杆的差分离散系统一个新的模态反问题

本文研究杆的差分离散系统一个新的模态反问题,所考虑的杆件是同一种均匀材料构成的,但横截面积不恒定.首先,我们给出了变截面杆的纵向自由振动方程,采用分离变量法,得到了模态方程.然后,在最一般的边界条件,即两端弹性支承的边界条件下,采用二阶中心差分公式,导出了杆的差分离散模型.结果表明,所得到的系统属于标准雅可比系统.只对...     

悬臂输流管道在基础激励与脉动内流联合作用下的参激振动

首先建立了悬臂输流管道在基础激励与脉动内流联合作用下的运动方程;然后基于Galerkin法研究了该系统的非线性动力学行为,分析了系统运动状态随激励频率和相位差的变化,以及混沌百分比随频率比(基础激励频率与脉动频率之比)和相位差的变化。结果表明,无论以激励频率还是以相位差为分岔参数,系统都具有多种形式的动态响应,包括周期运动、概周期运动和混沌运动,但进入和脱离混沌的途径不同。相位差和频率比对系统的混沌百分比有重要影响:相位差为π/2时系统混沌百分比最大;频率比为1时系统混沌百分比最小,频率比较小或较大时系统混沌百分比与只有基础激励时接近。     

Reduced order state‐space models from the pulse responses of a linearized CFD scheme

This paper describes a method for obtaining a time continuous reduced order model (ROM) from a system of time continuous linear differential equations. These equations are first put into a time discrete form using a finite difference approximation. The unit sample responses of the discrete system are calculated for each system input and these provide the Markov parameters of the system. An eigenvalue realization algorithm (ERA) is used to construct a discrete ROM. This ROM is then used to obtain a continuous ROM of the original continuous system. The focus of this paper is on the application of this method to the calculation of unsteady flows using the linearized Euler equations on moving meshes for aerofoils undergoing heave or linearized pitch motions. Applying a standard cell‐centre spatial discretization and taking account of mesh movement a continuous system of differential equations is obtained which are continuous in time. These are put into discrete time form using an implicit finite difference approximation. Results are presented demonstrating the efficiency of the system reduction method for this system. Copyright © 2003 John Wiley & Sons, Ltd.     

A Time Domain Method for Quasi-Static Analysis of Viscoelastic Thin Plates

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Bubbly flow undergoing a steep pressure gradient

The effects of a steep pressure gradient on bubbly flow were studied to determine the cause of noise emanating from components of a piping system. We used an orifice to generate a local pressure difference. The behavior of bubbles passing through the orifice was observed by using a video camera, and the noise was measured by a condenser microphone outside the pipe. It was found that the sound pressure level of noise generated by a bubbly flow was proportional to the pressure difference. An empirical formula for estimating noise level is proposed. The changes in size and number of bubbles passing through an orifice were found related to the breakup, which is affected by pressure difference rather than airflow rate. The breakup of a single bubble undergoing a steep pressure difference was observed to determine the mechanism of sound generation. It was found that a bubble was broken by impingement of an inward protrusion in the bubble. The growth rate of the protrusion depended on the pressure difference.     

土-结构相互作用体系合成模态阻尼比的振动台模型试验研究

本文籍振动台模型试验。研究了SSI体系的合成模态阻尼比问题。文中首先阐明了在SSI体系直接动力分析中应采用合成模态阻尼比的观点。研究了合成模态阻尼纟的实测确定方法。并在不同工况下，通过对模型不同部位测点的传递函数，基本频率，基本合成模态阻尼比等实测数据考虑，验证了SSI体系合成模态的存在性，合成模态阻尼比与相同应变下不考虑相互作用的单纯地基土体或刚性地基结构阻尼比的差异性及其在递增动力作用下的变化规律。     

A shock-capturing scheme for body-fitted meshes

A finite difference scheme based on flux difference splitting is presented for the solution of the two-dimensional Euler equations of gas dynamics in a generalized co-ordinate system. The scheme is based on numerical characteristic decomposition and solves locally linearized Riemann problems using upwind differencing. The decomposition is for a generalized co-ordinate system and a convex equation of state. This ensures good shock-capturing properties when incorporated with operator splitting and the advantage of using body-fitted co-ordinates. The resulting scheme is applied to supersonic flow of real air' past a circular cylinder.     

