy transfer spectrum.     

Self-induced jumping of a rigid body of revolution on a smooth horizontal surface

The article is devoted to the study of the motion of a rigid body of revolution on a rigid and perfectly smooth horizontal surface under the influence of the uniform gravitational field. Basic equations are listed and their solutions are given. The unilateral contact between the body and the plane at non-steady motion is investigated and the procedure of calculation of threshold values of the body energy above which the contact is broken is given. In contrast to Shimomura et al. [Dynamics of an axisymmetric body spinning on a horizontal surface. II. Self-induced jumping. Proc. R. Soc. A 461 (2005) 1775-1809], who assumed sliding friction in their analysis, it is found that the self-induced jumping can also occur in the absence of friction at the very beginning of the motion. The free motion after the contact is lost and impact of the body when it again makes contact with the plane is discussed. The motion of a spheroid and a disk which illustrate the results of the general theory are discussed in some detail.