2010 Vol. 31, No. 1

Display Method:
Spatio-Temporal Instability of Two-Layer Liquid Film at Small Reynolds Numbers
WANG Zhi-liang, S. P. Lin, ZHOU Zhe-wei
2010, 31(1): 1-11. doi: 10.3879/j.issn.1000-0887.2010.01.001
Abstract(1110) PDF(870)
The on set of the instability with respect to spatio-temporally growing disturbances in a viscosity-stratified two-layer liquid fiml flow was analyzed. The known results obtained from the temporal theory of instability showed that the flow was un stable in the lmiit of zero Reynolds numbers. The present theory predicted the neutral stability in the same limit. The discrepancy was explained. And based on the mechanical energy equation, a new mechanism of instability was found. The new mechanism was associated with the convective nature of the disturbance which was not Galilei invariant.
Criterion of Aerodynamic Performance of Large-Scale Offshore Horizontal-Axis Wind Turbines
CHENG Zhao-xue, LI Ren-nian, YANG Cong-xin, HU Wen-rui
2010, 31(1): 12-18. doi: 10.3879/j.issn.1000-0887.2010.01.002
Abstract(1247) PDF(885)
Taking offshore wind energy project as investigation object, the aerodynamic performance and geometric characteristics of wind turbine rotors with large capacity (1 MW to 10 MW) were analyzed in connection with their main characteristic parameters (e. g. rated wind speed, blade tip speed, and rotor solidity). First, it was pointed out that an essential criterion of high-performance wind turbine is its annual usable energy pattern factor, which should be as high as possible with its dimension possibly minimum as well, so that a maxmium wind energy would be captured and maxim al annual power output obtained. Then the in fluence of above-mentioned three parameters on the pattern factor and rotor geometry of wind turbine operated in Chinese offshore meteorological environment was investigated. The variation pattern of aerodynamic and geometric parameters were obtained, analyzed, and compared with each other. Finally, it was pointed out that the method for aerodynamic analysis and its result could be taken as a basis for evaluation of aerodynamic performance of large-scale offshore wind turbine rotors.
Stability of the Cubic Functional Equation in Intuitionistic Random Normed Spaces
ZHANG Shi-sheng, John Michael Rassias, Reza Saadati
2010, 31(1): 19-25. doi: 10.3879/j.issn.1000-0887.2010.01.003
Abstract(1187) PDF(829)
The purpose is first to introduce the notation of intuition isticrandom normed spaces, and then by virtue of this notation to study the stability of a cubic functional equation in the setting of these spaces under arbitrary triangle norms. Furthermore, the interdisciplinary relation among the theory of random spaces, the theory of intuitionistic spaces and the theory of functional equations are also presented.
Formation Control for Nonholonomic Agents Using Passivity Techniques
WU Fan, GENG Zhi-yong
2010, 31(1): 26-34. doi: 10.3879/j.issn.1000-0887.2010.01.004
Abstract(916) PDF(873)
The problem of formation control for multiple nonholonomic agents on a plane was studied. A dynamic feedback linearization method was used to transform each agent's dynamicalmodel in to two third-order in tegrator chains. Then a decentralized formation control law with inter-agent damping in jection was derived. A symptotical stability of the overall system was proved by Liapunov method. Simulation for a planar vehicles. formation maneuver shows the effectiveness of the proposed strategy.
On the Truth of Nanoscale for Nanobeams Based on Nonlocal Elastic Stress Field Theory: Equilibrium,Governing Equation and Static Deflection
C. W. Lim
2010, 31(1): 35-50. doi: 10.3879/j.issn.1000-0887.2010.01.005
Abstract(1114) PDF(1052)
This paper has success fully addressed three critical but overlooked issues in nonlocal elastic stress field theory for nanobeams: (ⅰ) why does the presence of in creasing nonlocal effects induce reduced nanostructural stiffness in many, but not consistently for all, cases of study, i. e. increasing static deflection, decreasing natural frequency and decreasing buckling load, although physical intuition according to the nonlocal elasticity field theory first established by Eringen tells otherwise? (ⅱ) the in triguing conclusion that nanoscale effects are missing in the solutions in many exemplary cases of study, eg. bending deflection of a cantilevernanobeam with a point load at its tip; and (ⅲ) the non-existence of additional higher-order boundary conditions for a higher-order governing differential equation. Applying the nonlocale lasticity field theory in nanomechanics and an exact variational principal approach, the new equilibrium conditions, domain governing differential equation and boundary conditions for bending of nanobeams were derived. These equations and conditions involved essential higher-orderd ifferential terms which were oppositein sign with respect to the previous studies in statics and dynamics of nonlocal nano-structures. The difference in higher-order terms resulted in reverse trends of nanoscale effects with respect to the conclusion. Effectively, this paper reported new equilibrium conditions, governing differential equation and boundary conditions and the true basic static responses for bending of nanobeams. It also concludes that the widely accepted equilibrium conditions of nonlocal nanostructures are in fact not in equilibrium, but they can be made perfect should the nonlocal bending moment be replaced by an effective non local bending moment. The conclusions above were substantiated, in a general sense, by other approaches in nanostructuralmodels such as strain gradient theory, modified couple stress models and experiments.