Rheology of an emulsion of viscoelastic drops in steady shear

Steady shear rheology of a dilute emulsion with viscoelastic inclusions is numerically investigated using direct numerical simulations. Batchelor's formulation for rheology of a viscous emulsion is extended for a viscoelastic system. Viscoelasticity is modeled using the Oldroyd-B constitutive equation. A front-tracking finite difference code is used to numerically determine the drop shape, and solve for the velocity and stress fields. The effective stress of the viscoelastic emulsion has three different components due to interfacial tension, viscosity difference (not considered here) and the drop phase viscoelasticity. The interfacial contributions – first and second normal stress differences and shear stresses – vary with Capillary number in a manner similar to those of a Newtonian system. However the shear viscosity decreases with viscoelasticity at low Capillary numbers, and increases at high Capillary numbers. The first normal stress difference due to interfacial contribution decreases with increasing drop phase viscoelasticity. The first normal stress difference due to the drop phase viscoelasticity is found to have a complex dependence on Capillary and Deborah numbers, in contrast with the linear mixing rule. Drop phase viscoelasticity does not contribute significantly to effective shear viscosity of the emulsion. The total first normal stress difference shows an increase with drop phase viscoelasticity at high Capillary numbers. However at low Capillary numbers, a non-monotonic behavior is observed. The results are explained by examining the stress field and the drop shape.     

基于惯导及声学浮标辅助的水下航行器导航定位系统

针对纯惯导系统误差发散和无线电信号在水下衰减快从而无法精确定位的问题,设计了一种基于声学浮标辅助惯导的水下定位系统,该系统由惯导系统和声学定位系统组成,其中声学定位系统由若干个浮标构成水听器阵,浮标的经纬度坐标由GPS提供,浮标完成对接收到的声源信号的处理,利用互相关测时延差的方法来进行定位。由于水下噪声、混响等因素会造成接收到的多路声信号出现模糊互相关峰,因此对接收信号应进行频域加权处理。最后利用声学系统的定位信息来校正惯导的误差。仿真结果表明:与基本互相关方法相比,加权处理能有效提高时延差的精度,所提出的惯导和声学浮标辅助设备导航系统能够使定位误差小于2 m,保证了水下航行器能够长时间在水下航行。     

Discrete and non-local elastica

In this paper, the buckling and post-buckling behavior of an elastic lattice system referred to as the discrete elastica problem is investigated using an equivalent non-local continuum approach. The geometrically exact post-buckling analysis of the elastic chain, also called Hencky system, is first numerically solved using the shooting method. This discrete physical model is also mathematically equivalent to a finite difference formulation of the continuum elastica. Starting from the exact difference equations of the discrete problem, a continualization method is applied for approximating the difference operators by differential ones, in order to better characterize the discrete system by an enriched continuous one. It is shown that the new continuum associated with the discrete system exactly fits the discrete elastica post-buckling problem, where the non-locality is of Eringen׳s type (also called stress gradient non-local model). An asymptotic expansion is performed for both the discrete and the non-local continuum models, in order to approximate the post-buckling branches of the discrete system. Some numerical investigations show the efficiency of the non-local approach, especially for capturing the scale effects inherent to the cell size of the lattice model.     

Cycle-to-cycle oscillations of heat release in a spark ignition engine

Fluctuations of combustion were studied using experimental time series of internal pressure in one of four cylinders in a spark ignition engine. Employing standard statistical methods like histograms and return maps, cycle-to-cycle variations of heat release were analyzed. A substantial difference in system behavior corresponding to quality of combustion was observed with a changing spark advance angle. Examining recurrence plots for a higher spark advance angle formation of specific patterns of vertical lines characteristic to intermittent behavior was found.     

Stationary response of strongly non-linear oscillator with fractional derivative damping under bounded noise excitation

The stochastic averaging method for strongly non-linear oscillators with lightly fractional derivative damping of order α (0<α≤1) subject to bounded noise excitations is proposed by using the generalized harmonic function. The system state is approximated by a two-dimensional time-homogeneous diffusion Markov process of amplitude and phase difference using the proposed stochastic averaging method. The approximate stationary probability density of response is obtained by solving the reduced Fokker–Planck–Kolmogorov (FPK) equation using the finite difference method and successive over relaxation method. A Duffing oscillator is taken as an example to show the application and validity of the method. In the case of primary resonance, the stochastic jump of the Duffing oscillator with fractional derivative damping and its P-bifurcation as the system parameters change are examined for the first time using the stationary probability density of amplitude.     

转台速率系统的相差／电压转换问题

本文介绍由相差／电压转换原理构成的一种高精度速率系统的原理及硬件电路的实现，并对各环节的关键技术进行了详细阐述。经实际调整证明，本方案容易实现，可靠性高，克服了增量编码器速率系统中使用锁相回路的若干缺点。     

径向辛体系一种新的差分格式

通过对Hellinger-Reissner变分原理进行坐标变换,将径向模拟为时间,导向辛体系,得到Hamilton对偶方程组.将微分形式的有限差分法引入弹性力学极坐标系下径向辛体系,把对偶方程组中的微分方程直接改用差分方程代替,推导出极坐标系下问题的辛差分方程,从而得到一种全新的径向辛体系差分格式.求解方程组,可直接得到位移和应力.编程计算曲梁等算例,结果表明该辛差分格式是有效的,丰富了弹性力学辛体系差分法的内容.     

