应用数学和力学

Substrate Elastic Deformation Due to Vertical Component of Liquid-Vapor Interfacial Tension

YU Ying-song

2012, 33(9): 1025-1042. doi: 10.3879/j.issn.1000-0887.2012.09.001

Abstract(2518) PDF(1842)

Abstract:
Young’s equation is one of the fundamental equations in capillarity and wetting. However, it just reflected the balance of the horizontal components of the three interfacial tensions with contact angle while there was no description of the vertical component of liquidvapor interfacial tension (VCLVIT). Nowadays, there is a clear consensus that the VCLVIT induces an elastic deformation of the solid substrate, which plays a significant influence on the fabrications of the microfluidic devices because of the wide use of the soft materials. The theoretical, experimental and numerical aspects of the investigations on this problem were reviewed. Moreover, the effects of the VCLVIT-induced surface deformation on wetting and spreading, the deflection of the microcantilever as well as elasto-capillarity and electroelasto-capillarity, were discussed. It seeks to offer not only a brief review of the historical and current advances, but also some suggestions on this problem for further investigations.

Global Bifurcations and Multi-Pulse Chaotic Dynamics of a Rectangular Thin Plate With One-to-One Internal Resonance

LI Shuang-bao, ZHANG Wei

2012, 33(9): 1043-1055. doi: 10.3879/j.issn.1000-0887.2012.09.002

Abstract(1826) PDF(940)

Abstract:
Global bifurcations and multipulse chaotic dynamics for a simply supported rectangular thin plate were studied using the extended Melnikov method for the first time. The rectangular thin plate was subjected to transversal and inplane excitations. A two-degree-of-freedom nonlinear non-autonomous system governing equations of motion for the rectangular thin plate was derived using the von Karman type equation and the Galerkin’s approach. The resonant case considered here is 1∶1 internal resonance. The averaged equation was obtained by the method of multiple scales. After transforming the averaged equation into a standard form, the extended Melnikov method was employed to show the existence of multi-pulse chaotic dynamics, which coudle be applied to explain the mechanism of modal interactions of thin plates. A skill for calculating the Melnikov function was given without the explicit analytical expression of homoclinic orbits. Furthermore, the restrictions on the damping, excitations and the detuning parameters were obtained, under which multi-pulse chaotic dynamics was expected. The results of numerical simulations are also given to indicate the existence of small amplitude multipulse chaotic responses for the rectangular thin plate.

Investigation on Creep Performance of PVC Aged at Relatively Near to Glass Transition Temperature

ZHOU Zhi-hong, HE Yao-long, HU Hong-jiu, ZHAO Feng<, ZHANG Xiao-long

2012, 33(9): 1056-1063. doi: 10.3879/j.issn.1000-0887.2012.09.003

Abstract(2178) PDF(955)

Abstract:
In order to predict mechanical performance of PVC at high operating temperature, a series of shortterm tensile creep tests (one-tenth the physical aging time) of PVC were carried out at 63°C imposing a small constant stress using a dynamic mechanical analyzer (DMA). The StruikKohlrausch (SK) formula and Struik shift factor method were attempted to describe these creep data for various physical aging times. A new phenomenological model based on multiple relaxation mechanisms of amorphous polymer was developed to quantitatively describe the SK parameters (initial creep compliance, characteristic retardation time and shape factor) determined by aging times. It was shown that momentary creep compliance curve of PVC at 63℃ coudle be very well fitted by SK formula for each aging time, respectively. However, the SK parameters for the creep curves are not constant during aging process at elevated temperatures, and the evolution of these parameters and creep rate versus aging time curves at double logarithmic coordinates have showed obvious nonlinear phenomenon. Moreover, the creep master curves obtained by the superposition with Struik shifting methods are unsatisfactory in such case. Finally, prediction results calculated from the present model incorporating SK formula are in excellent agreement with the creep experimental data for PVC isothermally aged at relatively near to glass transition temperature.

Generalized Hyperbolic Perturbation Method for Homoclinic Solutions of Strongly Nonlinear Autonomous Systems

CHEN Yang-yang, YAN Le-wei, SZE Kam-yim, CHEN Shu-hui

2012, 33(9): 1064-1077. doi: 10.3879/j.issn.1000-0887.2012.09.004

Abstract(1941) PDF(950)

Abstract:
A generalized hyperbolic perturbation method was presented for homoclinic solutions of strongly nonlinear autonomous oscillators, in which the perturbation procedure was improved for those systems whose exact homoclinic generating solutions could not be explicitly derived. The generalized hyperbolic functions were employed as the basis functions in the present procedure to extend the validity of the hyperbolic perturbation method. Several strongly nonlinear oscillators with quadratic, cubic and quartic nonlinearity were studied in details to illustrate the efficiency and accuracy of the present method.