Multiple Cell Elements and Regular Multifractals
YIN Ya-jun, LI Ying, YANG Fan, FAN Qin-shan
2010, 31(1): 51-60. doi: 10.3879/j.issn.1000-0887.2010.01.006
Abstract(1049) PDF(881)
Based on fractal super fibers and binary fractal fibers, the following objectives were approached: Firstly, the concept of multiple celle lements was induced and abstracted. Secondly, th rough multiple cell elements, regular multifractals with strict self-similarities were confirmed not only constructible, but also being of universal construction mode. Thirdly, through the construction mode, a regular multifractal was found to be equivalent to a generalized regular single fractal with multiple fine structures under the meaning of multiple cellelements. On the basis of this equivalence, the dimension of single fractals was extended to that of regular multifractals, and the geometry of single fractals was extended to that of regular multifractals. Fourthly, through regular multifractals a few golden fractals were constructed.
Interaction Between Cracks and Effect of Micro-Crack Zone on Main Crack Tip
XIA Xiao-zhou, ZHANG Qing, QIAO Pi-zhong, LI Li-juan
2010, 31(1): 61-70. doi: 10.3879/j.issn.1000-0887.2010.01.007
Abstract(1217) PDF(1005)
The mechanism in teraction between cracks with differen torientations was analyzed based on the principle of superposition and a flattening method. It is found that the maxmium interaction effect will not occur when the micro crack is along the direction parallel or perpendicular to the principal tensile stress, which is different from the conclusion drawn by Ortiz [ASME Journal of Applied Mechanics, 1987, 54(3): 54-58]. The production mechanism of microcrack and the effect of microcrack zone onmain crack tip were also studied. As a result, the microcrack zone hasmagnifying effecton main crack tip, and such a magnifying effect increases with the increase of micro crack density and length.
Approximation of Thermoelasticity Contact Problem With Nonmonotone Friction
Ivan Šestak, Bo>>ko S. Jovanović
2010, 31(1): 71-80. doi: 10.3879/j.issn.1000-0887.2010.01.008
Abstract(1396) PDF(813)
The formulation and approxmiation of a static thermoelasticity problem that described bilateral frictional contact between a deformable body and a rigid foundation was presented. The friction was in the form of nonmonotone and multivalued law. The coupling effect of the problem was neglected, therefore the thermic part of the problem was considered independently of the elasticity problem. For the displacement vector, a substationary problem for non-convex, locally Lipschitz continuous functional representing the total potential energy of the body was form ulated. All problems form ulated were approxmiated by the finite element method.
Analysis of Fully Coupled Flow-Induced Vibration of Structure Under Small Deformation With GMRES
ZHANG Li-xiang, GUO Ya-kun, ZHANG Hong-ming
2010, 31(1): 81-90. doi: 10.3879/j.issn.1000-0887.2010.01.009
Abstract(1267) PDF(738)
Lagrangian-Eulerian formulations, based on a generalized variational principle of coupling fluid and solid dynamics, was established to describe flow-induced vibration of a structure under small deformation in incompressible viscous fluid flow. The spatial discretization of the formulations was on multi-linear interpolating functions using the finite element method for both the fluid and solid structure. The generalized trapezoidal rule was used to obtain apparently nonsymm etric linear equations in in cremental form for the variables of the flow and vibration. The nonlinear convective term and tmie factors were contained in nonsymmetric coefficient matrix of the equations. Generalized minimum residual method (GMRES) was used to solve the incremental equations. A new stable algorithm of GMRES-Hughes-Newmark was developed to deal with flow-induced vibration with dynamical fluid-structure in teraction in complex geometry. Good agreement between the simulations and laboratory measurements of the pressure and blade vibration accelerations in a hydro turbine passage was obtained, indicating that the GMRES-Hughes-Newmark algorithm presented was suitable for dealing with the flowinduced vibration of structures under small deformation.
