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2012年 第33卷 第9期    刊出日期：2012-09-10

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论文

Substrate elastic deformation due to vertical component of liquid-vapor interfacial tension

余迎松

2012, 33(9):  1095-1114.  doi:10.1007/s10483-012-1608-x

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Young’s equation is a fundamental equation in capillarity and wetting, which reflects the balance of the horizontal components of the three interfacial tensions with the contact angle (CA). However, it does not consider the vertical component of the liquid-vapor interfacial tension (VCLVIT). It is now well understood that the VCLVIT causes the elastic deformation of the solid substrate, which plays a significant role in the fabrication of the microfluidic devices because of the wide use of the soft materials. In this paper, the theoretical, experimental, and numerical aspects of the problem are reviewed. The effects of the VCLVIT-induced surface deformation on the wetting and spreading, the deflection of the microcantilever, and the elasto-capillarity and electroelasto-capillarity are discussed. Besides a brief review on the historical development and the recent advances, some suggestions on the future research are also provided.

Global bifurcations and multi-pulse chaotic dynamics of rectangular thin plate with one-to-one internal resonance

李双宝;张伟

2012, 33(9):  1115-1128.  doi:10.1007/s10483-012-1609-9

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Global bifurcations and multi-pulse chaotic dynamics for a simply supported rectangular thin plate are studied by the extended Melnikov method. The rectangular thin plate is subject to transversal and in-plane excitation. A two-degree-of-freedom nonlinear nonautonomous system governing equations of motion for the rectangular thin plate is derived by the von Karman type equation and the Galerkin approach. A one-toone internal resonance is considered. An averaged equation is obtained with a multi-scale method. After transforming the averaged equation into a standard form, the extended Melnikov method is used to show the existence of multi-pulse chaotic dynamics, which can be used to explain the mechanism of modal interactions of thin plates. A method for calculating the Melnikov function is given without an explicit analytical expression of homoclinic orbits. Furthermore, restrictions on the damping, excitation, and detuning parameters are obtained, under which the multi-pulse chaotic dynamics is 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.

Creep performance of PVC aged at temperature relatively close to glass transition temperature

周志红;贺耀龙;胡宏玖;赵峰;张晓龙

2012, 33(9):  1129-1136.  doi:10.1007/s10483-012-1610-x

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

Generalized hyperbolic perturbation method for homoclinic solutions of strongly nonlinear autonomous systems

陈洋洋;燕乐纬;佘锦炎;陈树辉

2012, 33(9):  1137-1152.  doi:10.1007/s10483-012-1611-6

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A generalized hyperbolic perturbation method is presented for homoclinic solutions of strongly nonlinear autonomous oscillators, in which the perturbation proce-dure is improved for those systems whose exact homoclinic generating solutions cannot be explicitly derived. The generalized hyperbolic functions are 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 nonlin-earity are studied in detail to illustrate the efficiency and accuracy of the present method.

Response analysis based on smallest interval-set of parameters for structures with uncertainty

王晓军;王磊;邱志平

2012, 33(9):  1153-1166.  doi:10.1007/s10483-012-1612-6

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An integral analytic process from quantification to propagation based on limited uncertain parameters is investigated to deal with practical engineering problems. A new method by use of the smallest interval-set/hyper-rectangle containing all experimental data is proposed to quantify the parameter uncertainties. With the smallest parameter interval-set, the uncertainty propagation evaluation of the most favorable response and the least favorable response of the structures is studied based on the interval analysis. The relationship between the proposed interval analysis method (IAM) and the classical IAM is discussed. Two numerical examples are presented to demonstrate the feasibility and validity of the proposed method.

Free vibration of membrane/bounded incompressible fluid

S. TARIVERDILO;J. MIRZAPOUR;M. SHAHMARDANI;G. REZAZADEH

2012, 33(9):  1167-1178.  doi:10.1007/s10483-012-1613-8

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Vibration of a circular membrane in contact with a fluid has extensive applications in industry. The natural vibration frequencies for the asymmetric free vibra-tion of a circular membrane in contact with a bounded incompressible fluid are derived in this paper. Considering small oscillations induced by the membrane vibration in an incompressible and inviscid fluid, the velocity potential function is used to describe the fluid field. Two approaches are used to derive the free vibration frequencies of the sys-tem, which include a variational formulation and an approximate solution employing the Rayleigh quotient method. A good correlation is found between free vibration frequencies evaluated by these methods. Finally, the effects of the fluid depth, the mass density, and the radial tension on the free vibration frequencies of the coupled system are investigated.

Generation of linear and nonlinear waves in numerical wave tank using clustering technique-volume of fluid method

H. SAGHI;M. J. KETABDARI;S. BOOSHI

2012, 33(9):  1179-1190.  doi:10.1007/s10483-012-1614-9

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A two-dimensional (2D) numerical model is developed for the wave simulation and propagation in a wave flume. The fluid flow is assumed to be viscous and incompressible, and the Navier-Stokes and continuity equations are used as the governing equations. The standard k-ε model is used to model the turbulent flow. The Navier-Stokes equations are discretized using the staggered grid finite difference method and solved by the simplified marker and cell (SMAC) method. Waves are generated and propagated using a piston type wave maker. An open boundary condition is used at the end of the numerical flume. Some standard tests, such as the lid-driven cavity, the constant unidirectional velocity field, the shearing flow, and the dam-break on the dry bed, are performed to valid the model. To demonstrate the capability and accuracy of the present method, the results of generated waves are compared with available wave theories. Finally, the clustering technique (CT) is used for the mesh generation, and the best condition is suggested.

3D numerical simulation on fluid-structure interaction of structure subjected to underwater explosion with cavitation

张阿漫;任少飞;李青;李佳

2012, 33(9):  1191-1206.  doi:10.1007/s10483-012-1615-8

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In the underwater-shock environment, cavitation occurs near the structural surface. The dynamic response of fluid-structure interactions is influenced seriously by the cavitation effects. It is also the difficulty in the field of underwater explosion. With the traditional boundary element method and the finite element method (FEM), it is difficult to solve the nonlinear problem with cavitation effects subjected to the underwater explosion. To solve this problem, under the consideration of the cavitation effects and fluid compressibility, with fluid viscidity being neglected, a 3D numerical model of transient nonlinear fluid-structure interaction subjected to the underwater explosion is built. The fluid spectral element method (SEM) and the FEM are adopted to solve this model. After comparison with the FEM, it is shown that the SEM is more precise than the 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 the 3D submerged spherical shell and ship stiffened plates subjected to the underwater explosion is discussed, and the cavitation region and its influence on the structural dynamic responses are presented. The paper aims at providing references for relevant research on transient fluid-structure interaction of ship structures subjected to the underwater explosion.

MHD free convective flow past semi-infinite vertical permeable wall

R. K. SINGH;A. K. SINGH

2012, 33(9):  1207-1222.  doi:10.1007/s10483-012-1616-7

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In this paper, the basic equations governing the flow and heat transfer of an incompressible viscous and electrically conducting fluid past a semi-infinite vertical per-meable plate in the form of partial differential equations are reduced to a set of non-linear ordinary differential equations by applying a suitable similarity transformation. Approx-imate solutions of the transformed equations are obtained by employing the perturbation method for two cases, i.e., small and large values of the suction parameter. From the numerical evaluations of the solution, it can be seen that the velocity field at any point decreases as the values of the magnetic and suction parameters increase. 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 the sink parameter.