基于综合非线性优化方法的倒张型悬索桥非线性优化设计

提出随机优化、零阶优化和一阶优化相结合的综合非线性优化方法,并通过对ANSYS程序的二次开发编制全面优化设计和非线性有限元分析的综合辅助程序,从而对倒张型悬索桥进行非线性优化设计,以更合理地确定倒张型悬索桥设计中的关键因素,最终使倒张型悬索桥的受力和变形达到均匀合理的状态,以利于实际工程设计和应用.从优化设计前后的对比可以看出,本文的综合非线性优化方法和综合辅助程序简单有效,优化的效果显著.     

Multiplicity of steady solutions in a two-sided lid-driven cavity with different aspect ratios

This study presents a continuation method to calculate flow bifurcation in a two-sided lid-driven cavity with different aspect ratios for anti-parallel motion. In anti-parallel motion, the top and bottom walls of the cavity move in opposite directions simultaneously, while the two walls both moving to the right give parallel motion at the same speed. Comprehensive bifurcation diagrams of the cavity flows with different aspect ratios of the cavities are derived via Keller’s continuation method, and linear- stability analysis is used to identify the nature of the various flow solutions. The Reynolds number (1 ≤ Re ≤ 1,200) is used as the continuation parameter to trace the solution curves. In anti-parallel motion, the evolution of the bifurcation diagrams in cases with different aspect ratios (1 ≤ AR ≤ 2.5) is illustrated. Two stable symmetric flows and one stable asymmetric flow are identified, and the existent regions of the stable flows in the aspect ratios and Reynolds numbers are distinguished. The newly found asymmetric flow state can be obtained at a high aspect ratio and a low Reynolds number.     

Effects of nonlinear damping suspension on nonperiodic motions of a flexible rotor in journal bearings

Nonlinear damping suspension is a promising method to be used in a rotor-bearing system for vibration isolation between the bearing and environment. However, the nonlinearity of the suspension may influence the stability of the rotor-bearing system. In this paper, the motions of a flexible rotor in short journal bearings with nonlinear damping suspension are studied. A computational method is used to solve the equations of motion, and the bifurcation diagrams, orbits, Poincaré maps, and amplitude spectra are used to display the motions. The results show that the effect of the nonlinear damping suspension on the motions of the rotor-bearing system depends on the speed of rotor: (a) For low speeds, the rotor- bearing system presents the same motion pattern under the nonlinear damping ( \(p=0.5, 2, 3\) ) suspension as for the linear damping ( \(p=1\) ) suspension; (b) For high speeds, the effect of nonlinear damping depends on a combination of the damping exponent and damping coefficient. The square root damping model ( \(p=0.5\) ) shows a wider stable speed range than the linear damping for large damping coefficients. The quadratic damping ( \(p=2\) ) shows similar results to linear damping with some special damping coefficients. The cubic damping ( \(p=3\) ) shows more stable response than the linear damping in general.     

Stability of vertical oscillations in an electrodynamic suspension system with a discrete guideway structure

Conclusions 1. The coupling of the vehicle oscillation equation and the equations for the currents in the guideway structures must be taken into account in the stability analysis of vertical oscillations in an electrodynamic suspension system with a discrete guideway structure.2. The reported calculations indicate that vertical oscillations are unstable over a wide range of travel velocities. Consequently, the execution of steady-state vehicle motion requires vertical stabilization of the system.3. Effective stabilization can be achieved by means of a dynamic vibration damper. Even for a small relative mass =0.025 of the optimally tuned damper the perturbed motion decays rapidly.Physicotechnical Problems Branch of the Institute of Geotechnical Mechanics, National Academy of Sciences of Ukraine, Dnepropetrovsk. Translated from Prikladnaya Mekhanika, Vol. 31, No. 7, pp. 88–93, July, 1995.     

A study on validity of using average fiber aspect ratio for mechanical properties of aligned short fiber composites with different fiber aspect ratios

A closed-form solution using the actual distribution of the fiber aspect ratio is proposed for predicting the stiffness of aligned short fiber composite. The present model is the simplified form of Takao and Taya’s model and the extended version of Taya and Chou’s model, where Eshelby’s equivalent inclusion method modified for finite fiber volume fraction is employed. The validity of using average fiber aspect ratio for predicting the composite stiffness is justified in terms of the scatter of fiber aspect ratio, fiber volume fraction, and constituents‘ Young’s modulus ratio, comparing with the results by the present model. The guideline for selection of either the actual distribution or the average fiber aspect ratio is presented for the better prediction of the composite stiffness.     

