Modal stability of inclined cables subjected to vertical support excitation

In this paper the out-of-plane dynamic stability of inclined cables subjected to in-plane vertical support excitation is investigated. We compute stability boundaries for the out-of-plane modes using rescaling and averaging methods. Our study focuses on the 2:1 internal resonance phenomenon between modes that occurs when the excitation frequency is twice the first out-of-plane natural frequency of the cable. The second in-plane mode is excited directly, while the out-of-plane modes can be excited parametrically. An analytical model is developed in order to study the stability regions in parameter space. In this model we include nonlinear coupling effects with other modes, which have thus far been omitted from previous models of parametric excitation of inclined cables. Our study reflects the importance of such effects. Unstable parameter regions are defined for the selected cable configuration. The validity of the proposed stability model was tested experimentally using a small-scale cable actuator rig. A comparison between experimental and analytical results is presented in which very good agreement with model predictions was obtained.     

Non-linear responses of suspended cables to primary resonance excitations

We investigate the non-linear forced responses of shallow suspended cables. We consider the following cases: (1) primary resonance of a single in-plane mode and (2) primary resonance of a single out-of-plane mode. In both cases, we assume that the excited mode is not involved in an autoparametric resonance with any other mode. We analyze the system by following two approaches. In the first, we discretize the equations of motion using the Galerkin procedure and then apply the method of multiple scales to the resulting system of non-linear ordinary-differential equations to obtain approximate solutions (discretization approach). In the second, we apply the method of multiple scales directly to the non-linear integral-partial-differential equations of motion and associated boundary conditions to determine approximate solutions (direct approach). We then compare results obtained with both approaches and discuss the influence of the number of modes retained in the discretization procedure on the predicted solutions.     

Vibration analyses of an inclined flat plate subjected to moving loads

The object of this paper is to present a moving mass element so that one may easily perform the dynamic analysis of an inclined plate subjected to moving loads with the effects of inertia force, Coriolis force and centrifugal force considered. To this end, the mass, damping and stiffness matrices of the moving mass element, with respect to the local coordinate system, are derived first by using the principle of superposition and the definition of shape functions. Next, the last property matrices of the moving mass element are transformed into the global coordinate system and combined with the property matrices of the inclined plate itself to determine the effective overall property matrices and the instantaneous equations of motion of the entire vibrating system. Because the property matrices of the moving mass element have something to do with the instantaneous position of the moving load, both the property matrices of the moving mass element and the effective overall ones of the entire vibrating system are time-dependent. At any instant of time, solving the instantaneous equations of motion yields the instantaneous dynamic responses of the inclined plate. For validation, the presented technique is used to determine the dynamic responses of a horizontal pinned–pinned plate subjected to a moving load and a satisfactory agreement with the existing literature is achieved. Furthermore, extensive studies on the inclined plate subjected to moving loads reveal that the influences of moving-load speed, inclined angle of the plate and total number of the moving loads on the dynamic responses of the inclined plate are significant in most cases, and the effects of Coriolis force and centrifugal force are perceptible only in the case of higher moving-load speed.     

Multiple internal resonances and non-planar dynamics of shallow suspended cables to the harmonic excitations

In the present study, the nonlinear response of a shallow suspended cable with multiple internal resonances to the primary resonance excitation is investigated. The method of multiple scales is applied directly to the nonlinear equations of motion and associated boundary conditions to obtain the modulation equations and approximate solutions of the cable. Frequency–response curves and force–response curves are used to study the equilibrium solution and its stability. The effects of the excitation amplitude on the frequency–response curves of the cable are also analyzed. Moreover, the chaotic dynamics of the shallow suspended cable is investigated by means of numerical simulations.     

Transient stability of AC multi-strand superconducting cables

AC application, it is necessary to estimate the stability of multi-strand superconducting cable. Therefore, we have been studying the transient stability of non-insulated multi-strand cable when one strand in a cable turns into the normal state locally. In the quench process, local temperature rise produced by current redistribution among strands is not desirable for stability. In a previous work, we discussed the effect of Cu matrix allocated to each strand on the transient stability and showed that the Cu matrix allocation can improve the stability of non-insulated multi-strand cable through mainly numerical simulations. In this paper, we carried out experiments on three kinds of non-insulated three-strand cables; one consists of NbTi/CuNi strands and the others consist of NbTi/Cu/CuNi strands having different cross-sectional arrangement. These sample strands have almost the same diameter, the same matrix to superconductor ratio and the same B–J characteristics to evaluate the effect of Cu allocation quantitatively. We choose to define the transient stability in terms of the minimum quench energy (MQE) at each DC transport current. We also investigated the transient stability of sample cables when quench is initiated in two or three (all) strands simultaneously.     

