Articles in press have been peer-reviewed and accepted, which are not yet assigned to volumes /issues, but are citable by Digital Object Identifier (DOI).
Display Method:
A Rotated Mixed Scheme for Solving 2D Shallow Water Equations
ZHENG Supei, LI Xiao, ZHAO Qingyu, FENG Jianhu
 doi: 10.21656/1000-0887.420063
Abstract(47) HTML(31) PDF(35)
Abstract:
A rotated flux mixed scheme is proposed for solving 2D shallow water equations. In space,the algorithm uses the rotated invariance of the shallow water equations. In the normal direction and tangent direction of the element interface’s, both HLL, which can eliminate the carbuncle, and the entropy stability weighted hybrid numerical flux function satisfying the second law of thermodynamics are used for aweful numerical result. The third-order strongly stable Runge-Kutta method are used in time. The numerical results show that the new scheme has high resolution for solving two-dimensional shallow water equations.
Element-Free Galerkin Method for Time Fractional Diffusion-Wave Equations
WU Di, LI Xiaolin
 doi: 10.21656/1000-0887.420172
Abstract(87) HTML(56) PDF(2)
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Numerical application and theoretical analysis of the element-free Galerkin (EFG) method were presented to the time fractional diffusion-wave equation in the sense of Caputo. By discretizing the time variables in the equation with the L1 approximate formula, the time fractional diffusion-wave equation was transformed into a series of time independent integer order differential equations. Then, the penalty method was used to deal with the Dirichlet boundary condition and the EFG method was used to discretize the integer order differential equations. Error estimates of the EFG method for the time fractional diffusion-wave equation were derived theoretically. Finally, numerical examples were provided to show the accuracy and effectiveness of the proposed meshless method.
A High-order Finite Difference Scheme for the 3D Unsteady Convection Diffusion Reaction Equation
WEI Jianying, GE Yongbin
 doi: 10.21656/1000-0887.420151
Abstract(47) HTML(30) PDF(1)
Abstract:
Based on the fourth-order compact difference scheme for spatial discretization and Taylor series expansion and the error remainder correction method for temporal discretization, a high-order finite difference scheme for solving the three-dimensional (3D) unsteady convection diffusion reaction equation was proposed. The unconditional stability was proved by the Fourier analysis method. The scheme is second-order accuracy in time and fourth-order accuracy in space. At last, numerical examples are employed to validate the theory.
Posture Asymptotic Tracking Control of Sprayer Boom Profiling System With Position Uncertainty
LU Zeyang, LI Shujiang, WANG Xiangdong
 doi: 10.21656/1000-0887.420147
Abstract(36) HTML(21) PDF(0)
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An adaptive and robust backstepping method based on wavelet network approximation is proposed to solve the problems of load variation, unmodeled uncertainties, physical parameter perturbation and external disturbance in the sprayer boom profile system. Firstly, a complete mathematical model of the boom system with uncertain, unknowns and nonlinear terms is established and transformed into a state space form with strict feedback. Secondly, the designed wavelet primitive is used to construct the neural network, which approximates the virtual equivalent control part of the backstepping method under the condition that the optimal error is bounded. The adaptive update law is selected to estimate the unknown parameters. The robust compensation term is introduced to reduce the adverse effect of the composite interference on the system. The input command signal order requirement is reduced. Finally, constructing suitable function by means of Lyapunov stability theory, it has been proved that the position tracking error of the closed-loop system asymptotically converges to the origin. The simulation results show that the proposed control method can realize the rapid maneuver adjustment of the sprayer boom position and posture, which effectively enhanced the robust stability and control accuracy of the boom system.
Anti-Controlling Codimension-Two Bifurcation of Discrete Dynamical System in 1 ∶ 2 Resonance
YANG Yujiao, XU Huidong, ZHANG Jianwen
 doi: 10.21656/1000-0887.420118
Abstract(37) HTML(29) PDF(1)
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A set of nonlinear feedback control strategy is designed to realize the bifurcation solutions of codimensional bifurcations in discrete dynamical systems with 1∶2 resonance from the point of view of bifurcation anti-control. Firstly, aiming at the limitation of traditional bifurcation criterion in determining high codimensional bifurcation points, a new explicit criterion of codimension-two bifurcation in 1∶2 resonance is proposed. Based on this explicit criterion, linear control gain is designed to ensure the existence of such codimension-two bifurcation. Then, the central manifold of 1∶2 resonance is derived. Based on the normal form method, the types and stability of codimension-two bifurcation solution in 1∶2 resonance are analyzed by designing nonlinear control gain. Finally, an Arneodo-Coullet-Tresser mapping is taken as an example, and various bifurcation solutions with 1∶2 resonance bifurcation properties are realized by control at the specified parameter points, which further validates the theoretical analysis.
Mean-Square Synchronization and Stochastically Passive Synchronization of Delayed Gene Regulatory Networks With Markovian Switching
CAO Juan, REN Fengli
 doi: 10.21656/1000-0887.420256
Abstract(46) HTML(29) PDF(1)
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The research of Gene Regulatory Networks (GRNs) and its dynamic models are important in the post-genome era. Qualitative analysis of gene regulatory networks and their dynamics is of great significance to the understanding of organisms from a systematic perspective. In this article, a stochastic gene regulatory network model with time-varying delay and Markovian switching is proposed to study the properties of mean-square synchronization and stochastically passive synchronization. By designing appropriate Lyapunov-Krasovskii functional(LKF), the sufficient conditions of mean-square synchronization and stochastically passive synchronization are obtained by means of Lyapunov stability theory, linear matrix inequality method and random analysis techniques. In addition, the comparison between the results of this paper and some other literatures shows that the results have the theoretical meaning. The numerical simulation shows the validity of the obtained sufficient condition.