Bifurcation and nonlinear dynamic analysis of noncircular aerodynamic journal bearing system

This paper studies the bifurcation and nonlinear dynamic behaviors of a rigid rotor supported by a noncircular aerodynamic journal bearing system (NABS) with a specified rigid rotor. A hybrid numerical method combining the differential transformation method and the finite difference method are used to calculate pressure distribution of NABS and rotor orbits. The results obtained for the orbits of the rotor center are in good agreement with those obtained using the traditional finite difference approach. Moreover, the hybrid method avoids the divergence problem suffered by the finite difference scheme at low values of the rotor mass and computational time-step. The results presented summarize the changes which take place in the dynamic behavior of the NABS as the rotor mass and bearing number are increased and, therefore, provide a useful guideline for the bearing system.     

三角翼的双襟翼控涡作用的数值模拟研究

对装有“前端襟翼”和“前缘襟翼”的７４°后掠三角翼的不可压缩流场作了数值模拟,以研究襟翼的旋涡控制作用．数值模拟是用拟压缩性方法求解一般曲线坐标系下的三维不可压缩Ｎａｖｉｅｒ－Ｓｔｏｋｅｓ方程,时间离散用向后Ｅｕｌｅｒ差分,空间无粘项的离散用二阶迎风ＴＶＤ格式,所得的离散方程用对角化形式的近似隐式因子分解格式求解．湍流模型用Ｂａｌｄｗｉｎ－Ｌｏｍａｘ代数模式．计算了三种平面形状的机翼在迎角范围为１０°～５０°的绕流和气动特性．计算和实验的比较表明,襟翼向下偏转可以推迟旋涡破裂,且对提高机翼的减阻能力、升阻比和改善失速前后的气动特性有明显效果,双襟翼具有更佳的控涡效果．     

Persistence of Exponential Trichotomy for Linear Operators: A Lyapunov–Perron Approach

In this article we revisit the perturbation of exponential trichotomy of linear difference equation in Banach space by using a Perron–Lyapunov fixed point formulation for the perturbed evolution operator. This approach allows us to directly re-construct the perturbed semiflow without using shift spectrum arguments. These arguments are presented to the case of linear autonomous discrete time dynamical system. This result is then coupled to Howland semigroup procedure to obtain the persistence of exponential trichotomy for non-autonomous difference equations.     

Finite element analysis of incompressible laminar boundary layer flows

A numerical procedure was developed to solve the two-dimensional and axisymmetric incompressible laminar boundary layer equations using the semi-discrete Galerkin finite element method. Linear Lagrangian, quadratic Lagrangian, and cubic Hermite interpolating polynomials were used for the finite element discretization; the first-order, the second-order backward difference approximation, and the Crank-Nicolson method were used for the system of non-linear ordinary differential equations; the Picard iteration and the Newton-Raphson technique were used to solve the resulting non-linear algebraic system of equations. Conservation of mass is treated as a constraint condition in the procedure; hence, it is integrated numerically along the solution line while marching along the time-like co-ordinate. Among the numerical schemes tested, the Picard iteration technique used with the quadratic Lagrangian polynomials and the second-order backward difference approximation case turned out to be the most efficient to achieve the same accuracy. The advantages of the method developed lie in its coarse grid accuracy, global computational efficiency, and wide applicability to most situations that may arise in incompressible laminar boundary layer flows.     

The influence of the injection system on drag reduction

The influence of the injection system for centerline injected polymer solutions (threads) on drag reduction in a turbulent pipe flow was studied using injectors of different length and grids. Compared with a short injector, the long injector showed a different behavior: the drag reduction was lower and its onset point was shifted to higher Reynolds numbers.The velocity profiles for the polymer-phase and the water-phase were measured simultaneously with a combination of laser-Doppler-velocimetry LDV and laser-induced fluorescence LIE It was found that the analysis of the LDV measurements with respect to the difference in velocity between the polymer-phase and the water-phase can give information about the mixing between both phases. For a Reynolds number of 30000 the difference between the phases is comparatively large for low drag reduction and very small for high drag reduction. The results indicate that the drag reduction achieved by injecting a concentrated polymer solution is mainly caused by a mixing process between polymer and water.     

长药室装药中多点点传火一维两相流数值模拟

针对药室长度超过3m的长药室装药设计问题,设计了以电点火具为点火源的多点点火系统,在点传火模拟实验装置上进行了多点点火的实验研究.同时,建立了点传火模拟实验装置中多点点传火过程的数学物理模型,采用MacCormack差分格式进行了数值求解,得到了点传火模拟装置中传火管的压力分布、固相和气相速度以及空隙率等数值解,分析了...