Transient bending waves in plates studied by hologram interferometry

Propagating bending waves are studied in plates made of aluminum and wood. The waves are generated by the impact of a ballistic pendulum. Hologram interferometry, with a double pulsed ruby laser as the light source, is used to record the out of plane motion of the waves. Elliptic-like fringes visualize differences in wave speed for different directions in the anisotropic plate and circular ones are obtained for the isotropic plate. The experimental data for the isotropic plate compare favorably with analytical results derived from the Kirchhoff-plate equation with a point impact of finite duration. A similarity variable is found when starting conditions are modeled as a Dirac pulse in space and time, that brings new understanding to the importance of specific parameters for wave propagation in plates. A formal solution is obtained for a point force with an arbitrary time dependence. For times much larger than the contact time, the plate deflection is shown to be identical to that from a Dirac pulse applied at the mean contact time. A method for determining material parameters, and the mean contact time, from the interferograms is hence developed.     

Stability and dispersion analysis of reproducing kernel collocation method for transient dynamics

A reproducing kernel collocation method based on strong formulation is introduced for transient dynamics. To study the stability property of this method, an algorithm based on the von Neumann hypothesis is proposed to predict the critical time step. A numerical test is conducted to validate the algorithm. The numerical critical time step and the predicted critical time step are in good agreement. The results are compared with those obtained based on the radial basis collocation method, and they are in good agreement. Several important conclusions for choosing a proper support size of the reproducing kernel shape function are given to improve the stability condition.     

First-passage failure of strongly non-linear oscillators with time-delayed feedback control under combined harmonic and wide-band noise excitations

A procedure for studying the first-passage failure of strongly non-linear oscillators with time-delayed feedback control under combined harmonic and wide-band noise excitations is proposed. First, the time-delayed feedback control forces are expressed approximately in terms of the system state variables without time delay. Then, the averaged Itô stochastic differential equations for the system are derived by using the stochastic averaging method. A backward Kolmogorov equation governing the conditional reliability function and a set of generalized Pontryagin equations governing the conditional moments of first-passage time are established. Finally, the conditional reliability function, the conditional probability density and moments of first-passage time are obtained by solving the backward Kolmogorov equation and generalized Pontryagin equations with suitable initial and boundary conditions. An example is worked out in detail to illustrate the proposed procedure. The effects of time delay in feedback control forces on the conditional reliability function, conditional probability density and moments of first-passage time are analyzed. The validity of the proposed method is confirmed by digital simulation.     

Experimental investigation of slosh dynamics of liquid-filled containers

This paper is concerned with the experimental studies on the sloshing response of liquid-filled containers. A three-dimensional finite element analysis is carried out for the numerical simulation of this problem. The effects of sloshing are computed in the time domain using Newmark's time integration scheme. A simple experimental setup is designed and fabricated in-house to conduct experiments for measuring some of the basic parameters of sloshing. A sensor device is especially developed to record the free-surface wave heights. Each wave height sensor is a capacitance probe that detects the change in level of liquid (water) precisely with no time lag. The sensors are used in conjunction with a signal-processing unit in which the capacitance values are transduced to a voltage signal between 0 V and 10 V. These wave height sensors simultaneously record the slosh wave height near the periphery of the container wall from 16 predetermined locations to give the free-surface profiles of liquid at desired time steps. The experimental results are compared with those obtained from the present theoretical analysis, and good agreements are observed.     

A method for analysing nesting techniques for the linearized shallow water equations

A method for analysing different nesting techniques for the linearized shallow water equations is presented. The problem is formulated as an eigenvector–eigenvalue problem. A necessary condition for stability is that the spectral radius of the propagation matrix is less than or equal to one. Two test cases are presented. The first test case is analysed, and effects of enforcing volume conservation and nudging in time are studied. A nesting technique is found that causes no growth of any eigenvectors for reasonable time steps. This nesting technique is then used on both test cases, and results are compared to an everywhere refined model and a coarse grid model. Copyright © 2002 John Wiley & Sons, Ltd.     

Space time on the Poincare diagrams

Relations between the experience of space technology and theory of space and time arefound in this paper.A nontraditional approach to the concepts of space and time isintroduced.The approach is based upon the the analysis of the detailed mechanism of radarmeasurement and nonlinear Doppler effects as measured by an astronaut.The Lorentzfactor and four-dimensional interval t~2-x~2/c~2 may be interpreted fromthe point of view of a space technologist.A“geometrical mean”notion for computing timeinterval is introduced parallelly with the usual arithmetic mean formulas,giving resultscomparable with those of special relativity theory.Space time relationships aredemonstrated on the Poincare diagrams.     

