碰摩裂纹转子轴承系统的周期运动稳定性及实验研究

根据碰摩裂纹耦合故障转子轴承系统的非线性动力学方程，利用求解非线性非自治系统周期解的延拓打靶法，研究了系统周期运动的稳定性。研究发现，小偏心量下系统周期运动发生Hopf分岔，大偏心量下系统周期运动发生倍周期分岔，偏心量的加大使周期解的稳定性明显降低；系统碰摩间隙变小，碰摩影响了油膜涡动的形成，使失稳转速有所提高；裂纹深度的加大降低了系统周期运动的稳定性。本文的研究为转子轴承系统的安全稳定运行提供了理论参考。     

Effects of thermo-magneto-electro nonlinearity characteristics on the stability of functionally graded piezoelectric beam

Due to the increasing interests in using functionally graded piezoelectric materials(FGPMs) in the design of advanced micro-electro-mechanical systems, it is important to understand the stability behaviors of the FGPM beams. In this study, considering the effects of geometrical nonlinearity, temperature, and electricity in the constitutive relations and the effect of the magnetic field on the FGPM beam, the Euler-Bernoulli beam model is adopted, and the nonlinear governing equation of motion is derived via Hamilton's principle. A perturbation method, which can decompose the deflection into static and dynamic components, is utilized to linearize the nonlinear governing equation. Then,a dynamic stability analysis is carried out, and the approximate analytical solutions for the nonlinear frequency and boundary frequencies of the unstable region are obtained.Numerical examples are performed to verify the present analysis. The effects of the static deflection, the static load factor, the temperature change, and the magnetic field flux on the stability behaviors of the FGPM beam are discussed. From the proposed analytical solutions and numerical results, one can easily and clearly find the effects of various controlled parameters, such as geometric and physical properties of the system, on the mechanical behaviors of structures, and the conclusions are very important and useful for the design of micro-devices.     

On the exponential stability of the permanent rotational motion of a gyrostat

This paper is devoted to the study of the problem of exponential asymptotic stability of the rotational motion of a gyrostat using servo-control moments which are applied to the internal rotors. The servo-control moments which impose the rotational motion are obtained. The stabilizing servo-control moments are obtained from the conditions to ensure exponential asymptotic stability of the desired motion. Estimations of the phase coordinations as exponential functions are presented. The method based on a choice of the structural form of the servo-control moments such that the equations of motion reduce to a system of differential equations with exponential asymptotic stability of an special solution.     

Parametric vibration stability and active control of nonlinear beams

The vibration stability and the active control of the parametrically excited nonlinear beam structures are studied by using the piezoelectric material. The velocity feedback control algorithm is used to obtain the active damping. The cubic nonlinear equation of motion with damping is established by employing Hamilton’s principle. The multiple-scale method is used to solve the equation of motion, and the stable region is obtained. The effects of the control gain and the amplitude of the external force on the stable region and the amplitude-frequency curve are analyzed numerically. From the numerical results, it is seen that, with the increase in the feedback control gain, the axial force, to which the structure can be subjected, is increased, and in a certain scope, the structural active damping ratio is also increased. With the increase in the control gain, the response amplitude decreases gradually, but the required control voltage exists a peak value.     

On the control of programmed motion of satellite-gyrostat containing fluid

This article is devoted to study the control of the relative programmed motion of satellite-gyrostat containing fluid with the help of internal moving bodies. Using the Lyapunov function the asymptotic stability of the relative programmed motion is proved. The control moments corresponding to the programmed motion are obtained. The control moments ensuring the asymptotic stability of this motion are obtained. The existence of the fluid is shown to give more freedom to the control. This study is characterized by the fact that the control forces are exactly as non-linear functions of phase coordinates.     

A Motion Amplifier Using an Axially Driven Buckling Beam: II. Modeling and Analysis

In this paper, the nonlinear behavior of a motion amplifier used to obtain large rotations from small linear displacements produced by a piezoelectric stack is studied. The motion amplifier uses elastic (buckling) and dynamic instabilities of an axially driven buckling beam. Since the amplifier is driving a large rotary inertia at the pinned end and the operational frequency is low compared to the resonant frequencies of the beam, the mass of the buckling beam and the dynamics of the PZT stack are neglected and the system is modeled as a single-degree-of-freedom, nonlinear system. The beam simply behaves as a nonlinear rotational spring having a prescribed displacement on the input end and a moment produced by the inertial mass acting on the output end. The moment applied to the mass is then a function of the beam end displacement and the mass rotation. The system can, thus, be modeled simply as a base-excited, spring–mass oscillator. Results of the response for an ideal beam using this reduced-order model agree with the experimental data to a high degree. Inclusion of loading and geometric imperfections show that the response is not particularly sensitive to these imperfections. Parameter studies for the ideal buckling beam amplifier were conducted to provide guidance for improving the design of the motion amplifier and finding the optimal operating conditions for different applications. An erratum to this article can be found at     