Direct Numerical Simulation of Flow in a Channel With Time-Dependent Wall Geometry
GE Ming-wei, XU Chun-xiao, CUI Gui-xiang
2010, 31(1): 91-101. doi: 10.3879/j.issn.1000-0887.2010.01.010
Abstract(1166) PDF(876)
A numerical scheme was developed to extend the scope of the spectralm ethod without solving the covariant and contra-variant form of Navier-Stokes equations in curvilinear coordinates. The primitive variables were rep resented by Fourier series and Chebyshev polynomials in computational space. The time advan cement was accom plished by a high-order tmie-splitting method, and a corresponding high-order pressure condition at the wall was in troduced to reduce the splitting error. Compared with the previous pseudo-spectral scheme, in which the Navier-Stokes equations were solved in covariant and contra-variant form, the present scheme reduced the computational cost, at the same time kept the spectral accuracy. The scheme was tested by the simulation of turbulent flow in a channel with a static streamwise wavy wall and turbulent flow over a flexible wallundergoing streamwise traveling wave motion. Turbulent flow over an oscillating dimple was studied using present numerical scheme, and the periodic generation of vortical structures was analyzed.
Joule Heating Effect of Electroosmosis in a Finite-Length Microchannel Made of Different Materials
CHAO Kan, WU Jian-kang, CHEN Bo
2010, 31(1): 102-110. doi: 10.3879/j.issn.1000-0887.2010.01.011
Abstract(1053) PDF(806)
A numerical analysis was presented to study Joule heating effect of electroosmosis in a finite-length microchannel made of glass and PDMS polymer. Poisson-Boltzmann equation of electric double layer, Navier-Stokes equation of liquid flow and liquid-solid coupled heat transfer equation were solved to investigate temperature behavior of electroosmosis in two-dmiensional microchannel. The feedback effect of temperature variation on liquid properties (dielectric constant, viscosity, thermal and electric conductivities) was taken in to account. Numerical results indicate that there exists a heat developing length near channel in let where flow velocity, temperature, pressure, electric field rapidly vary. The flow velocity, electric field and temperature approach to a steady state after heat developing length, which may occupy a considerable portion of the microchannel in cases of thickchip and high electric field. Liquid temperature of steady state increases with increase of applied electric field, channel thickness and chip thickness. The temperature on PDMS wall is higher than that on glass wall due to difference of heat conductivities. Temperature variations are found in both longitudinal and tran sverse derictions of the microchannel. Temperature increase on wall decreases charge density of the electric double layer. Longitudinal temperature variation induces a pressure gradient and changes behavior of electric field in microchannel. In flow liquid temperature does not change liquid temperature of steady state and heat developing length.
Dynamical Behavior of Traveling Wave Solutions in the Ion Acoustic Plasma Equations
LI Shu-min, HE Tian-lan
2010, 31(1): 111-116. doi: 10.3879/j.issn.1000-0887.2010.01.012
Abstract(1479) PDF(807)
By using the theory of planar dynamical systems to the ion acoustic plasm a equations, the existence of smooth and non-smooth solitary wave solution s and uncountably infinite smooth and non-smooth periodic wave solutions is obtained. Furthermore, Under given parametric conditions, the sufficient conditions which guarantee the existence of the above solutions are given.
A 17-Node Quadrilateral Spline Finite Element Using the Triangular Area Coordinates
CHEN Juan, LI Chong-jun, CHEN Wan-ji
2010, 31(1): 117-126. doi: 10.3879/j.issn.1000-0887.2010.01.013
Abstract(1313) PDF(887)
A 17-node quadrilateral element had been developed using the bivariate quartic spline interpolation basis and the triangular area coordinates, which could exactly model the quartic field. Some appropriate examples are employed to illustrate that the element possesses high precision and is insensitive to mesh distortions.