High temperature fracture parameter for a weld interface crack

A fracture parameter is introduced to characterize crack growth at elevated temperature for a weld interface crack. Finite element analyses are made for a compact tension (CT) specimen under constant load where an interface is modeled along the crack plane to simulate the dividing line of the weld metal (WM) and base metal (BM). A constitutive relation for an elastic-creeping material is used. The proposed time dependent fracture parameter is obtained for different creep constants of WM and BM. A transition time and fracture parameter for the homogeneous and welded specimens are defined such that the results can be normalized and presented in a general form for assessing the crack growth life.     

Stress wave propagation in plates subjected to a transient line source

A method of treating the response of plates to a transient load, which was recently proposed, is here elaborated for the particular case of a plate subjected to a transient line source. Expressions presenting the various stresses as functions of time and position are derived. A numerical scheme, by which these stresses are calculated, is described. Some results concerning the behavior of stresses in the course of time are illustrated and discussed.     

Berechnung instationärer Temperaturfelder mit finiten Elementen in Raum- und Zeitdimension

A programme is demonstrated which apart from linear finite elements in time also includes elements with shape functions of the second and third degree. The algorithm for discretization in the time dimension is described and, using the example of a parabolic time element, the coefficients required to form the element matrices are given. A parabolic alteration within a time element is taken into consideration for the boundary conditions, this being of special importance in reproducing periodic processes. On the basis of certain test examples the efficiency of the process is examined by comparison with the customary mean difference method.     

线性系统模态控制及其时滞补偿

对线性系统模态控制及其时滞补偿进行研究。模态控制分控制全部模态和控制有限模态两种情况 ,时滞补偿采用移相补偿。最后结合算例对两种控制模态下的控制效果和控制有限模态时的时滞补偿进行了数值计算和结果对比     

三维对流扩散方程的高精度全隐式多重网格方法

提出了数值求解三维非定常变系数对流扩散方程的一种高精度全隐紧致差分格式,该格式在空间上具有四阶精度,时间具有二阶精度。为了克服传统迭代法在每一个时间步上迭代求解隐格式时收敛速度慢的缺点,采用多重网格加速技术,建立了适用于本文高精度全隐紧致格式的多重网格算法,从而大大加快了迭代收敛速度。数值实验结果验证了本文方法的精确性、稳定性和对高网格雷诺数问题的强适应性。     

柔性机械臂的时滞最优跟踪控制

采用最优跟踪控制方法对柔性机械臂线性化主动控制中的时滞问题进行研究。首先采用一种积分变换,将包含时滞项的动力学方程转换成形式上不包含时滞项的标准形式,然后根据最优跟踪控制理论设计控制律。在每一步控制律的计算中,不但包含有当前步的状态反馈,而且包含有前若干步控制的线性组合。文中还给出了一个模态坐标的提取方法。仿真结果显示,若对时滞不处理,控制系统会在很小时滞量时出现发散;当控制系统中的时滞量不大时,本文的线性化时滞控制设计能够取得较好的控制效果;当系统存在较大时滞量时,线性化时滞控制设计的有效范围是有限的。     

PRODUCTION, ISOLATION AND SPECTROSCOPIC STUDIES OF THE ENDOHEDRAL FULLERENE Sc_2@C_(80)(I-III)

Introduction C80 and C80-based endohedral metallofullerenes (named as Mn@C80 hereafter) have attracted extensive attention due to their special properties. C80 has an extremely low abundance in soot produced by arc discharge and it is only until recently that two isomers of C80(D2) were isolated by Kappes (Hennrich et al., 1996) and us (Wang et al., 2000). In contrast, some Mn@C80 have a relatively high abun-dance and so far the isolation of Mn@C80 has been achieved for both dimetallofull…     

Feedback minimization of first-passage failure of quasi non-integrable Hamiltonian systems

The non-linear stochastic optimal control of quasi non-integrable Hamiltonian systems for minimizing their first-passage failure is investigated. A controlled quasi non-integrable Hamiltonian system is reduced to an one-dimensional controlled diffusion process of averaged Hamiltonian by using the stochastic averaging method for quasi non-integrable Hamiltonian systems. The dynamical programming equations and their associated boundary and final time conditions for the problems of maximization of reliability and of maximization of mean first-passage time are formulated. The optimal control law is derived from the dynamical programming equations and the control constraints. The dynamical programming equations for maximum reliability problem and for maximum mean first-passage time problem are finalized and their relationships to the backward Kolmogorov equation for the reliability function and the Pontryagin equation for mean first-passage time, respectively, are pointed out. The boundary condition at zero Hamiltonian is discussed. Two examples are worked out to illustrate the application and effectiveness of the proposed procedure.     

