On the problem of free deceleration of a rigid body in a resisting medium

A mathematical model of the influence of a medium on a rigid body with some part of its external surface being flat is considered with due allowance for an additional dependence of the moment of the medium action force on the angular velocity of the body. A full system of equations of motion is given under quasi-steady conditions; the dynamic part of this system forms an independent third-order system, and an independent second-order subsystem is split from the full system. A new family of phase portraits on a phase cylinder of quasi-velocities is obtained. It is demonstrated that the results obtained allow one to design hollow circular cylinders (“shell cases”), which can ensure necessary stability in conducting additional full-scale experiments.     

Random loading on a spherical pressure vessel of Hooke-Norton material

A spherical pressure vessel of non-linearly viscoelastic material (Hooke-Norton type) is analysed. The internal pressure consists of a small randomly varying part superposed on a constant part. A perturbation technique is used to find stresses and deformations. The effect of the redundancy of the system on stresses and deformations is studied, and a simple approximate method is suggested for the slightly redundant case of a thin-walled sphere.     

NOTES ON A STUDY OF VECTOR BUNDLE DYNAMICAL SYSTEMS (Ⅱ)─PART 2

In the part 2, theorem 3.1 studied in part 1^[15] is proved first. The proof is obtained via a way of changing variables to reduce the original system of differential equations to a form concerning standard systems of equations in the theory of differentiable dynamical systems. Then by using theorem 3.1 together with the preliminary theorem 2.1, the main theorem of this paper announced in part 1 is proved. The definition of admissible perturbation is contained in the appendix of part 2. The meanings of the main theorem is described in the introduction of part 1.     

Asymptotic solutions of a linear system with a small parameter in the coefficients of a part of derivatives

Using a transformation matrix, we reduce a system of differential equations with a small parameter in the coefficients of a part of derivatives and a turning point to an integrable system of equations.     

Force at a point in the interior of a layered elastic half space

This study formulates, by the technique of integral transforms, the solution of a layered half space subjected to a concentrated force which may act either vertically or horizontally in the interior of the system. Accurate approximations of the reciprocals of the common denominators in the solution integrals are suggested in such a way that the latter are in standard closed forms and can be identified by two parts. The first part is the singular part of Mindlin's solution which is singular at the point of application of the force, and the second is non-singular. The solutions for plane problems are also obtained in closed forms by performing appropriate integrations of the solutions for the corresponding three-dimensional cases.     

一种双通道测角系统的设计

本文介绍一种由旋转变压器和感应同步器作敏感元件组成的双通道采样测角系统。该测角系统采用双相激磁，单相输出鉴相工作方式，具有精度高、可靠性好、易实现、温度鲁棒性好等优点，能满足高精度惯导测试的要求，是高精度转台的重要组成部分。     

Dynamics and control of a self-sustained electromechanical seismographs with time-varying stiffness

This paper is concerned with the nonlinear dynamics and vibration control of an electromechanical seismograph system with time-varying stiffness. The instrument consists of an electrical part coupled to mechanical one and is used to record the vibration during earthquakes. An active control method is applied to the system based on cubic velocity feedback. The electromechanical system is subjected to parametric and external excitations and modeled by a coupled nonlinear ordinary differential equations. The method of multiple scales is used to obtain approximate solutions and investigate the response of the system. The results of perturbation solution have been verified through numerical simulations, where different effects of the system parameters have been reported.     

Transonic Shocks in Compressible Flow Passing a Duct for Three-Dimensional Euler Systems

