应用数学和力学

2020 Vol. 41, No. 10

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Inhibition of Low Pressure on Interfacial Damage in Polymer Bonded Explosive Under Temperature Fluctuation

ZHANG Chao, LIU Zhanfang

2020, 41(10): 1057-1071. doi: 10.21656/1000-0887.410092

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Abstract:
The influence of low pressure on polymer-bonded explosive (PBX) interfacial damage under temperature fluctuation was investigated. Firstly, a 2D geometric model was built with the Voronoi method. The change of interfacial bonding property was studied under temperature changes, with the particles considered as elasto-plastic, the binder as 2-layer viscoplastic and the zero-thickness cohesion model to reflect the interfacial bonding conditions. Then, the inhibition effect of low pressure on the interfacial damage of PBX under temperature fluctuation was studied based on the thermo-mechanical coupling method, and the curve of normal traction changing with low pressure was fitted. The results show that, the initial damage is mainly caused by the tangential traction of the interface in the heating stage, and the interfacial damage is mainly caused by the normal traction in the cooling stage. What’s more，the temperature drop is more likely to cause interfacial damage than the temperature rise. Regardless of temperature rise or fall, a certain low pressure can inhibit the interfacial damage, but a too high pressure may cause new damages; to inhibit the interfacial damage, the pressure required in the cooling process should be higher than that in the heating process, which is consistent with the larger interfacial damage in the cooling stage.

A Design Method of Impact Failure Criteria for Timoshenko Beams Under Support Excitations

WANG Le, LI Dong

2020, 41(10): 1072-1082. doi: 10.21656/1000-0887.400318

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Abstract:
A design method of impact failure criteria for Timoshenko beams under support excitations was established. The system motion equations were solved and combined with the boundary conditions to give the natural frequency equations and the mode shapes for the system. To overcome the difficulty of solving impact responses under support excitations, the presumed displacement response of the Timoshenko beam was used to obtain the linear and angular displacements of the system, and in turn the internal forces and maximum equivalent von Mises stresses on related cross sections. Based on the von Mises yield criterion, the method determining the failure criteria of displacement, velocity and acceleration was given. The calculated impact responses of a typical example show that, there are 3 failure modes for the Timoshenko beam within the frequency range of 20 Hz to 5 000 Hz, i.e., yield failures at the root, the middle and the end. For each failure mode, the impact failure criteria expressed with the maximum available displacement amplitude, velocity amplitude and acceleration amplitude were given.

The Stress Intensity Factor of a FiniteWidth Plate With a Mode-Ⅰ Center Crack Subjected to Uniform Stress on the Crack Surface Near the Crack Tip

LI Ya, YI Zhijian, WANG Min, SU Kang

2020, 41(10): 1083-1091. doi: 10.21656/1000-0887.410130

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Abstract:
With the crack line analysis method for stress intensity factors, the stress intensity factor of a finite-width plate with a mode-Ⅰ center crack subjected to uniform stress on the crack surface near the crack tip was studied analytically. Through analytical solution of the stress field and correction of the stress components on the crack line of an infinite-width plate with a mode-Ⅰ crack under uniform stress on the crack surface near the crack tip, the corrected stress components on the crack line of the corresponding finite-width plate were further deduced. Reasonable requirements on the corrected stress field at the crack line were proposed, the stress intensity factor of the finite-width plate was derived, and the correction coefficient of the stress intensity factor of the finite-width plate relative to the corresponding infinite-width plate was obtained. When the width of the finite-width plate approaches infinity, the stress intensity factor of the finite-width plate will be consistent with that of the corresponding infinite-width plate.

Continuous Dependence of Solutions to a Class of Double Diffusion Perturbation Models for Porous Media

SHI Jincheng, XIAO Shengzhong

2020, 41(10): 1092-1102. doi: 10.21656/1000-0887.410128

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Abstract:
The structural stability of solutions to a class of double diffusion perturbation models for porous media defined in bounded domains was studied. The nonhomogeneous Robin boundary conditions were imposed on the model. With the energy analysis method and the differential inequality technique, some useful a priori estimate of the solution was obtained, and in turn the differential inequality related to the solution was formulated. Then, integration of the differential inequality gave the result of continuous dependence on Lewis number L_e.The result shows that, the double diffusion perturbation model proposed to describe the fluid flow is accurate for porous media.