有界噪声和谐和激励联合作用下一类非线性系统的混沌研究

研究一类有界噪声和谐和激励联合作用下的非线性系统，首先用多尺度方法将该系统约化，针对约化后的平均系统，利用随机Melnikov过程方法结合均方值准则导出随机系统可能产生混沌运动的临界条件，结果表明在一定的参数范围内，随着Weiner过程强度参数值的增大，混沌的临界激励幅值先递减继而递增. 同时，用两类数值方法即最大Lyapunov指数法和Poincare截面法验证了解析结果. 关键词： 有界噪声 多尺度 随机Melnikov过程 混沌     

有界噪声与谐和激励联合作用下Duffing-Rayleigh振子的Melnikov混沌

研究了有界噪声与谐和激励作用下的Duffing-Rayleigh振子的动力学行为.首先运用随机Melnikov过程方法得到系统出现混沌的条件,结果表明随着非线性阻尼参数的增加系统会从混沌运动到周期运动,随着Wiener过程强度参数的增加,系统由混沌进入周期的临界幅值会先递增后不变.最后,用两类数值方法即最大Lyapunov指数与Poincare截面验证了上述结果. 关键词： 有界噪声 随机Melnikov过程 混沌运动 周期运动     

Scaling for the ensemble statistics prediction of a random system subjected to harmonic excitations

This paper is concerned with the ensemble statistics of the dynamic responses of a random system subjected to harmonic excitations. Random point process theory is employed to derive general scaling laws with the Gaussian orthogonal ensemble assumption about the system natural frequencies. A scaled model is built to simulate the high-frequency vibrations of the original system. Specific forms of the scaling laws are presented for a mass-loaded plate regarding the scaling factors for the structural parameters. The ensemble statistics predicted from the scaled model are compared favorably with those obtained from the original system.     

Vibration analysis of horizontal self-weighted beams and cables with bending stiffness subjected to thermal loads

This paper aims at proposing an analytical model for the vibration analysis of horizontal beams that are self-weighted and thermally stressed. Geometrical nonlinearities are taken into account on the basis of large displacement and small rotation. Natural frequencies are obtained from a linearization of equilibrium equations. Thermal force and thermal bending moment are both included in the analysis. Torsional and axial springs are considered at beam ends, allowing various boundary conditions. A dimensionless analysis is performed leading to only four parameters, respectively, related to the self-weight, thermal force, thermal bending moment and torsional spring stiffness. It is shown that the proposed model can be efficiently used for cable problems with small sag-to-span ratios (typically , as in Irvine's theory). For beam problems, the model is validated thanks to finite element solutions and a parametric study is conducted in order to highlight the combined effects of thermal loads and self-weight on natural frequencies. For cable problems, solutions are first compared with existing results in the literature obtained without thermal effects or bending stiffness. Good agreement is found. A parametric study combining the effects of sag-extensibility, thermal change and bending stiffness is finally given.     

Dynamic stability of rotor-bearing systems subjected to random axial forces

This paper investigates the lateral vibration of a spinning disk-shaft system supported by a pair of ball bearings and subjected to a pair of random axial forces at both ends. The axial forces are assumed as the sum of a static force and a random process with a zero mean. Due to the random axial forces, the rotor-bearing system may experience parametric random instability under certain situations. In this work, the finite element method is applied to yield a set of discretized system equations first. The set of discretized system equations is partially uncoupled by the modal analysis procedure suitable for gyroscopic systems. The stochastic averaging method is then adopted to obtain Ito's equations for the response amplitudes of the system. Finally the first- and second-moment stability criteria are utilized to determine the stability boundaries of the system. Numerical results show that the rotor-bearing system is always stable in the sense of the first-moment stability, and the effects of the average axial compressive force and the disk mass, which will lower all frequencies of the system, tend to destabilize the second-moment stability of the system.     

Parametric instability of a cantilever beam subjected to two electromagnetic excitations: Experiments and analytical validation

An electromagnetic device, acting like a spring with alternating stiffness, has been designed to parametrically excite the cantilever beam. However, only one parametric excitation (induced by one electromagnetic device) was considered in current research, and the effects of the design parameters of the device upon the instability were studied inadequately. Actually, multiple parametric excitations with various phases and amplitudes would bring significant impacts to the system instability. The electromagnetic device with various design parameters could cause the unstable regions to change evidently. Thus, the parametric instability of a cantilever beam subjected to two electromagnetic excitations is studied experimentally and analytically in the paper. The governing equations for the beam system are established utilizing the assumed mode method, and then verified through a DC current test. Based upon these, the instability experiments for the cantilever beam with one or two electromagnetic excitations are conducted in detail. Two design parameters of the device (magnet spacing and device location) are investigated, respectively, for their effects upon the instability regions. When two electromagnetic devices operate together to bring two parametric stiffness excitations with various phases and amplitudes to the cantilever beam, the variations of both simple and combination instability regions with coil current are observed and discussed. The above experimental results are all found to agree well with the analytical ones.     

