应用数学和力学

2004 Vol. 25, No. 8

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Linear Active Structures and Modes(Ⅰ)——Basic Concepts and Properties

ZHANG Jing-hui, GONG Jing, WANG Yong-gang

2004, 25(8): 771-778.

Abstract(2515) PDF(814)

Abstract:
Some basic concepts about the active structures were firstly explained, and the main subjects to study in the field of active structure dynamics were synthesized. For the linear active structures, the annotations on the modes were done in detail. The physical meanings of the right and left eigenvectors were explained. The right eigenvectors are the modal shapes and the modal responses of an active structure depend on the left ones. The adjoint structure of an active structure was defined and the reciprocity theorem was interpreted. For two active structures, which are adjoint to each other and with the reciprocal gain-matrices, the right and left eigenvector are reciprocal. The relationship between an active structure and the corresponding passive structure is expressed with the transfer functions, which is employed to resolve the estimation problems.

Linear Active Structures and Modes(Ⅱ)——Discrete Systems and Beams

WANG Yong-gang, GONG Jing, ZHANG Jing-hui

2004, 25(8): 779-786.

Abstract(2501) PDF(490)

Abstract:
The basic concepts about the active structures and some attributes of the modes were presented in paper Liner Active Structures and Modes (I). The characteristics of the active discrete systems and active beams were discussed, specially, the stability of the active structures and the orthogonality of the eigenvectors. The notes about modes were portrayed by a model of a seven-storeyed building with sensors and actuators. The concept of the adjoint active structure was extended from the discrete systems to the beams that were the representations of the continuous structures. Two types of beams with different placements of the measuring and actuating systems were discussed in detail. One is the beam with the discrete sensors and actuators, and the other is the beam with distributed sensor and actuator function. The orthogonality conditions were derived with the modal shapes of the active beam and its adjoint active beam. An example shows that the variation of eigenvalues with feedback amplitude for the homo-configuration and non-homo-configuration active structures.

On Decentralized Stabilization of Linear Large Scale Systems With Symmetric Circulant Structure

JIN Chao-yong, ZHANG Xiang-wei

2004, 25(8): 787-795.

Abstract(2361) PDF(639)

Abstract:
The decentralized stabilization of continuous and discrete linear large scale systems with symmetric circulant structure was studied. A few sufficient conditions on decentralized stabilization of such systems were proposed. For the continuous systems, by introducing a concept called the magnitude of interconnected structure, a very important property that the decentralized stabilization of such systems is fully determined by the structure of each isolated subsystem that is obtained when the magnitude of interconnected structure of the overall system is given. So the decentralized stabilization of such systems can be got by only appropriately designing or modifying the structure of each isolated subsystem, no matter how complicated the interconnected structure of the overall system is. A algorithm for obtaining decentralized state feedback to stabilize the overall system is given. The discrete systems were also discussed. The results show that there is a great dfference on decentralized stabilization between continuous case and discrete case.

Some Dynamical Behavior of the Stuart-Landau Equation With a Periodic Excitation

CHEN Fang-qi, LIANG Jian-shu, CHEN Yu-shu

2004, 25(8): 796-800.

Abstract(3163) PDF(544)

Abstract:
The lock-in periodic solutions of the Stuart-Landau equation with a periodic excitation are studied. Using singularity theory, the bifurcation behavior of these solutions with respect to the excitation amplitude and frequency were investigated in detail, respectively. The results show that the universal unfolding with respect to the excitation amplitude possesses codimension 3. The transition sets in unfolding parameter plane and the bifurcation diagrams are plotted under some conditions. Additionally, it has also been proved that the bifurcation problem with respect to frequence possesses infinite codimension. Therefore the dynamical bifurcation behavior is very complex in this case. Some new dynamical phenomena are presented, which are the supplement of the results obtained by Sun Liang et al.

Differential Quadrature Method for Bending of Orthotropic Plates With Finite Deformation and Transverse Shear Effects

LI Jing-jing, CHENG Chang-jun

2004, 25(8): 801-808.