Minimum Rank Correction Damage Identification Based on Modal Reduction

LI Guoqing, LUO Shuai, ZHANG Li

2020, 41(10): 1103-1109. doi: 10.21656/1000-0887.410138

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Abstract:
To solve the problem that the measured modal parameters and the finite element analysis modal parameters do not match in damage identification, the residual force vector formula and the minimum rank update formula based on the modal reduction method were derived. Through the calculation of the residual force vectors of damaged and undamaged structures, the change rate of the residual force vector was obtained, and the absolute values of the residual force change rate vector elements were defined as the improved residual force vector. With the improved residual force vector, the correct number of modes used in the minimum rank update method was determined, and the minimum rank update formula based on modal reduction was used to calculate the damage extent. The results show that, under noise interference, the presented method could well locate the damage with incomplete modal data. The damage extent identification based on the derived minimum rank update formula is reliable. The method is robust and accurate in structural damage identification for measured incompleteDOF structures.

A Modified Roe Scheme and Stability Analysis

HU Lijun, ZHAO Kunlei

2020, 41(10): 1110-1124. doi: 10.21656/1000-0887.400388

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Abstract:
Low dissipation shock-capturing methods, including the popular Roe scheme, will encounter the shock instability phenomenon in the computation of the multidimensional strong shock wave problems. This will seriously affect the schemes’ accurate simulation of the hypersonic flow problems. The small perturbation analysis of the Roe scheme was carried out. The results show that, all perturbations in the longitudinal direction of the shock front are damped, but the perturbations of density and shear velocity in the transverse direction are undamped. The viscosities corresponding to the entropy wave and shear wave were added to the flux transverse to the shock front to suppress instability of the Roe scheme. To prevent the improper viscosity from influencing the resolution of contact discontinuity and shear layers, 2 switching functions were defined, so that the viscosity was only added to the transverse flux in the subsonic region of the shock layer. The numerical tests show that, the modified Roe scheme not only retains the merit of high resolution of the original Roe scheme, but also has better robustness and eliminates the shock wave instability.

Power-Law Fluid Droplet Dynamic Behaviors in T-Junction Micro-Channels With the Lattice Boltzmann Method

HUANG Yifan, LOU Qin

2020, 41(10): 1125-1145. doi: 10.21656/1000-0887.400341

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Abstract:
The dynamic behavior of a power-law fluid droplet passing through a T-junction micro-channel and phase diagrams of droplet flow patterns were studied with the lattice Boltzmann method. The effects of power-law exponent n on the droplet deformation characteristics including the neck thickness, the droplet motion distance and phase diagrams of droplet flow patterns were addressed. The numerical results show that, there exist 3 flow patterns for power-law droplets in T-junction micro-channels, i.e., breakup with obstruction, breakup with a tunnel and non-breakup. In the case of breakup with obstruction, the droplet neck thickness decreases with time during the evolution process, and the decrease rate drops with n.At the same time, the droplet tip motion distance increases linearly with time during the evolution process, and the distance also increases with n.In the case of breakup with a tunnel, the droplet neck thickness decreases with time, and the decrease rate drops with n.However, the droplet tip motion distance increases rapidly at first and then slowly, the droplet-wall gap width grows approximately logarithmically with time. Furthermore, the fluctuations of both the droplet neck thickness and the droplet tip motion distance occur in the non-breakup pattern of the droplet. Moreover, it is easier to break up a droplet with a larger value of power-law index n,while it is hard to reach the breakup with obstruction in this case. Eventually, several phase diagrams with power-law correlations for droplet flow patterns were obtained. The fitting functions can be used to describe the critical boundary lines between different flow patterns.

