应用数学和力学

2020 Vol. 41, No. 5

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Response Parameter Analysis of Submerged Floating Tunnels Under Underwater Shock

LUO Gang, ZHANG Yulong, PAN Shaokang, JIA Hanghang, LIU Chang

2020, 41(5): 467-479. doi: 10.21656/1000-0887.400249

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Abstract:
To investigate the dynamic responses of submerged floating tunnels (SFTs) subjected to near-field non-contact explosions, the SFT was simplified as a constant-section-and-stiffness Bernoulli-Euler elastic-support beam to establish the SFT dynamic model under underwater shock load. The differential equation for the vibration was resolved with the Galerkin method. The displacement, velocity and acceleration were analyzed for the SFT, the influences of the explosive quantity, the blasting distance and the vertical stiffness of anchor cables were discussed, and the results were also used to analyze the damage of tunnels and human bodies. The results show that, the impact of the blasting distance on the kinematic parameters of the SFT is significant. Moreover, the maximum displacement of the tunnel decreases in inverse proportion to the blasting distance. Compared with those of the blasting distance of 10 m, the displacements of the tunnel body of 20m and 30 m decrease by 50.7% and 66.6%, respectively. The impact of the explosive quantity on the kinematic parameters of the SFT is significant. Also, the maximum displacement of the tunnel decreases approximately in a low-order power function with the explosive quantity. Compared with those of the explosive of 20 kg, the displacements of the tunnel body of 40 kg and 60 kg increase by 29.8% and 51.3%, respectively. The impact of the vertical stiffness of anchor cables on the kinematic parameters of the SFT is significant. Besides, the maximum displacement of the tunnel decreases approximately in a step-like form with the vertical stiffness of anchor cables. Compared with those of the vertical anchor stiffness of 5×105 N/m, the maximum displacement of the tunnel body of 5×10⁶ N/m and 5×10⁷ N/m decrease by 53.0% and 86.2%, respectively. However, there is an efficiently acting interval for the anchor cable stiffness. The stiffness has significant influence on the displacement of the tunnel body within the interval, but has little influence outside the interval (large or small).

Bifurcation Analysis of Dual-Mode Dynamics for Marine Risers

SUN Yunqing, WU Zhiqiang, ZHANG Guoqi, WANG Yuancen

2020, 41(5): 480-490. doi: 10.21656/1000-0887.400257

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Abstract:
To study the vortex-induced vibration (VIV) of top tension risers (TTRs) under shear flow, the non-linear dynamic model of VIV for TTRs was constructed, in which the riser was simplified as an Euler-Bernoulli beam model and the van der Pol wake oscillator was used to describe the effect of fluid. Based on the 2nd-order Galerkin modal discretization model, the harmonic balance method, the Poincaré mapping method and the Lyapunov exponential method were used to reveal the system response characteristics. The results show that periodic responses and quasi-periodic responses occur alternately with the increase of the flow velocity, and the periodic response region corresponds to the vortex-induced resonance region. The approximate periodic solution obtained with the harmonic balance method can predict the amplitude and frequency of the periodic solution in the vortex-induced resonance region, and the main frequency components of the quasi-periodic solution in the non-vortex-induced resonance region.

Numerical Simulation Research of Effects of Pulsating Air Flow on Liquid Film Evaporation Over Vertical Plates

ZHONG Yin, LING Changming, XIE Gongnan

2020, 41(5): 491-498. doi: 10.21656/1000-0887.400386

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Abstract:
A 2D physical and mathematical model for vertical plate falling film evaporation was established. The effects of pulsating airflow on the falling film evaporation process were studied through numerical simulation. The change rule of the Sherwood number under different average air velocities, amplitudes and frequencies was analyzed. The results show that, when the relative amplitude of pulsation is 5/6, the mass transfer efficiency of the vertical falling film will increase by 6.6%; when the Womersley number is greater than 26, the mass transfer efficiency will increase by 8.3%. Compared with uniform airflow, the pulsating airflow can effectively enhance the convective mass transfer of falling film evaporation.

Numerical Study of Fluidelastic Instability Fluid Force Model for Normal-Triangle Tube Arrays

LIU Jian, ZHANG Yixiong, FENG Zhipeng, YE Xianhui, CHEN Guo, QI Huanhuan

2020, 41(5): 499-508. doi: 10.21656/1000-0887.400269

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Abstract:
To study the fluidelastic instability (FEI) fluid force model, the FEI process controlled by the fluid damping mechanism was taken as the research object, and the fluid-tube interaction was simulated with one elastic tube in the middle of a normal-triangle tube array under a series of free stream flow velocities. A polynomial function was chosen as the fluid force model, the simulated fluid forces and the tube displacements were used to calculate the unknown coefficients in the fluid force model. The influence of the flow velocity on the fluid force model was introduced and the relationship between fluid force coefficients and inlet flow velocities was fit. A fluid force model related to tube displacements, tube velocities and flow velocities was obtained. The predicted FEI critical flow velocities with the proposed fluid force model were compared to the experimental data and numerical results given by literatures. The fluid force model, constructed with the proposed method based on numerical results and the given mathematical function, can capture the main characteristics in the flow tube array interaction, and reasonably predict the FEI critical velocity.