Abstract(2718) PDF(530)

Abstract:
Based on the Reddy's theory of plates with the effect of higher-order shear deformations, the governing equations for bending of orthotropic plates with finite deformations were established. The differential quadrature method of nonlinear analysis to the problem was presented. DQWB approach was extended to handle the multiple boundary conditions of plates. The techniques were also further extended to simplify nonlinear computations. The numerical convergence and comparison of solutions were studied. The results show that the DQ method presented is very reliable and valid. Moreover, the influences of geometric and material parameters as well as the transverse shear deformations on nonlinear bending were investigated. Numerical results show the influence of the shear deformation on the static bending of orthotropic moderately thick plate is significant.

On the Study of the Initiation of the Micro Crack on the Smooth Surface of Polycrystalline

YUE Zhu-feng

2004, 25(8): 809-814.

Abstract(2417) PDF(652)

Abstract:
Crystallographic plasticity was applied to study the initiation of micro cracks on the smooth surface of polycrystalline under uniform applied stress. Even under the uniform external stress, due to the different crystallographic orientations of the grains in the polycrystalline, there is un-uniform stress distribution and the deformation is also not uniform. Under the fatigue loading, the roughness increases with the number of fatigue, and deformation will localize in some places, where micro cracks form.

Analytic Solutions of Incompressible Laminar Flow in the Inlet Region of a Pipe

MENG Qing-guo

2004, 25(8): 815-818.

Abstract(2769) PDF(919)

Abstract:
The laminar analytic solutions of velocities and pressure in the central zone of the inlet region of pipe flow are given under the condition of uniform inflow, based on the Navier-Stokes equations of incompressible viscous flow.

Hamilton Operators and Homothetic Motions in R³

Yusuf Yayli, Nergiz Yaz, Murat Kemal Karacan

2004, 25(8): 819-823.

Abstract(2820) PDF(462)

Abstract:
Quaternion is a division ring. It is shown that planes passing through the origin can be made a field with the quaternion product in R³. The Hamiltonian operators help us define the homothetic motions on these planes. New characterizations for these motions are investigated.

Large Eddy Simulation and Spectrum Analysis of Flow Around Two Square Cylinders Arranged Side by Side

WEI Ying-jie, ZHU Meng-sheng, HE Zhong-yi

2004, 25(8): 824-830.

Abstract(2406) PDF(656)

Abstract:
Large eddy simulation cooperated with the second order full extension ETG finite element method was applied to simulate the flow around two square cylinders arranged side by side at a spacing ratio of 1.5. The second order full extension ETG finite element method was developed by Wang and He. By means of Taylor expansion of terms containing time derivative, time derivative is replaced by space derivative. The function of it is equal to introducing an artificial viscosity term. The streamlines of the flow at different moments were obtained. The time history of drag coefficient, lift coefficient and the streamwise velocity on the symmetrical points were presented. Furthermore, the symmetrical problem of the frequency spectrum of flow around two square cylinders arranged side by side were studied by using the spectral analysis technology. The data obtained at the initial stage are excluded in order to avoid the influence of initial condition on the results. The power spectrums of drag coefficient, lift coefficient, the streamwise velocity on the symmetrical points were analyzed respectively. The results show that although the time domain process of dynamic parameters is non-symmetrical, the frequency domain process of them is symmetrical under the symmetrical boundary conditions.

Structure of Wave Front and Organization Center in Excitable Media

LIU Shen-quan

2004, 25(8): 831-836.

Abstract(2339) PDF(475)

Abstract:
With help of establishing the moving coordinate on the wave front surface and the perturbation analysis in the boundary layer, the structures of wave front and organization center in excitable media were studied. The eikonal equation of wave front surface and general equation of organization center were obtained. These eikonal equations reveal the wave front surfaces have structures of twisted scroll wave and M bius band, the organization centers have structures of knotted and linked ring. These theoretical results not only explain the wave patterns of BZ chemical reaction but also give several possibility structures of wave front surface and organization center in general excitable media.

Short- and Resonant-Range Interactions Between Scales in Turbulence and Their Applications

GAO Zhi

2004, 25(8): 837-846.