基于Steffens-Newton法的空间索形悬索桥初始平衡状态分析

空间索形悬索桥的主缆、吊索相互耦合,用数值解析法精确求解其初始平衡状态时,面临收敛困难、算法要求严格的问题。本文建立了空间缆索的平衡方程,推导了误差调整方程。分别证明了平面索形所常用的线形变化刚度法及影响矩阵法在空间索形中不再适用。基于可调参数的Steffens-Newton法,提出一种高效的空间缆索耦合体系分析方法,...     

New results on stability and stabilization of a class of nonlinear fractional-order systems

The asymptotic stability and stabilization problem of a class of fractional-order nonlinear systems with Caputo derivative are discussed in this paper. By using of Mittag–Leffler function, Laplace transform, and the generalized Gronwall inequality, a new sufficient condition ensuring local asymptotic stability and stabilization of a class of fractional-order nonlinear systems with fractional-order α:1<α<2 is proposed. Then a sufficient condition for the global asymptotic stability and stabilization of such system is presented firstly. Finally, two numerical examples are provided to show the validity and feasibility of the proposed method.     

Experimental research on heat transfer of natural convection in vertical rectangular channels with large aspect ratio

This work presents the experimental research on the steady laminar natural convection heat transfer of air in three vertical thin rectangular channels with different gap clearance. The much higher ratio of width to gap clearance (60–24) and the ratio of length to gap clearance (800–320) make the rectangular channels similar with the coolant flow passage in plate type fuel reactors. The vertical rectangular channels were composed of two stainless steal plates and were heated by electrical heating rods. The wall temperatures were detected with the K-type thermocouples which were inserted into the blind holes drilled in the steal plates. Also the air temperatures at the inlet and outlet of the channel were detected. The wall heat fluxes added to the air flow were calculated by the Fourier heat conduction law. The heat transfer characteristics were analyzed, and the average Nusselt numbers in all the three channels could be well correlated with the Rayleigh number or the modified Rayleigh number in a uniform correlation. Furthermore, the maximum wall temperatures were investigated, which is a key parameter for the fuel’s integrity during some accidents. It was found that even the wall heat flux was up to 1500 W/m², the maximum wall temperature was lower than 350 °C. All this work is valuable for the plate type reactor’s design and safety analysis.     

外挂物对大展弦比直机翼颤振特性的影响

为提高带外挂物大展弦比直机翼的颤振速度,基于假设模态法提出一种带集中质量弯扭组合梁模态分析手段,结合片条理论考察外挂物不同质量及布置形式对机翼颤振特性的影响。首先,基于弯扭组合梁建立带外挂物大展弦比直机翼的结构动力学模型,并利用假设模态法得到其弯曲和扭转模态。其次,引入片条理论近似计算有限翼展升力面的气动力,调整外挂物的质量、数目及其在机翼展向和弦向的相对位置,得到外挂物对机翼颤振特性的影响规律。最后,利用在机翼前缘附近悬吊小质量外挂物可提高机翼颤振速度的优势,探究颤振速度恢复方法并提出颤振速度恢复的优化问题,使得携带外挂物的机翼与不携带外挂物的机翼颤振速度基本相同。研究结果表明,外挂物的不同悬挂方式可引起机翼颤振模态的跳转,在以俯仰为颤振主模态的机翼上可调整外挂物位置以恢复原机翼的颤振速度。     

谐波激励下斜拉桥面内非线性振动试验研究

斜拉桥拉索的振动问题一直是桥梁工程领域的研究热点。为揭示拉索大幅振动的力学机理,课题组建立了斜拉桥的全桥精细化模型,本文测试和研究了单频激励下的斜拉桥可能的非线性振动行为。首先,通过自由振动试验测试了模型的模态参数,并与两类有限元模型（OECS模型和MECS模型）进行对比,结果吻合良好。其次,试验研究了在单个竖向简谐激励下斜拉桥模型的非线性响应。研究发现：当激励频率与斜拉桥某阶全局模态频率接近时,主梁产生主共振,并引起多根长索产生大幅的参强振动;当激励频率与某根斜拉索面内一阶频率之比为1：2或者2：1时,可以观测到索中产生超谐波和亚谐波共振现象。     

Nonreciprocity of energy transfer in a nonlinear asymmetric oscillator system with various vibration states

The nonreciprocity of energy transfer is constructed in a nonlinear asymmetric oscillator system that comprises two nonlinear oscillators with different parameters placed between two identical linear oscillators. The slow-flow equation of the system is derived by the complexification-averaging method. The semi-analytical solutions to this equation are obtained by the least squares method, which are compared with the numerical solutions obtained by the Runge-Kutta method. The distribution of the ...     