In this paper we study the transonic shock in steady compressible flow passing a duct. The flow is a given supersonic one at the entrance of the duct and becomes subsonic across a shock front, which passes through a given point on the wall of the duct. The flow is governed by the three-dimensional steady full Euler system, which is purely hyperbolic ahead of the shock and is of elliptic–hyperbolic composed type behind the shock. The upstream flow is a uniform supersonic one with the addition of a three-dimensional perturbation, while the pressure of the downstream flow at the exit of the duct is assigned apart from a constant difference. The problem of determining the transonic shock and the flow behind the shock is reduced to a free-boundary value problem. In order to solve the free-boundary problem of the elliptic–hyperbolic system one crucial point is to decompose the whole system to a canonical form, in which the elliptic part and the hyperbolic part are separated at the level of the principal part. Due to the complexity of the characteristic varieties for the three-dimensional Euler system the calculus of symbols is employed to complete the decomposition. The new ingredient of our analysis also contains the process of determining the shock front governed by a pair of partial differential equations, which are coupled with the three-dimensional Euler system. The paper is partially supported by National Natural Science Foundation of China 10531020, the National Basic Research Program of China 2006CB805902, and the Doctorial Foundation of National Educational Ministry 20050246001.     

Exponential stability and spectral analysis of a delayed ring neural network with a small-world connection

This paper addresses the dynamical behavior of the linearized delayed ring neural network system with a small-world connection. The semigroup approach is adopted in investigation. The asymptotic eigenvalues of the system are presented. It shows that the spectrum of the system is located in the left half complex plane and its real part goes to ??? when the connection weights between neurons are well-defined. The spectrum determined growth condition is held true and the exponential stability of the system is then established. Moreover, we present the necessary conditions for the neuron and feedback gains, for which the closed-loop system is delay-independent exponentially stable, and we further provide the sufficient and necessary conditions when the concrete number of neurons and the location of small-world connection are given. Finally, numerical simulations are presented to illustrate the convergence of the state for the system and demonstrate the effect of the feedback gain on stability.     

Controlling natural convection in a closed thermosyphon using neural networks

The aim of this paper is to present a neural network-based approach to identification and control of a rectangular natural circulation loop. The first part of the paper defines a NARMAX model for the prediction of the experimental oscillating behavior characterizing the fluid temperature. The model has been generalized and implemented by means of a Multilayer Perceptron Neural Network that has been trained to simulate the system experimental dynamics. In the second part of the paper, the NARMAX model has been used to simulate the plant during the training of another neural network aiming to suppress the undesired oscillating behavior of the system. In order to define the neural controller, a cascade of several couples of neural networks representing both the system and the controller has been used, the number of couples coinciding with the number of steps in which the control action is exerted.     

Indentation of a Punch with a Fine-Grained Base into an Elastic Foundation

The linear contact problem for a system of small punches located periodically on a part of the boundary of an elastic foundation is studied. An averaged contact problem is derived using the Marchenko–Khruslov averaging theory. An asymptotic formula is obtained for the translational capacity of a smooth punch with a fine-grained flat base.     

On Loads Acting on a Structure with a Seismic Damper

The problem on amplification of the translation acceleration by a seismoisolated structure is considered with regard for the nonlinearity of friction and the multifrequency nature of the external perturbation. The equivalent coefficients of Coulomb and turbulent friction that provide a transient time equal to that of a system with viscous friction are calculated. Spectral curves that reflect the dependence of the ratio of the maximum absolute acceleration to the maximum translation acceleration on the natural part of a vibrating system are plotted for various equivalent parameters of nonlinear friction     

Stability and dynamics of a plastic softening oscillator

This paper deals with the stability of a single-degree-of-freedom plastic softening oscillator. Understanding such an elementary model concerns, for instance, the seismic behaviour of concrete or steel structures. The associated dynamic system is a complex hysteretic system. Using appropriate internal variables, it can be written as a singular autonomous system. Liapounov stability of the solutions is then studied. A domain of perturbations associated with a stable solution is exhibited. This domain looks like a truncated cone in the three-dimensional phase space. It can be read as a critical displacement or energy that the oscillator can support during a seismic excitation. The difference with the “equivalent” linearized elastic system is highlighted. The unloading part of the response of the inelastic system has a stabilising effect.     