Stability of motion of two rigid bodies connected by a cable in the atmosphere

The spatial motion of two rigid bodies connected by a weightless inextensible cable in the atmosphere is considered. They are assumed to be bodies of revolution with static and dynamic symmetry. The condition of static stability of the system angular motion with respect to the direction of the incident airflow velocity vector is written out and analyzed. The influence of gyroscopic terms and damping moments on the stability condition is studied. An example of analysis of motion in the atmosphere of two connected bodies that are cones with a spherical tip is given. It is shown that the stable motion in the atmosphere can always be ensured by an appropriate matched choice of the parameters of the entire system on the basis of the obtained stability conditions. A numerical example of estimating the cable tension forces arising as the system descends on a ballistic trajectory in the atmosphere is presented.     

Stability of piston flow motion in a traveling magnetic field

A formulation is given of the problem of the stability of piston-flow motion in a traveling magnetic field. It is shown that this question reduces to the problem of stability of motion in the presence of constantly acting perturbing forces. The second Lyapunov method is used as the basis to present the sufficient criteria for stability of the flow motion with respect to certain specified quantities.     

On the stability behaviour of the rotational motion in a circular orbit for an elastic — rigid body

In this paper the stability of motion of a symmetric satellite-gyrostat, with Visco-elastic square plate attached to it, around the center of mass in a circular orbit under a central gravitational field is studied. The gyrostat has a rotor oriented inside it such that the rotor becomes dynamically as well as statically stable with respect to the whole system. A study of the stability of this system has been done by using the method of separation of motion and averaging. Furthermore, we have solved the problem where there is no rotor.     

Piezoelectric energy harvesting from morphing wing motions for micro air vehicles

Wing flapping and morphing can be very beneficial to managing the weight of micro air vehicles through coupling the aerodynamic forces with stability and control. In this letter, harvesting energy from the wing morphing is studied to power cameras, sensors, or communication devices of micro air vehicles and to aid in the management of their power. The aerodynamic loads on flapping wings are simulated using a three-dimensional unsteady vortex lattice method. Active wing shape morphing is considered to enhance the performance of the flapping motion. A gradient-based optimization algorithm is used to pinpoint the optimal kinematics maximizing the propellent efficiency. To benefit from the wing deformation, we place piezoelectric layers near the wing roots. Gauss law is used to estimate the electrical harvested power. We demonstrate that enough power can be generated to operate a camera. Numerical analysis shows the feasibility of exploiting wing morphing to harvest energy and improving the design and performance of micro air vehicles.     

Stability of spatial motion of a body with flow separation and rotation about the symmetry axis

A model describing the spatial motion (without separation and with nonsymmetric separation of the flow in the medium) of a body rotating about its symmetry axis in a resisting medium is constructed. Several criteria for stability of the body rectilinear motion are obtained in the case of frozen axial velocity. The influence of retardation on the stability of rectilinear motion of a cone is considered.     

One Variant of the Sufficient Conditions for Practical Stability of a Manipulator Effector

General conditions for practical stability of a system that simulate a manipulator effector interacting with a dynamic medium are established. Sufficient conditions for practical stability of the motion of the manipulator effector are obtained for a specific model of the dynamic medium. The qualitative analysis of the motion of the manipulator effector for practical stability involves the construction of an auxiliary Lyapunov function     

Stability and chaotic motion in columns of nonlinear viscoelastic material

ＩｎｔｒｏｄｕｃｔｉｏｎＴｈｅｐｒｏｂｌｅｍｏｆｔｈｅｄｙｎａｍｉｃａｌｓｔａｂｉｌｉｔｙｏｆｖｉｓｃｏｅｌａｓｔｉｃｓｔｒｕｃｔｕｒｅｓｉｓｍｏｒｅｃｏｍｐｌｉｃａｔｅｄｔｈａｎｔｈａｔｏｆｅｌａｓｔｉｃｓｔｒｕｃｔｕｒｅｓ,ｓｉｎｃｅｔｈｅｓｔｒｅｓｓ＿ｓｔｒａｉｎｒｅｌａｔｉｏｎｏｆｖｉｓｃｏｅｌａｓｔｉｃｍａｔｅｒｉａｌｓｏｆｔｅｎｌｅａｄｓｔｏａｎｉｎｔｅｇｒｏ＿ｄｉｆｆｅｒｅｎｔｉａｌｅｑｕａｔｉｏｎｏｆｍｏｔｉｏｎ .Ｉｎｔｈｅｅａｒｌｙｒｅｓｅａｒｃｈｅｓｏｎｌｉｎｅａｒｖｉｓｃｏ…     

