2020 Vol. 41, No. 7

Display Method:
Scattering and Diffraction by the Hill-Canyon Composite Topography for Incident Plane P- and SV-Waves
BA Zhenning, WU Mengtao, LIANG Jianwen, YU Zhiying
2020, 41(7): 695-712. doi: 10.21656/1000-0887.400333
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Abstract:
As a common composite site, the hill-canyon topography has complex coherence effects on seismic wave scattering. However, the publications of related research are still very limited. Therefore, a multi-domain indirect boundary element method was proposed to solve the scattering of in-plane elastic waves, and the scattering and diffraction of plane P-SV waves by hill-canyon topography were studied. The method takes advantages of both full-space Green’s function and half-space Green’s function to construct the scattered field in the independent closed region and the half-space open region, respectively. Combined with the auxiliary function method, dynamic wavefield solutions for the hill-canyon site were given, with the calculation accuracy ensured and the solution efficiency improved. The proposed method was verified through comparison of the results with published ones, and numerical calculations were performed in the frequency domain and time domain in the case of a Gaussian hill-canyon site. Results show that, the distribution of the surface displacement amplitude is very complex. There is significant dynamic interaction between the hill and the canyon, and the frequency-domain response depends on the frequency and angle of the incident wave. The presence of hills has an inhibition effect on the canyon for vertically incident waves, which significantly changes the peak acceleration and spectrum characteristics inside the canyon. Different height-to-width ratios of hills will cause changes in the seismic effect, and the presence of bedrock will also obviously amplify the seismic effect of the overall terrain.
The Anti-Plane Problem of Regular n-Polygon Holes With Radial Edge Cracks in 1D Hexagonal Piezoelectric Quasicrystals
LIU Xingwei, LI Xing, WANG Wenshuai
2020, 41(7): 713-724. doi: 10.21656/1000-0887.400334
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Abstract:
The heat conduction is a common problem in engineering practice. Compared with those of isotropic materials, the heat conduction problem of anisotropic materials is more complicated, so it is of great significance to accurately predict the internal temperature distribution. The numerical manifold method (NMM) was developed to solve typical continuous and discontinuous heat conduction problems in anisotropic materials. According to the governing differential equation, boundary conditions and variational principles, the NMM discrete equations for such problems were derived. Several representative examples involving continuous and discontinuous situations were analyzed with the uniform mathematical cover independent of all physical boundaries. The results prove the feasibility and accuracy of the method and indicate that the NMM can simulate the heat conduction problem of anisotropic materials well. Besides, the influences of the material properties and crack configurations on the temperatures were also investigated.
Dynamic Characteristics Analysis of Composite Box Girders With Corrugated Steel Webs Based on the Equivalent Principle
JI Wei, ZHANG Jingwei, LUO Kui
2020, 41(7): 725-734. doi: 10.21656/1000-0887.400244
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Abstract:
To simplify the 3D finite element modeling process for composite box girders with corrugated steel webs, the finite element model for 3D corrugated steel webs was reduced to one for 2D orthotropic plates with the equivalent stiffness and displacement method. The simplified finite element model has a trim geometric shape, a much smaller element number and less degrees of freedom, reduced calculation time, and improved computation efficiency. Comparison between the calculated results of the natural frequencies of the 3D corrugatedsteelweb composite box girder model, the calculated natural frequencies of the equivalent 2D orthotropicplate girder model, and the measured frequency values shows good agreement, which verifies the correctness and reliability of the equivalent method. The research provides a simple finite element modeling method for composite box girders with corrugated steel webs.