Nonexistence of Global Solutions to the Semilinear Moore-Gibson-Thompson Equation with Space-dependent Coefficient and Source Terms
OUYANG Baiping
 doi: 10.21656/1000-0887.420094
Abstract(112) HTML(83) PDF(6)
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Blow-up of solutions to a semilinear Moore-Gibson-Thompson(MGT) equation with space-dependent coefficient and source terms. By choosing suitable energy functional and test functions and using an iteration argument and some differential inequality methods, the nonexistence of global solutions to the Cauchy problem in the subcritical case is obtained. Furthermore, the upper bound estimate of solutions of the lifespan is derived.
Numerical Analysis on Effects of Wall Structures on Bubble Groups
WANG Jincheng, GUAN Hui, WEI Zhijun, WU Chuijie
 doi: 10.21656/1000-0887.420041
Abstract(57) HTML(36) PDF(4)
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With the volume of fluid (VOF) method for a dam-break problem, the effects of wall structures on compressible bubble groups were studied through measurement of the spatial average pressure on the wall. An obstacle was set up at the bottom of the tank, which helps create air bubbles in the collapsing water impacting on it. Three kinds of structures were set up on the left wall, namely, a cuboidal structure, an ellipsoidal structure and a conical structure. It is found that when water hits the left wall, the topology of the bubble wrapped in the water will be changed by the wall structure, which leads to the change of pressure on the wall. The example analysis shows that, the cuboidal structure has the maximum effect in reducing the average pressure amplitude on the wall among those three kinds of wall structures. Especially, a proper adjustment of the position and the size of the cuboidal structure can eliminate the oscillation of the wall pressure.
Theoretical Analysis on Dynamic Stability of a Rotating Pipe Conveying Fluid
ZHANG Bo, SHI Tianzi, ZHANG Yilin, SUN Dongsheng, YUAN Congmin, DING Hu, CHEN Liqun
 doi: 10.21656/1000-0887.420135
Abstract(44) HTML(30) PDF(5)
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The dynamic model was built for a rotating pipe conveying fluid based on Lagrange principle and assumed mode method. The eigenvalue problem of the system was solved via the method of “reducing the order and increasing the dimension”. The free vibration characteristics of the rotating pipe conveying fluid was analyzed. The variations of the eigenvalue trajectories with the fluid velocity were illustrated under different tip masses and rotating speeds. The effects of system parameters on the critical fluid velocity were revealed. It is found that the flowing fluid has significant effects on the dynamic characteristics of the rotating pipe. Different internal resonances relationship between the first several modes of the system could exist under certain parameter condition. The rich dynamic phenomena of the rotating pipe conveying fluid are indicated.
Research Progress of Wavelet Methods and Their Applications in Mechanics
LIU Xiaojing, ZHOU Youhe, WANG Jizeng
 doi: 10.21656/1000-0887.420388
Abstract(44) HTML(26) PDF(3)
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Wavelet theory shows very unique time-frequency locality and multi-resolution analysis ability in signal processing and function approximation. Wavelet basis function can have excellent mathematical properties such as orthogonality, compactness, low-pass filtering and interpolation, which makes wavelet analysis theory have great application potential in the fields of computational mathematics and computational mechanics, it has also further ushered in new opportunities for breakthrough development in these fields. Since the 1990s, a large number of studies have proved that the numerical method based on wavelet theory has very obvious advantages in solving differential equations, but at the same time, it also exposed some limitations of numerical calculation application caused by wavelet basis function itself and its unique approximation method. In order to promote the innovative application of wavelet theory in the field of computational mathematics and mechanics and provide researchers with a new research perspective, this paper briefly combs the development background of wavelet analysis and the research history of numerical methods based on wavelet theory, it also focuses on the problems faced by the latter and the research progress made in recent years. These conclusions and comments are expected to provide a meaningful reference for the further development and improvement of quantitative mathematical solution methods based on wavelet theory and its application in mechanics and even a wide range of engineering problem solving.
Airfoil Optimization Method Based on Convolutional Neural Network Aerodynamic Reduced Order Model
WANG Muchen, LI Lizhou, ZHANG Jun, HUANG Yuqi, ZHANG Lin, SHI Yue
 doi: 10.21656/1000-0887.420137
Abstract(54) HTML(35) PDF(2)
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To solve the nonlinear problem induced by shape large perturbation in airfoil optimization, an optimization method is proposed based on convolutional neural network (CNN) aerodynamic order reduced model (ROM). In the method, the aerodynamic forces of different airfoils are used as the training data of the ROM proposed. The ROM is used to maximize the lift-drag ratio of the airfoil. The ROMs with the parameter pooling method and radial basis function fitting method for training data dimensionality reduction are compared with the CNN ROM without training data dimensionality reduction. The results show that the ROM method proposed can be used to predict the airfoil aerodynamic forces of large shape perturbations and the ROMs with training data dimension reduction have higher accuracy than the ROM without training data dimension reduction.
Active Control on Band Gap and Interface Transmission of Elastic Waves in Piezoelectric Metamaterial Beam
SUN Wenjing, WANG Yize
 doi: 10.21656/1000-0887.420125
Abstract(49) HTML(38) PDF(1)
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In this work, the active control on band gap properties of elastic wave metamaterials is studied by the negative capacitance circuits which are attached to piezoelectric patches periodically. The system uses external circuits to change the material constants of the connected piezoelectric materials, which can tune the equivalent parameters of the structure and control band gap characteristics. By tuning the unit cell, the generation and disappearance can be observed with the active control system. Then, an elastic wave metamaterial beam with the interface is constructed to discuss the effect of the active control system on the interface transmission.