An operator splitting scheme for the stream‐function formulation of unsteady Navier–Stokes equations

A fictitious time is introduced into the unsteady equation of the stream function rendering it into a higher‐order ultra‐parabolic equation. The convergence with respect to the fictitious time (we call the latter ‘internal iterations’) allows one to obtain fully implicit nonlinear scheme in full time steps for the physical‐time variable. For particular choice of the artificial time increment, the scheme in full time steps is of second‐order of approximation. For the solution of the internal iteration, a fractional‐step scheme is proposed based on the splitting of the combination of the Laplace, bi‐harmonic and advection operators. A judicious choice for the time staggering of the different parts of the nonlinear advective terms allows us to prove that the internal iterations are unconditionally stable and convergent. We assess the number of operations needed per time step and show computational effectiveness of the proposed scheme. We prove that when the internal iterations converge, the scheme is second‐order in physical time and space, nonlinear, implicit and absolutely stable. The performance of the scheme is demonstrated for the flow created by oscillatory motion of the lid of a square cavity. All theoretical findings are demonstrated practically. Copyright © 2006 John Wiley & Sons, Ltd.     

Finite time stability analysis of PD fractional control of robotic time-delay systems

A finite time stability test procedure is proposed for robotic system where it appears a time delay in PD^α fractional control system. Paper extends some basic results from the area of finite time and practical stability to linear, continuous, fractional order time invariant time-delay systems given in state-space form. Sufficient conditions for this kind of stability, for particular class of fractional time-delay systems are derived.     

ACTIVE CONTROL OF A FLEXIBLE CANTILEVER PLATE WITH MULTIPLE TIME DELAYS

Active control of a flexible cantilever plate with multiple time delays is investigated using the discrete optimal control method. A controller with multiple time delays is presented. In this controller, time delay effect is incorporated in the mathematical model of the dynamic system throughout the control design and no approximations and assumptions are made in the controller derivation, so the system stability is easily guaranteed. Furthermore, this controller is available for both small time delays and large time delays. The feasibility and efficiency of the proposed controller are verified through numerical simulations in the end of this paper.     

A time‐accurate pseudo‐compressibility approach based on an unstructured hybrid finite volume technique applied to unsteady turbulent premixed flame propagation

A preconditioning approach based on the artificial compressibility formulation is extended to solve the governing equations for unsteady turbulent reactive flows with heat release, at low Mach numbers, on an unstructured hybrid grid context. Premixed reactants are considered and a flamelet approach for combustion modelling is adopted using a continuous quenched mean reaction rate. An overlapped cell‐vertex finite volume method is adopted as a discretisation scheme. Artificial dissipation terms for hybrid grids are explicitly added to ensure a stable, discretised set of equations. A second‐order, explicit, hybrid Runge–Kutta scheme is applied for the time marching in pseudo‐time. A time derivative of the dependent variable is added to recover the time accuracy of the preconditioned set of equations. This derivative is discretised by an implicit, second‐order scheme. The resulting scheme is applied to the calculation of an infinite planar (one‐dimensional) turbulent premixed flame propagating freely in reactants whose turbulence is supposed to be frozen, homogeneous and isotropic. The accuracy of the results obtained with the proposed method proves to be excellent when compared to the data available in the literature. Copyright © 2004 John Wiley & Sons, Ltd.     

Application of streamwise diffusion to time-dependent free convection of liquid metals

A numerical analysis is given for the application of streamwise diffusion to high-intensity flows with marginal spatial resolution. Terms are added to the momentum equation which are similar to those used in the Petrov-Galerkin, Taylor-Galerkin and balancing tensor diffusivity methods. Values for the streamwise viscosity are obtained from mesh refinement studies. An illustration is given for the time-dependent free convection of a liquid metal in a cavity with differentially heated sided walls. The spatial problem is solved with the Galerkin finite element method and the time integration is performed with the backward Euler method. Solution quality and computation time are compared for results with and without added streamwise diffusion. For the cases presented, streamwise diffusion eliminates spurious oscillations and saves computation time without compromising the solution.     

Analysis of Detached-Eddy Simulation for the Flow Around a Circular Cylinder with Reference to PIV Data

A detailed validation study is presented for the detached-eddy simulation (DES) of the flow around a circular cylinder at a high sub-critical Reynolds number. Good comparability with unsteady experimental field data is facilitated by the confined and clearly-defined geometry, although some uncertainty remains regarding the free stream turbulence intensity. The combination of DES with an appropriate low-dissipative hybrid numerical convection scheme and high temporal resolution delivers excellent agreement with the experiment for the time and phase-averaged fields as well as the spectral content. A strong sensitivity of the solution to the numerical time step size has been identified, which is attributed to time-filtering effects damping the development of resolved turbulence in the early shear layer. Recommendations are made concerning a CFL-type criterion for the temporal resolution of DES and future studies involving a still finer time step are outlined.