Comparative Analysis of Dynamic Responses of Timoshenko Beams on Visco-Elastic Foundations Under Moving Loads
HUANG Qiang, LIU Ganbin, Lü Qing, HUANG Hongwei, ZHENG Rongyue
2020, 41(7): 735-746. doi: 10.21656/1000-0887.400235
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Abstract:
The dynamic responses of 3D, 2D and 1D track-ground models under moving loads were analyzed based on the Fourier transformation technique. The track was modelled as a Timoshenko beam, and response discrepancies between the 3 models were compared in terms of different load speeds and ground thicknesses. The results indicate that, there is an equivalent ground stiffness in the 3D track-ground model, which is a function of the wave number and the frequency. The critical velocities of 2D and 3D track-ground models are almost the same, but are much smaller than that of the 1D model. When the load speed is less than the critical speed, the Timoshenko beam deflection of the 3D model is the smallest, that of the 2D model is the intermediate, and that of the 1D model is the largest. However, when the load speed reaches or exceeds the critical velocity, the T beam deflection of the 2D model becomes the largest, and the time history curves of the T beam deflection for the 3 models are significantly different. In the 2D and 3D models, the longitudinal ground displacement firstly increases with the soil depth to a peak value and then decreases, but the vertical displacement decreases continuously with the soil depth.
Fluid-Structure Coupling Wind-Induced Vibration Analysis of Transmission Lines Across 2 Close Hills
ZHANG Jin, ZHU He
2020, 41(7): 747-759. doi: 10.21656/1000-0887.400241
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Abstract:
Based on the 2D fluid-structure coupling theory, the wind-induced vibration responses of transmission lines across 2 close hills were calculated. Both the load on the wire by the mountain wind and the surface wind pressure change caused by wire vibration with its influence on the flow field were considered. Firstly, the correctness of the method was verified in comparison with the existing literature results. Then, the numerical wind tunnel model for the transmission line across 2 close hills was established. The average wind speed characteristics of the canyon and mountain pass topography as well as the distribution characteristics of the corresponding wind pressure were analyzed. The distributions of aerodynamic coefficients and vertical displacements were analyzed. The numerical results show that, in the transient wind field, the acceleration effect of the mountain pass is more significant than that of the canyon, and the acceleration ratio at the middle of the line is more important. The distribution of wind pressure around the wire is also inconsistent due to the influence of different topographic wind fields. Under the canyon topography, the distribution of wind pressure around the wire is stable with time. Under the mountain pass topography, the wind pressure around the wire fluctuates with time. The smaller the distance between the 2 hills is, the greater the variation range of the resistance coefficient time history curve will be, so is the change of wind pressure. The updraft under the mountain pass topography makes the wire subject to greater lifting force and vertical wind deviation.
Numerical Simulation of SloshingMitigating Structures in Tank Trucks With the SPH Method
HUANG Zhitao, YANG Yu, SHAO Jiaru, ZHANG Yueyue
2020, 41(7): 760-770. doi: 10.21656/1000-0887.400234
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Abstract:
Based on the smooth particle hydrodynamics (SPH) method, the stability of the tank truck and the mitigating effects of different baffles were studied. Firstly, the liquid sloshing pressure in a rectangular container was simulated with results in agreement with experimental ones, to validate the effectiveness and accuracy of the SPH model. Secondly, a 2D elliptic tank truck model was established, which was filled with 93# gasoline. The impact pressure on the tank wall and the trajectory of the liquid barycenter were analyzed under different horizontal sinusoidal excitations and roll excitations. The results show that, the liquid sloshing is violent with no mitigating baffle, and the mitigating effects of the baffle will be influenced by the forms of external excitations. When the angle between the normal direction of the mitigating baffle and the inflow is small, the stability of the tank truck will be improved.