等效刚度对非线性压电俘能系统性能影响研究

基于Hamilton原理,考虑几何非线性和梁的不可伸长条件,建立了五层压电双晶片叠合梁俘能器在直接和参数激励作用下的运动微分方程。利用Galerkin法和谐波平衡法获得了俘能器的位移、输出电压和输出功率的解析解。引入随时间变化的扰动,提出了非线性方程解的稳定性条件。为了对压电俘能器的结构-性能关系进行综合分析,研究了被动层的配置形式、被动层与主动层的厚度比和弹性模量对压电俘能系统性能的影响。结果表明,在叠合梁厚度不变的情况下,采用五层的压电双晶片叠合结构,选择合理的被动层与主动层厚度比、被动层弹性模量、被动层厚度比和负载电阻,可以有效提高能量俘获的效率。     

ON THE GLOEAL STABILITY OF THE ROTATIONAL MOTION AND THE QUALITATIVE ANALYSIS OF THE BEHAVIOUR OF DISTURBED MOTION OF A RIGID BODY HAVING A LIQUID-FILLED-CAVITY

This paper is a continuation of[1].In this paper we inves-tigate the distribution of steady motions of the liquid-filled-cavity body,decide the stability of each steady motion and findout the corresponding regions of stability and instability.Be-sides.the behaviour of disturbed motion is analysed qualitatively.     

On the stability of an equilibrium position and rotational motion of a gyrostat

This article is devoted to study the compulsory stability of equilibrium position and rotational motion of a rigid body containing fluid with the help of three rotors carried on the body. The control moments on the rotors using that condition which impose the stabilization of equilibrium position of the rigid body and rotational motion are obtained.     

Stability of the forced vibrational motion of a vehicular body supported by rubber shear mountings with quadratic response

The stability of the harmonic solution of the forced Duffing equation governing the relative motion of a load on an inclined plate rotating at a constant angular speed about an arbitrary axis is studied. The load is supported by two identical simple shear springs made of a quadratic rubber-like material. It is found that the stability of motion about the center points is governed by the solutions of Hill's equation with three parameter. For certain values of the design parameters, Hill's equation reduces to the Mathieu equation and stability of the motion is studied following the standard procedure. In the general case, an intermediate bifurcation of the response amplitude occurs for motions about the negative center points. It is shown that the position of the center of mass of the load with respect to the plate center in the undisturbed state affects the nature of the response to a great extent. Without extensive analysis, the stability of motion in the general case is predicted for a specific range of the values of the angular speed of the plate.     

非对称势阱对三稳态压电俘能器性能的影响分析

为了探讨具有非对称势能函数的三稳态压电俘能器的优点,提出了一种具有不对称势能函数的三稳态结构。基于广义Hamilton变分原理,考虑梁端磁铁偏心距和转动惯量的影响,建立了非对称三稳态压电悬臂梁俘能系统的动力学方程,利用龙格-库塔法和多尺度法分析了初始振动点、外界激励等对存在非对称势阱的磁力式三稳态压电俘能系统响应的影响。结果表明:合适的起振位置和外部激励频率能使系统进入高能轨道,产生大幅阱间运动,提高系统的俘能效率。相比于忽略梁端磁铁偏心距和转动惯量的传统模型,修正模型的系统阱间运动频带宽度及输出功率峰值的计算结果均明显增大。     

Surface roughness effect on the aerodynamic characteristics of a blunt body

Conclusion The use of a smooth surface, for small projectiles, may lead to a reduction of drag at zero angle of attack. However, for specific configurations, especially those with blunt aft sections, an adverse normal force characteristic may develop, causing stability problems, similar to the one described by Schneider (1978). On the other hand, a skilful use of the separation-zone motion could serve as a maneuvering tool for unguided projectiles that are required to perform a search motion, and a built-in instability could maintain the desired motion.     

Bifurcation of a shaft with hysteretic-type internal friction force of material

IntroductionItwasfoundlongtimeagothattheinternalfrictionofmaterialcancauseinstabilityofrotatingshaft.Soitisalwaysoneoftheimportantsubjectsinrotordynamics[1].Earlyinvestigationswerefocusedonthedynamicalstabilityproblemofrotorinfluencedbythelinearinternalfrictionofmaterial,aimingtoobtainthecriterionofstability[2～4 ].Asthedevelopmentofnonlineardynamics,moreandmoreattentionswerepaidtothestudyoftheself_excitedmotionofrotatingshaft,thatisthebifurcation .Thestabilityregionsandbifurcationsofbothanau…