Response Analysis Based on Smallest Interval Set of Parameters for Structures With Uncertainty

WANG Xiao-jun, WANG Lei, QIU Zhi-ping

2012, 33(9): 1078-1090. doi: 10.3879/j.issn.1000-0887.2012.09.005

Abstract(1617) PDF(836)

Abstract:
An integral analytic process from quantification to propagation based on limited uncertain parameters was investigated for dealing with practical engineering problems. A new method using the smallest intervalset/hyperrectangle containing all the experimental data was proposed to quantify the uncertainties of parameters. By virtue of the smallest parameter interval-set, the study of uncertainty propagation evaluating the most favorable response and the least favorable response of structures based on interval analysis was then presented. Furthermore, the relationship between the proposed interval analysis method and the classical interval analysis method was discussed. Two numerical examples were performed to demonstrate the feasibility and validity of the developed method.

Free Vibration of Membrane/Bounded Incompressible Fluid

S.Tariverdilo, J.Mirzapour, M.Shahmardani, Gh.Rezazadeh

2012, 33(9): 1091-1101. doi: 10.3879/j.issn.1000-0887.2012.09.006

Abstract(1803) PDF(802)

Abstract:
Vibration of circular membrane in contact with fluid had extensive applications in the industry. The natural vibration frequencies for asymmetric free vibration of circular membrane in contact with incompressible bounded fluid were derived. Considering small oscillations induced by the membrane vibration in incompressible and inviscid fluid, velocity potential function was used to describe the fluid field. Two approaches were used to derive the free vibration frequencies of the system. These included a variational formulation and an approximate solution employing the Rayleigh quotient method. Good correlation was found between free vibration frequencies evaluated using the two methods. Finally, the effects of the fluid depth and mass density, and radial tension on the free vibration frequencies of the coupled system were investigated.

Generation of Linear and Nonlinear Waves in a Numerical Wave Tank Using CT-VOF Method

H.Saghi, M.J.Ketabdari, S.Booshi

2012, 33(9): 1102-1114. doi: 10.3879/j.issn.1000-0887.2012.09.007

Abstract(2004) PDF(802)

Abstract:
A two-dimensional numerical model was developed for wave simulation and propagation in a wave flume. The fluid flow was assumed to be viscous and incompressible and NavierStokes and continuity equations were used as governing equations. Standard k-ε model was used to model turbulent flow. The Navier-Stokes equations were discretized using staggered grids finite difference method and solved by SMAC method. Waves were generated and propagated using a piston type wave maker. An open boundary condition was used at the end of numerical flume. Some standard tests such as lid-driven cavity, constant unidirectional velocity field, shearing flow and dambreak on dry bed were performed to validate the model. To demonstrate the capability and accuracy of the present method, the results of generated waves were compared with available wave theories. Finally, clustering technique (CT) was used for mesh generation and the best condition was suggested.

3D Numerical Simulation on the Fluid-Structure Interaction of Structure Subjected to Underwater Explosion With Cavitation

ZHANG A-man, REN Shao-fei, LI Qing<, LI Jia

2012, 33(9): 1115-1128. doi: 10.3879/j.issn.1000-0887.2012.09.008

Abstract(1868) PDF(745)

Abstract:
In an underwatershock environment, cavitation occurs near the structural surface. The dynamic response of fluidstructure interaction is influenced seriously by the cavitation effects. It is also the difficulty in the field of underwater explosion. With traditional boundary element method and finite element method (FEM), it is difficult to solve the nonlinear problem with cavitation effects subjected to underwater explosion. To solve this problem, in consideration of the cavitation effects and fluid compressibility, with fluid viscidity neglected, a 3D numerical model of transient nonlinear fluid-structure interaction subjected to underwater explosion was built. Fluid spectral element method (SEM) and finite element method were adopted to solve this model. After comparison with FEM, it is shown that SEM is more precise than FEM, and the SEM results are in good coincidence with benchmark results and experiment results. Based on this, combined with ABAQUS, the transient fluidstructure interaction mechanism of 3D submerged spherical shell and ship stiffened plates subjected to underwater explosion were discussed, and the cavitation region and its influence on the structural dynamic responses were presented. The reference for relevant researches on transient fluidstructure interaction of ship structure subjected to underwater explosion is provided.

MHD Free Convective Flow Past a Semi-Infinite Vertical Permeable Wall

R.K.Singh, A.K.Singh

2012, 33(9): 1129-1142. doi: 10.3879/j.issn.1000-0887.2012.09.009

Abstract(1929) PDF(793)

Abstract:
The basic equations governing the flow and heat transfer of an incompressible viscous and electrically conducting fluid past a semi-infinite vertical permeable plate in the form of partial differential equations were reduced to a set of nonlinear ordinary differential equations by applying a suitable similarity transformation. Approximate solutions of the transformed equations were obtained by employing the perturbation method for two cases of suction parameter i.e., small and large values. From the numerical evaluations of the solution it is seen that the velocity field at any point decreases as the value of the magnetic and suction parameters increases. The effect of the magnetic parameter is to increase the thermal boundary layer. It is also found that the velocity and temperature fields decrease with the increase in sink parameter.

2012 Vol. 33, No. 9