Optimal Leader-Following Consensus of Fractional-Order Multi-Agent Systems Based on Actor-Critic Algorithm
MA Lixin, LIU Chen, LIU Lei
 doi: 10.21656/1000-0887.420124
Abstract(97) HTML(68) PDF(2)
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Aiming at the optimal leader-following consensus problem of fractional multi-agent systems, a reinforcement learning strategy based on intermittent event triggering was designed. Taking the periodic intermittent strategy as the basic mechanism, the event trigger and the Actor-Critic algorithm in reinforcement learning were organically integrated. According to the first-order approximation of the fractional differential, the reinforcement learning algorithm structure based on the periodic intermittent event trigger strategy was proposed. Finally, the feasibility and effectiveness of the algorithm is proved by numerical simulation experiments.
Study on Droplet Impinging on Orifice Plates With Different Wettability Based on Lattice Boltzmann Method
LIANG Jia, GAO Ming, CHEN Lu, WANG Dongming, WANG Zhiyun, ZHANG Lixin
 doi: 10.21656/1000-0887.420076
Abstract(61) HTML(58) PDF(1)
Abstract:
Based on lattice Boltzmann method, the numerical simulation of droplet impinging on orifice plates with different wettability was carried out. The influence of weber number (We) number, wettability of orifice surface and orifice size on different states of droplet passing through orifice plate during droplet impact was studied. The numerical simulation results show that different phenomena will occur in the process of droplet impacting the orifice plate: when the orifice plate is hydrophilic, the droplet will not detach from the surface of the orifice plate, but adhere to the lower surface of the orifice plate at a lower We number, and the droplet will rise a certain distance in the orifice channel under the action of capillarity, forming liquid plugging phenomenon. At higher We numbers, droplets will pass through the orifice plate and rupture will occur. When the orifice plate is hydrophobic, the droplets can not pass through the orifice plate and can not migrate to the lower surface at a lower We number, and finally stabilize on the orifice channel. At higher We numbers, droplets can pass through the orifice plate, and when they pass through, they will break, leaving droplets remaining on the surface of the orifice plate. When the orifice size was changed, it was found that the droplet was not easy to pass through when the orifice size was smaller or the orifice thickness was thicker.
Structure-Preserving Layout Optimization on Precision Devices in Spacecraft
JIANG Ruisong, XU Mengbo, ZHANG Fan, HU Weipeng, DENG Zichen
 doi: 10.21656/1000-0887.420095
Abstract(83) HTML(42) PDF(2)
Abstract:
It is well known that, the stability and the precision of the precision devices installed in spacecrafts are determined by the local vibration characteristics of the spacecraft. In return, the local vibrational characteristics of the spacecraft are affected by the layout of the precision devices, which implies that, rational layout of the precision devices in the spacecraft is the precondition of the stable and efficient work of the precision devices. The dynamic model for a flexible panel cohered with several precision devices was presented and the structure-preserving method was developed to investigate the local vibrational characteristics of the panel. Considering the sizes of the precision devices, the heat dissipative spaces between the precision devices, the layout optimization for the precision devices was performed to minimize the weighted values of the out-of-plane vibrational accelerations of the precision devices. From the optimization results, it can be found that, benefiting from the excellent structure-preserving properties of the numerical method employed during the vibration analysis, the weighted values of the out-of-plane vibrational accelerations of the precision devices decreases about 88.05% after the layout optimization was performed, which provides some guides for the layout scheme of the precision devices in the spacecraft to improve the stability of the precision devices.
Nonlinearly Numerical Simulation of Finite Element Based on Fiber Beam Element Considering Shear Effect for Structures
LI Jiayu, CHEN Mengcheng, WANG Kaixin
 doi: 10.21656/1000-0887.420032
Abstract(79) HTML(68) PDF(8)
Abstract:
The classical fiber beam model based on Eurler-Bernoulli beam theory ignores the influence of shear deformation on the section, in order to get a more accurate beam element model, in this paper, based on the fiber beam element considering the shear effect and the Timoshenko beam theory, the stiffness matrix of the fiber beam element is deduced, and the dual effects of geometric nonlinearity and material nonlinearity are considered at the same time, combined with elastic-plastic incremental theory, then, the nonlinear finite element analysis theory of the structure under the complex stress state of compression, bending and shear is established. Finally, the complied program MATLAB was used to analyze finite element numerical simulation on the typical compression, bending and shear members of reinforced concrete and rectangular concrete-filled steel tube, and the nonlinear full process curve of load-displacement is obtained. It is shown by the analysis of the numerical examples that the nonlinear finite element analysis theory established in this paper is universal, feasible and correct.
Finite Time Adaptive Synchronization of Quaternion-Value Neural Networks With Time Delays
ZHAO Wei, REN Fengli
 doi: 10.21656/1000-0887.420068
Abstract(123) HTML(92) PDF(3)
Abstract:
This paper is concerned with the finite time synchronization of quaternion-value neural networks with time delays. Based on finite time control technique, the protocol of adaptive control is first proposed. Then by utilizing Lyapunov function method and inequalities skills, some sufficient conditions are derived to ensuring master systems and slave systems achieved synchronization in finite time, the settling time can also be theoretically given. Finally, the numerical simulation on quaternion-value neural networks with time delays is included to show the effectiveness of the theorem.
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2021, Volume 42, Issue 12 publish date:December 01 2021
Display Method:
Solid Mechanics
Buckling Behaviors of Elastomers With Periodic Elliptical Holes Under Negative Pressure Activation
LIANG Guanpo, FU Yuxin, LOU Benliang, XIE Yuxin
2021, 42(12): 1221-1228.   doi: 10.21656/1000-0887.420100
Abstract(57) HTML(15) PDF(21)
Abstract:

The buckling behaviors of 2D structures with periodic elliptical holes were studied through numerical simulations and theoretical analysis. A theoretical model was established for the modal analysis corresponding to different buckling modes. The analysis results indicate that, there is a transformation between the buckling modes of the 2D structure with elliptical holes, with the change of the geometrical parameters of the holes. The theoretical analysis and the numerical results match up. Furthermore, in the numerical simulation, a modified force boundary condition for a unit cell under negative pressure activation, being different from the displacement loading, should be considered to ensure the completeness conditions are fulfilled. The confusion in the application of appropriate boundary conditions for the unit cell will result in errors. The choice of the unit cell and the derivation of correct boundary conditions, combined with finite structures, were discussed.

Buckling Analysis of Stepped Columns Based on the Improved Fourier Series Method
LU Jianwei, BAO Siyuan, SHEN Feng
2021, 42(12): 1229-1237.   doi: 10.21656/1000-0887.410373
Abstract(121) HTML(71) PDF(21)
Abstract:

The elastic buckling of stepped columns with variable cross sections was studied. Firstly, based on the improved Fourier series method, the displacement function of the column was established in the local coordinate system, then the linear equations for buckling loads were obtained with the constrained variational principle of potential energy. The problem was transformed into a matrix eigenvalue problem and the buckling load was obtained from solution of the matrix eigenvalues. Finally, the parameter values in the method were discussed through numerical examples, and the obtained results were compared with the finite element results and previous literature results so as to verify the accuracy of the method. In the presented model the translational and rotational springs were arranged at the 2 ends and the setback cross sections. The method can determine the buckling loads of stepped columns with various elastic boundary conditions accurately in engineering design.