某重型车床横向进给系统传动刚度分析与实验研究

进给伺服系统的性能对数控机床的跟踪及定位精度、加工表面质量等有着重要的作用。针对某重型车床的横向进给系统,综合考虑了轴的扭转刚度、齿轮的啮合刚度、丝杠螺母副接触刚度和丝杠支承轴承的轴向刚度等因素,建立了等效单自由度力学模型,分析刚度因素对工作台输出行为的影响。通过仿真计算分析了中间传动链各个刚度环节对工作台综合刚度的贡献量,找出了传动链的刚度薄弱环节。现场实验测试了工作台不同进给位置下的临界爬行速度,得到了临界爬行速度与丝杠的轴向刚度的关系,理论分析与实验结果相吻合。所得结论为该重型车床横向进给系统的优化设计提供了理论支持。     

Multiple-Camera Instrumentation of a Single Point Incremental Forming Process Pilot for Shape and 3D Displacement Measurements: Methodology and Results

A multiple-camera system (more than two cameras) has been developed to measure the shape variations and the 3D displacement field of a sheet metal part during a Single Point Incremental Forming (SPIF) operation. The modeling of the multiple-camera system and the calibration procedure to determine its parameters are described. The sequence of images taken during the forming operation is processed using a multiple-view Digital Image Correlation (DIC) method and the 3D reconstruction of the part shape is obtained using a Sparse Bundle Adjustment (SBA) method. Two experiments that demonstrate the potentiality of the method are described.     

盘-销摩擦系统摩擦接触力测试与特性分析

测量分析动态摩擦接触力是研究摩擦振动与噪声发生机理的关键.本文中建立了盘-销系统摩擦尖叫试验台架,成功再现了摩擦尖叫.采用三向力传感器对有无摩擦尖叫条件下的动态摩擦接触力进行了测量,并利用小波信号分解、概率密度函数、功率谱密度函数、时频分析等方法进行了分析和讨论.研究发现:在发生摩擦尖叫时,动态摩擦力和法向力发生高频波动,是系统噪声的激励源;无摩擦尖叫时的摩擦力和法向力的动态分量为典型的白噪声随机过程,呈非高斯分布;有摩擦尖叫时的摩擦力和法向力为窄带高频类谐波信号,摩擦力呈非高斯分布,而法向力近似为高斯分布;模态耦合是导致盘-销系统发生动态接触力高频波动以及摩擦尖叫的原因.     

Numerical method and models for anti-plane strain of a system with a thin elastic wedge

The paper presents a general method to find asymptotics for a (multi-)wedge system containing a thin wedge. It employs separation of the symmetric and anti-symmetric parts of the boundary displacements and tractions of the wedge. The method is applicable when the angle of the thin wedge turns to zero. A physical interpretation of the derived equations is obtained by using power expansions of non-polynomial functions, which appear after the Mellin transform. We establish that the first term in the expansion of the symmetric part corresponds to shear, while the first term of the anti-symmetric part describes deflection of the wedge axis. Numerical experiments, performed by using a code developed on the basis of the theory, show that using only the first terms of the expansions insignificantly influence accuracy: the approximate results coincide with the exact values of roots to the third significant digit even for the wedge angle of 30°.     

Permeability Changes During the Evolution of a Geothermal Field Due to the Dissolution and Precipitation of Quartz

The changes in permeability and porosity associated with quartz deposition in an evolving geothermal reservoir are investigated. We review the processes associated with permeability changes in a geothermal reservoir and also review recent work on quartz solubility and deposition rates. Porosity and permeability changes are calculated for two reservoir models. The first is a generic model of a Taupo Volcanic Zone geothermal reservoir and the second is based on the model of the deep circulation system at Kakkonda published by Hanano. We find that when a reservoir experiences BPD conditions during part of its lifetime the lower reservoir becomes impermeable and a hydrothermal circulation system is only present in the upper part of the reservoir.     

Periodic vibro-impacts and their stability of a dual component system

The coexisting periodic impacting motions and their multiplicity of a kind of dual component systems under harmonic excitation are analytically derived. The stability condition of a periodic impacting motion is given by analyzing the propagation of small, arbitrary perturbation from that motion. In numerical simulations, the periodic impacting motions are classified according to the system states before and after an impact. The numerical results show that there exist many types of vibro-impacts and the bifurcation of periodic vibro-impacts is not smooth. Project supported in part by National Natural Science Foundation of China under the grant 59572024 and in part by Trans-century Training Program Foundation for the Talents by the State Education Commission of China