Mapping Calculation of Meandering River Well Locations Based on the Schwarz-Christoffel Transform
ZHANG Guangsheng, WANG Yufeng, JI Anzhao, LIU Xuefen, CHEN Zhanjun
2020, 41(7): 771-785. doi: 10.21656/1000-0887.400315
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Abstract:
The diversion of a meandering river made the properties of sedimentary reservoir distribute along the direction of channel extension. The conventional geostatistics method depends on the range and direction of the variogram in the prediction of reservoir parameters. According to the basic principle of the Schwarz-Christoffel transform, the mathematical model for a polygon region boundary-to-rectangle region conformal mapping was established, and the numerical calculation method for the mapping mathematical model was proposed. In the whole mapping process, the strip transition region was needed. In the process of calculating the mapping from a polygonal region to a strip transition region, the 2D particle swarm optimization (PSO) algorithm was used to get the initialization points of the transition region. According to the mapping mathematical model and boundary mapping results, the initial points in the strip transition region were taken as the end points of integration, and the nearest points between the initial points and the boundary of the strip transition region were taken as the starting points of integration. The Gauss-Jacobi integration method was used to get the calculated points in the polygonal region. The square sum of errors between actual and calculated points was adopted as the objective function, and the optimized PSO algorithm was applied to obtain the calculated points in the strip transition region. With the corresponding rules of transformation scales from the strip transition region to the rectangular region, the initialization method for point positions in the rectangular area was proposed. With Newton’s method, the Jacobi elliptic function was solved for the mapping point positions in the rectangular area. To verify the model reliability, 38 wells of the depositional X sandstone reservoir along an Ordos Basin meandering river was taken as the example. The results show that, the well positions keep in a certain geometric similarity before and after the mapping. Therefore, through the Schwarz-Christoffel mapping transform, the meandering river can be mapped to a rectangular direction along the river direction, which provides a theoretical basis for the transformation of geological modeling of complex meandering river sedimentary reservoirs to rectangular regions.
Solution of Generalized Nonlinear Schrodinger Equations and (2+1)-Dimensional Nonlinear Ginzburg-Landau Equations With a Riccati-Bernoulli Auxiliary Equation Method
SHI Lanfang, WANG Mingcan, QIAN Zhengya
2020, 41(7): 786-795. doi: 10.21656/1000-0887.400271
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Abstract:
The Riccati-Bernoulli auxiliary equation method was proposed to seek the exact travelling solutions to the generalized nonlinear Schrodinger equation and the (2+1)-dimensional nonlinear Ginzburg-Landau equation. The solutions can be expressed with the rational functions, the trigonometric functions, the hyperbolic functions and the exponential functions. Being effective and concise, the method is important to obtain the exact travelling solutions for more nonlinear partial differential equations in the field of mathematics and physics.
Analysis of a Rotavirus Transmission Model With Temporary Immunity and Protection From Maternal Antibody
LU Kun, LI Jianquan, TAN Hongwu
2020, 41(7): 796-806. doi: 10.21656/1000-0887.400391
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Abstract:
Rotavirus is the leading cause of severe diarrhea in children worldwide. To study the spread of rotavirus, a rotavirus transmission model was proposed based on the characteristics of temporary immunity after infection and maternal antibody protecting the newborn. By means of dynamic analysis, the basic reproduction number deciding the persistence of the infection was obtained. Based on the local stability analysis of the feasible equilibria, it was proved that the diseasefree equilibrium will be globally asymptotically stable if the basic reproduction number is no more than 1, through construction of appropriate Lyapunov functions. The disease will persist in the population if the basic reproduction number is more than 1 according to the Fonda lemma.
Singularly Perturbed Solutions of Burgers Equations With Initial Value Discontinuities
BAO Liping, HU Yubo, WU Liqun
2020, 41(7): 807-816. doi: 10.21656/1000-0887.400270
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Abstract:
The wave model generated for laser plasma was discussed, which can be expressed as the Riemann problem of Burgers equations with initial value discontinuity. The singularly perturbed asymptotic solution of the Burgers equations with discontinuous initial values was obtained with the singularly perturbed expansion method. The solution was divided into 2 parts: an outer solution and an inner layer correction term. Since the initial condition is constant, the wave will generate the characteristic boundary in the process of propagation, and the correction term will make the parabolic characteristic boundary. The external solution was corrected at the internal layer along the characteristic lines. The existence and uniqueness of the asymptotic solution was proved through the HopfCole transform, Fourier transform and the extremum principle. Then the asymptotic expansion is obtained with the uniform validity proved.