A Symplectic Approach for Buckling Analysis of Natural Fiber Reinforced Composite Shells Under Hygrothermal Aging
ZHANG Junlin, NI Yiwen, LI Qingdong, TONG Zhenzhen, ZHOU Zhenhuan, XU Xinsheng
2021, 42(12): 1238-1247.   doi: 10.21656/1000-0887.420018
Abstract(127) HTML(75) PDF(12)
Abstract:

The buckling analysis of natural fiber reinforced (NFRC) cylindrical shells was performed based on Reissner’s shell theory and the symplectic approach. The governing buckling equations for axially-compressed NFRC cylindrical shells were established in the Hamiltonian system. Therefore, the original problem was reduced to a symplectic eigen-problem in the symplectic space. Accurate critical loads and analytical buckling mode shapes were directly obtained from the symplectic eigenvalues and eigensolutions. With numerical examples, the effects of hygroscopic aging on the expressions of eigensolutions were investigated. In addition, the influences of the aging time, the fiber content and the geometric parameters on the buckling behavior of NFRC cylindrical shells were discussed in detail.

Effects of Structure Parameters on Dynamic Performances of Electrostatic Drive Micro-Machined Gyroscopes
LI Xinye, WANG Yaxue, ZHANG Huabiao, ZHANG Lijuan, YU Tao
2021, 42(12): 1248-1257.   doi: 10.21656/1000-0887.410316
Abstract(6) HTML(9) PDF(3)
Abstract:

In view of the cubic nonlinear stiffness and the nonlinear electrostatic force in fraction form, a 2DOF model was analyzed with the harmonic balance method and the residue theorem, and the effects of structure parameters on dynamic performances of micro-machined gyroscopes were studied. The variations of the capacitance with the driving force frequency and the carrier angular velocity were obtained for different thicknesses and gaps of driving electrode comb teeth, different electrode plate areas and different detecting electrode gaps. In addition, the variations of sensitivity and nonlinearity with these structure parameters were also presented. It is found that, the variation curves of the detection capacitance with the driving force frequency show obvious nonlinear characteristics. In other words, the 2nd peak leans rightward, which results in jumping. The effects of thicknesses and gaps of driving electrode comb teeth, and gaps between detecting electrode plates on the variation curves of the capacitance with the carrier angular velocity are much greater than those of detecting electrode plate areas. The variations of sensitivity and nonlinearity with thicknesses and gaps of driving electrode comb teeth and detecting electrode plate areas, are approximately linear, however, those with gaps between detecting electrode plates are nonlinear.

Asymptotic Solutions of Plastic Stress and Displacement at V-Notch Tips Under Anti-Plane Shear
LI Cong, HU Bin, NIU Zhongrong
2021, 42(12): 1258-1275.   doi: 10.21656/1000-0887.420045
Abstract(138) HTML(85) PDF(19)
Abstract:

An efficient method was developed to determine the first- and high-order terms of asymptotic solutions of plastic stress and displacement near V-notch tips under anti-plane shear in power-law hardening materials. Through introduction of the asymptotic series expansions of stress and displacement fields around the V-notch tip into the fundamental equations of the elastoplastic theory, the governing ordinary differential equations (ODEs) with the stress and displacement eigen-functions were established. Then the interpolating matrix method was employed to solve the resulting nonlinear and linear ODEs. Consequently, the high-order stress exponents and the associated eigen-solutions were obtained. The presented method, being capable of dealing with the V-notches with arbitrary opening angles and strain hardening indexes under anti-plane shear, has the advantages of great versatility and high accuracy. Typical examples were given to demonstrate the accuracy and effectiveness of this method.