Abstract(2381) PDF(496)

Abstract:
Interactions between different scales in turbulence were studied starting from the incompressible Navier-Stokes equations. The integral and differential formulae of the short-range viscous stresses, which express the short-range interactions between contiguous scales in turbulence, were given. A concept of the resonant-range interactions between extreme contiguous scales was introduced and the differential formula of the resonant-range viscous stresses was obtained. The short- and resonant-range viscous stresses were applied to deduce the large-eddy simulation (LES) equations as well as the multiscale equations, which are approximately closed and do not contain any empirical constants or relations. The properties and advantages of using the multiscale equations to compute turbulent flows were discussed. The short-range character of the interactions between the scales in turbulence means that the multiscale simulation is a very valuable technique for the calculation of turbulent flows. A few numerical examples were also given.

Structure of Nonnegative Nontrivial and Positive Solutions of Singularly Perturbed p-Laplace Equations

ZHANG Zheng-ce, LI Kai-tai

2004, 25(8): 847-854.

Abstract(2979) PDF(688)

Abstract:
Structure of nonnegative nontrivial and positive solutions was precisely studied for some singularly perturbed p-Laplace equations. By virtue of sub- and supersolution method, it is shown that there are many nonnegative nontrivial spike-layer solutions and positive intermediate spike-layer solutions. Moreover, the upper and lower bound on the measure of each spike-layer were estimated when the parameter is sufficiently small.

One-Dimensional Consolidation of Layered Soils With Impeded Boundaries Under Time-Dependent Loadings

CAI Yuan-qiang, LIANG Xu, WU Shi-ming

2004, 25(8): 855-862.

Abstract(2756) PDF(578)

Abstract:
On the basis of Terzaghi's one-dimensional consolidation theory, the variation of effective stress ratio in layered saturated soils with impeded boundaries under time-dependent loading was studied. By the method of Laplace transform, the solution was presented. Influences of different kinds of cyclic loadings and impeded boundaries conditions were discussed. Through numerical inversion of Laplace transform, useful illustrations were given considering several common time-dependent loadings. Pervious or impervious boundary condition is just the special case of the problem considered here. Compared with average index method, the results from the method illustrated are more accurate.

Numerical Simulation of Transient Thermal Field in Laser Melting Process

YAO Guo-feng, CHEN Guang-nan

2004, 25(8): 863-868.

Abstract(2138) PDF(581)

Abstract:
Numerical simulation of thermal field was studied in laser processing. The 3-D finite element model of transient thermal calculation is given by thermal conductive equation. The effects of phase transformation latent are considered. Numerical example is given to verify the model. Finally the real example of transient thermal field is given.

Green Function on Two-Phase Saturated Medium by Concentrated Force in Two-Dimensional Displacement Field

DING Bo-yang, DING Cui-hong, CHEN Yu, TAO Hai-bing

2004, 25(8): 869-874.

Abstract(2446) PDF(785)

Abstract:
The Green function on two-phase saturated medium by concentrated force has a broad and important use in seismology, seismic engineering, soil mechanics, geophysics, dynamic foundation theory and so on. According to the Green function on two-phase saturated medium by concentrated force in three-dimentional displacement field obtained by Ding Bo-yang et al, it gives out the Green function in two-dimensional displacement field by infinite integral method along X₃ direction derived by De Hoop and Manolis. The method adopted in the thesis is simpler. The result will be simplified to the boundary element method of dynamic problem.

Theoretical Model and Numerical Method on Online Identification of Dynamical Characteristics of Structural System

YAO Zhi-yuan, WANG Feng-quan

2004, 25(8): 875-880.

Abstract(2373) PDF(685)

Abstract:
An online method of identification of dynamic characteristics only using measured ambient response of structural dynamic system is widely focused on. The Ibrahim and ARMAV methods are basic identification methods. A model on dynamic system suffered by random ambient excitation was researched into, and a subspace decomposition method being different from traditional harmonic retrieval method was introduced. Robustness and effectiveness of this approach on identification of vibration characteristics are demonstrated on numerical experiment.