Effects of particle migration on suspension flow in a hydraulic fracture

An asymptotic model of a hydraulic-fracture flow of a sedimenting concentrated suspension is formulated on the basis of the two-fluid approach with account of transverse particle migration. In the thin-layer approximation, a two-dimensional system of equations averaged across the fracture is constructed with account for a nonuniform distribution of the particle concentration. As compared to the similar model without particle migration, the averaged two-dimensional equations contain modified coefficients which explicitly depend on the width of the flow core occupied by the particles. Using the model constructed, a numerical simulation is performed, which shows that the particle migration towards the fracture center results in the increase in the depth of particle penetration into the fracture and the suppression of gravitational convection in the vicinity of the leading front. The calculations are compared with available experimental data and an analytical formula for the height of the dense packed sediment. A good agreement between the analytical theory, the experiments, and the two-dimensional calculations is attained.     

Output feedback stabilization based on dynamic surface control for a class of uncertain stochastic nonlinear systems

In this paper, the dynamic surface control (DSC) algorithm is proposed for a class of stochastic nonlinear systems with nonminimum phase and the standard output-feedback form. The proposed algorithm is a stochastic vision by combining the traditional back-stepping together with the DSC technique, which can overcome the problem of ‘explosion of complexity’ in the back-stepping designing procedure for the stochastic nonlinear systems. Thus, it can reduce the computation complexity and is easy to be used in the actual implementation. It is shown that all the signals of the resulting closed-loop system are uniformly ultimately bounded.     

Effects of magnetohydrodynamic flow past a vertical plate with variable surface temperature

An analysis is performed to study the magnetohydrodynamic flow of an electrically conducting, viscous incompressible fluid past a semi-infinite vertical plate with variable surface temperature under the action of transversely applied magnetic field. The heat due to viscous dissipation and the induced magnetic field are assumed to be negligible. The dimensionless governing equations are unsteady, two-dimensional, coupled and non-linear governing equations. It is found that the magnetic field parameter has a retarding effect on the velocities of air and water.     

Influence of inhomogeneity on the nonlinear stabilization of acoustic vibrations of a heat releasing medium in a confined space

The problem of determining the amplitudes of unstable acoustic vibrations when they are stabilized in a confined heat releasing medium by transfer of energy from the unstable mode to the damped mode as a result of their nonlinear interaction has been considered by Artamonov and Vorob'ev [1]. Their treatment applied to a gas with volume heat release filling a channel of finite length under the assumption that the parameters of the gas in the steady state are constant over the volume. In the present paper an investigation is made in the nonlinear approximation of the stability of a weakly inhomogeneous heat releasing gas that fills a channel of finite length with respect to acoustic vibrations propagating along its axis in the direction of the gradients of the steady parameters. It is shown that the spatial inhomogeneity of the gas leads to breakdown of the resonance of the excited acoustic vibrations, which in turn leads to a higher level of the steady vibrations compared with the case of a spatially homogeneous medium.     

Effects of surface mass transfer on unsteady mixed convection flow over a vertical cone with chemical reaction

The unsteady mixed convection boundary layer flow over a vertical cone is considered to investigate the combined effects of the buoyancy force, thermal and mass diffusion in the presence of the first order chemical reaction and surface mass transfer. The unsteadiness is caused by the time dependent free stream velocity varying arbitrarily with time. The governing boundary layer equations are transformed into a non-dimensional form by a group of non-similar transformations. The resulting system of coupled non-linear partial differential equations is solved numerically by the combination of quasi-linearization technique and an implicit finite difference scheme. Numerical computations are performed for different values of the parameters to display the velocity, temperature and concentration profiles graphically. Both accelerating and decelerating free stream velocities are considered. Numerical results are presented for the velocity, temperature and concentration profiles as well as for the skin-friction coefficient, local Nusselt number and local Sherwood number. The obtained results are compared with previously reported ones and are found to be in excellent agreement.     

Effects of thermophoresis and radiation on laminar flow along a semi-infinite vertical plate

The present contribution deals with the thermophoresis particle deposition and thermal radiation effects on the flow, heat and mass transfer characteristics in a viscous fluid over a semi-infinite vertical porous plate. The governing boundary layer equations are written into a dimensionless form by similarity transformations. The transformed coupled nonlinear ordinary differential equations are solved numerically by means of the fourth-order Runge–Kutta method with a shooting technique. The effects of different parameters on the dimensionless velocity, temperature, and concentration profiles are shown graphically. In addition, results for the local skin-friction coefficient, the local Nusselt number, and the local Sherwood number are tabulated and discussed.