Suspended bridges subjected to moving loads and support motions due to earthquake

The paper deals with the vibration of suspended bridges subjected to the simultaneous action of moving loads and vertical support motions due to earthquake. The basic partial integro-differential equation is applied to the vertical vibration of a suspended beam. The dynamic actions of traffic loads are modelled as a row of equidistant moving forces, while the earthquake is considered by vertical motions of supports. The governing equation is solved first analytically to receive an ordinary differential equation and next numerically. Moreover, the designed world's largest suspended bridge—Messina Bridge—is investigated (central span of length 3.3 km). The paper studies the effect of various lags of the earthquake arrival because the earthquake may appear at any time when the train moves along a large-span bridge. The modified Kobe earthquake records have been applied to calculations. The results indicate that the interaction of both the moving and seismic forces may substantially amplify the response of long-span suspended bridges in the vicinity of the supports and increase with the rising speed of trains.     

Flow structures around an inclined substrate subjected to a supersonic impinging jet in laser cutting

In laser cutting, the flow structure around a substrate significantly affects the material removal rate, the cutting depth and the surface finish of the cutting front. In this paper, the phenomena of shock wave that is induced by a supersonic impinging jet emanating from a straight nozzle onto a substrate with varying inclined angles has been simulated numerically and visualized experimentally. The numerical model offers fairly good prediction in comparison with the experiments. It transpires that the angle of inclination has a significant and dramatic effect on the flow structure and that a large wall pressure with a steep gradient can be built up when the angle is large.     

Dynamic stability of spinning pretwisted beams subjected to axial random forces

This paper studies the dynamic stability of a pretwisted cantilever beam spinning along its longitudinal axis and subjected to an axial random force at the free end. The axial force is assumed as the sum of a constant force and a random process with a zero mean. Due to this axial force, the beam may experience parametric random instability. In this work, the finite element method is first applied to yield discretized system equations. The stochastic averaging method is then adopted to obtain Ito's equations for the response amplitudes of the system. Finally the mean-square stability criterion is utilized to determine the stability condition of the system. Numerical results show that the stability boundary of the system converges as the first three modes are taken into calculation. Before the convergence is reached, the stability condition predicted is not conservative enough.     

Dynamic stability of thermoelastic coupling moving plate subjected to follower force

The dynamic characteristics and stability of the moving thermoelastic coupling rectangular plate subjected to uniformly distributed tangential follower force are investigated. Based on the heat conduction equation containing the thermoelastic coupling term and the thin plate theory, the thermoelastic coupling differential equation of motion of the rectangular plate under the action of uniformly distributed tangential follower force is established. Dimensionless complex frequencies of the moving thermoelastic coupling rectangular plate with four edges simply supported, two opposite edges simply supported and other two edges clamped are calculated by the differential quadrature method. The effects of the dimensionless thermoelastic coupling factor and dimensionless moving speed on the stability and critical load of the moving plate are analyzed. The results show that the divergence loads of the first order mode increase with the increase of the dimensionless thermoelastic coupling factor, and decrease with increasing the dimensionless moving speed.     

Heat transfer and friction factor characteristic of spherical and inclined teardrop dimple channel subjected to forced convection

An experimental and numerical investigation is performed in order to determine the outcome of dimple geometries on the heat transfer and friction factor in a dimple cooling channel subjected to turbulent flow. Two geometries taken into consideration are spherical and inclined teardrop. In order to have a better comparison between the two different dimple channel, the dimple depth, total wetted area of dimple, and dimple pitch have been kept constant. In case of spherical and inclined teardrop dimple channels, heat transfer augmentation, friction losses, and flow pattern have been obtained for a Reynolds Number range from 14,000 to 65,000. The investigation shows that the dimple geometry has a significant contribution to increasing the heat transfer augmentation and determining the flow pattern. The inclined teardrop dimple arrangement shows the maximum heat transfer that is 17% higher than the spherical dimple channel, whereas inclined teardrop dimple results in the rise of friction factor of about 5.93–16.14% times as compared to the spherical dimple within the specified Reynolds number. The inclined teardrop and spherical dimple channel show the heat transfer enhancement of 2.74 to 3.20 times and 2.38 to 2.68 times than that of smooth channels provided thermal boundary conditions and flow conditions are kept same. The numerical study has been performed, which provided a detailed insight into the flow structures and vortex formations in spherical and inclined teardrop dimple channel.     

ITER聚变装置重力支撑有限元模态分析

运用有限元分析软件ANSYS建立了ITER装置重力支撑结构环向20°的三维有限元模型,采用子空间法对ITER重力支撑结构系统进行了有限元模态分析,求出了重力支撑系统的前10阶固有频率和振型,并对振型特点进行了分析。