20-Node Hexahedron Symplectic Elements for Stress Analysis of Composite Laminates

TONG Yao, YAO Yuzhe

2020, 41(5): 509-516. doi: 10.21656/1000-0887.400283

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Abstract:
Usually, the accuracy of the stresses obtained with the conventional displacement finite element method is one-order lower than that of the displacements, and the out-of-plane stresses can hardly meet the continuity requirements. Then, combined with the minimum potential energy principle and the H-R variational principle, a 20-node hexahedral symplectic element involving displacement and out-of-plane stress variables was established. Incompatible displacement terms are needless in the element since the 2 kinds of variables are approximated with higher-order interpolation functions. Hence, the derivation process of the theory is very simple. Unlike in the partially mixed Hamiltonian element, the variables involved in the symplectic element are discretized in 3 coordinate directions without restriction of the element thickness and the structure geometry. Numerical examples show that, the 20-node symplectic elements exhibit stable convergence. Under the coarse mesh, the out-of-plane stresses obtained with the proposed element are closer to the exact solution than those by the incompatible 8-node symplectic element.

Shear Lag Effects of Continuous Corrugated Steel Web-Steel Bottom-Concrete Top Composite Box Girders

MA Chi, LIU Shizhong, LI Aijun, JIN Xuejun

2020, 41(5): 517-529. doi: 10.21656/1000-0887.400236

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Abstract:
With different moduli of the concrete top and the steel bottom, the governing differential equations and boundary conditions for shear lag effects of corrugated steel web-steel bottom-concrete top (CSWSBCT) composite box girders were derived with the variational method. The formula for shear lag coefficients of the 2-span continuous CSWSBCT box girder under concentrated load and uniformly distributed load was established. The shear lag effects of the continuous composite box girder under 2 loading conditions were analyzed through model beam tests. The results show that, the theoretical values are in good agreement with the measured values of model tests and the finite element values on the top and bottom plates of the box girder, and the changing trend is consistent, which verifies the correctness of the calculation formula. The maximum shear lag coefficients of the top and bottom plates at the support section under uniform load are larger than those under the concentrated load. The shear lag effects at the junctions of the corrugated steel web, the concrete top and the steel bottom at the middle support section are prominent under 2 loading conditions.

Near-Singularity Cancellation With the Angle-Distance Transformation Method for Boundary Integral Equations

ZHOU Fenglin, XIE Guizhong, ZHANG Jianming, LI Luoxing

2020, 41(5): 530-540. doi: 10.21656/1000-0887.400229

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Abstract:
To address the nearsingularity computation problem involved in the boundary element analysis of thinwalled structures, an angledistance combined transformation method was developed. With this combined method, the computational accuracy and efficiency can be significantly improved. The near singularity was found not only in the radial direction of the basic transformed space, but also in the circumferential direction. In the case that the nearest point in the integral element to the collocation point is close to the edge of the integral element, the integral kernel exhibits significant near singularity with regard to the circumferential direction. Through angle transformation for circumferential variables and distance transformation for radial variables, the near singularity with regard to both directions can be cancelled. Numerical examples illustrate the efficiency and accuracy of the presented method.

Analytical Stress Solutions Around Tunnels With Arbitrary-Excavation Cross Sections Based on Conformal Mapping From a Unit Circle to the Tunnel Exterior

SHI Gaoping, ZHU Jianghong, YANG Jianhui

2020, 41(5): 541-556. doi: 10.21656/1000-0887.400220

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Abstract:
The stresses around tunnels with arbitrary-excavation cross sections were studied with the stress field simplified as a uniform stress field at an angle to the horizontal axis at infinity. The conformal mapping function was introduced to express the stress functions of surrounding rock with variable ζ instead of variable z. Then the Cauchy integral operator was applied to the stress boundary equation for tunnel wall. The general analytical solutions to stress functions and analytical solutions of surrounding rock stresses were obtained for tunnels with arbitrary-excavation cross sections according to the integrand analyticity and the residue theorem. Moreover, with the stress boundary conditions for elliptical tunnels substituted into the general analytical solutions, the obtained particular solutions to stress functions consisted with the results in literatures. The surrounding rock stresses were analyzed for 2-lane road tunnels based on the explicit general analytical solutions and the results accorded with engineering rules. The stress distribution of tunnel wall was analyzed with the ABAQUS finite element method, and the results coincided with the analytical solution. The analytical calculation can be expediently carried out for underground tunnels with arbitrary-excavation cross sections as long as their conformal mapping functions are presented from the unit circle exterior to the tunnel exterior.

Effects of Age Structure, Contact Patterns and Vaccination on Transmission of the Hand-Foot-Mouth Disease

ZHOU Feng, ZHU Guanghu, TANG Tian

2020, 41(5): 557-567. doi: 10.21656/1000-0887.400175

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Abstract:
In order to further reveal the transmission mechanism and optimize the immune strategy of the hand-foot-mouth disease (HFMD), a new HFMD transmission model was proposed under the effects of age structure, contact patterns and vaccination. The next generation matrix was used to calculate the basic reproduction number, and the theory of stability and dynamics was used to prove the existence and global stability of the disease-free and endemic equilibria. Finally numerical simulation was conducted to explore the effects of model parameters. It is found that age structure, contact matrices and vaccination have significant influence on the transmission, and the heterogeneity of age structure may worsen the infection, but quarantining patients and improving vaccination coverage vaccination rates can effectively help to control the disease. The results provide a scientific reference for the prevention and control of HFMD transmission.

Analysis of the Predator-Prey Model With Nonlinear Impulsive Control

LI Changtong

2020, 41(5): 568-580. doi: 10.21656/1000-0887.400226

Abstract(1508) HTML (300) PDF(308)

Abstract:
Due to limited resources and population densities, the actual pest control strategies such as spraying pesticide and releasing natural enemies have saturation effects or nonlinearity. Therefore, a predator-prey model with nonlinear impulsive control due to resource limitation was proposed and analyzed. With the Floquet theory and the differential comparison principle, the condition for global stability of the predator-free periodic solution was provided. It is shown that once a threshold condition is met, a stable nontrivial periodic solution will emerge via a supercritical bifurcation. The numerical results show that the predator-prey model with nonlinear pulse has rich dynamical behaviors.