Growth and Dynamics of Convection Patterns With Horizontal Flow

NING Lizhong, NING Bibo, HU Biao, TIAN Weili

2020, 41(10): 1146-1156. doi: 10.21656/1000-0887.410104

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Abstract:
The growth and dynamic characteristics of convection patterns with horizontal flow for Prandtl number Pr=0.72 were numerically simulated with 2D basic equations of fluid mechanics. The results show that, for given relative Rayleigh number Ra_r=5(Rayleigh number Ra=8 540) and Reynolds number Re=22.5, the growth of the traveling wave convection pattern can be divided into 3 stages: the convection development stage, the exponential growth stage and the periodic variation stage (including the transition adaptation region and the stable periodic variation region). The average wave number in the traveling wave convection decreases with time or with the growth of the convection pattern. The exponential growth stage length in traveling wave convection becomes shorter and the growth rate of the maximum vertical velocity of convection increases with relative Rayleigh number Ra_r.For Reynolds number Re=5,the growth rate of the maximum vertical velocity of convection relates with the variation of relative Rayleigh number Ra_r in the form of γ_m=0.004 8Ra^{6.065 3}_r.In the periodic variation stage, after the transition adaptation region of the convection pattern and parameters in traveling wave convection, the convection enters the stable periodic variation region of the convection pattern and parameters. For given relative Rayleigh number Ra_r=5,dimensionless period T_t of traveling wave convection varying with Re can be expressed as T_t=0.001 4Re^{2.363 5}.

Effects of Bubble Spacings on Interface Properties and Wake Flow for 2 Contaminated Spherical Bubbles

SUN Tao, PANG Mingjun, FEI Yang

2020, 41(10): 1157-1170. doi: 10.21656/1000-0887.410099

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Abstract:
To understand the influence of the interaction between contaminated bubbles on the hydrodynamic characteristics, with a surfactant as the contamination medium, the interface parameters, the flow field and the wake characteristics of bubbles with different spacings were investigated with the improved stagnation cap model. A stably contaminated interface was formed through solution of the adsorption and desorption equations between the bubble interface and the fluid zone, and in view of the influence of the local flow and the Marangoni effect. The Langmuir equation was used to correlate the shear stress with the surfactant concentration of the interface to evaluate the bubble interface shear stress. The results indicate that, the change of the bubble spacing cannot significantly influence the interface parameters of bubble 1, but has great effects on those of bubble 2. The wake vortex of bubble 1 approaches the upstream interface of bubble 2, which changes the interface parameters of bubble 2. The influence of the wake vortex on the surfactant distribution on the interface of bubble 2 is different from that of the convection, which can drag the surfactant on the downstream interface of bubble 2 back to the upstream one, thus changing the distribution trend of the interface parameters of bubble 2, and there appear low and highinfluence stages. The vortex length and the vertical position of the vortex center of bubble 1 depend on the interface concentration on the upstream interface of bubble 2 and the bubble spacing. The vortex parameters of bubble 2 decrease with its interface concentration on the upstream interface till zero.

Intermittent Turbulence Characteristics in the Stokes Layer for a Transitional Reynolds Number

KONG Wei, LI Jia

2020, 41(10): 1171-1182. doi: 10.21656/1000-0887.400382

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Abstract:
The characteristics of intermittent turbulence induced by wall surface roughness in a finite Stokes layer were investigated numerically, including the velocity gradient at the wall, the velocity profile and the Reynolds stress, etc.， with a transitional Reynolds number Re=495.The results show that, the velocity profile does not follow the logarithmic law in most phases, but does only in some rare phases during the decelerating stage. The comparison between the Reynolds stress and the result in the case of the incompressible boundary layer indicates that, the Reynolds stress distribution in the turbulence stage is similar to that in the case of the incompressible boundary layer, including the peak amplitude and the peak position, but there is significant discrepancy in the turbulence core region between the 2 cases. Above characteristics reveal the strong nonequilibrium behaviors of intermittent turbulence in the Stokes layer.