A Stress Analysis Model for CFRP Repaired Defective Steel Plates
ZHOU Daocheng, CHANG Lichen
2021, 42(12): 1276-1286.   doi: 10.21656/1000-0887.420006
Abstract(113) HTML(103) PDF(9)
Abstract:

In the repairing method with CFRP for steel structures with corrosion defects, the stresses of CFRP and adhesive layers are key to determine the bearing capacity of CFRP repaired structures. Based on the assumption of plane sections, the distributions of stresses and strains under bending moments were obtained; based on the adhesive shear model, the relationship between the adhesive shear stress and the displacements of the CFRP as well as the steel plate was obtained; based on the force balance, the stress relationship of the CFRP and the steel plate was obtained. Combined with the relationships between various materials, the analytical stress distribution solutions of the CFRP and the adhesive layer under the combined action of the axial force and the bending moment were derived. Numerical analysis was also conducted to calculate the defective steel plate repaired with CFRP bonded on both sides, and the results are consistent with the analytical ones. The stress distribution characteristics of the defective steel plate with CFRP bonded on both sides and the possible failure position of the component were obtained, which provides a basis for calculation of the ultimate bearing capacity of the component.

Upper Bound Analysis on the Stability of Cracked Slopes at Tunnel Entrance Subjected to Pore Water Pressure
ZHANG Jingwu, ZHANG Haiyang, LI Mingdong, GUAN Zhongmin
2021, 42(12): 1287-1295.   doi: 10.21656/1000-0887.420054
Abstract(202) HTML(86) PDF(19)
Abstract:

The stability of the cracked slope at tunnel entrance subjected to pore water pressure was studied. The upper-bound limit analysis method and the logarithmic spiral rotation failure mechanism were adopted. A formula for calculating the stability coefficient reflecting the critical slope height was derived. The rationality of the proposed method was verified through comparison of the calculated results with those without effects of the pore water pressure. The distribution of the most critical crack position at the top of slope and the safety factor of the slope were studied by an example analysis. The results show that, the greater the crack depth is, the larger the internal friction angle and the slope angle will be, and the shallower the water level is, the closer the crack position will be to the edge of the slope. The greater the pore water pressure coefficient and the cracking depth are, the smaller the stability coefficient of the slope top will be. The deeper the crack is, the higher the pore water pressure coefficient and the steeper the slope will be, and the more unstable the slope will be. However, the lower the water level is, the more stable the slope will be.

Applied Mathematics
The Wave Speed Signs for Bistable Traveling Wave Solutions in 3-Species Competition-Diffusion Systems
ZHENG Jingpan
2021, 42(12): 1296-1305.   doi: 10.21656/1000-0887.420093
Abstract(58) PDF(49)
Abstract:
In the bistable competition-diffusion model, the wave speed signs for the traveling waves can predict which species are more dominant and will eventually occupy the whole habitat. Therefore, it is of great biological significance to study the speed signs for the traveling waves. Firstly, the Lotka-Volterra competition-diffusion system was transformed into a cooperative system. Under the comparison principle, the comparison theorem for the bistable wave speed and the specific upper-lower solution wave speeds of wave profile equations was obtained. Then, according to the comparison theorem and through construction of suitable upper-lower solutions, some sufficient conditions for determining the bistable traveling wave speed signs were obtained. The results help predict and control the competition results of biological populations.
Analysis and Application of a COVID-19 Transmission Model With Tracking and Isolation Measures
CUI Jin
2021, 42(12): 1306-1316.   doi: 10.21656/1000-0887.420107
Abstract(71) PDF(17)
Abstract:

The novel coronavirus epidemic, appearing at the end of December 2019, spread rapidly due to the large-scale population movement in the Spring Festival travel rush in 2020. Since January 23, 2020, China has taken various measures to effectively control the epidemic. For example, the closure of Wuhan, the tracking and isolation of close contacts of confirmed cases, and the home isolation of Hubei people, etc. Based on the actual transmission of novel coronavirus (COVID-19) in Shanxi province, a dynamic model was established for tracking and isolation of close contacts with imported and confirmed cases. Without regard to the imported cases, the dynamic behavior of the model was analyzed. By means of the case data of novel coronavirus in Shanxi province, the real-time reproduction number was calculated. It is found that the closure of villages and streets in Shanxi province on January 25, 2020 effectively controls the spread of COVID-19 epidemic, that is, the real-time reproduction number is less than 1, which verifies the effectiveness of prevention and control measures from a macro perspective. Further, through the numerical simulation of the model, it is concluded that the prevention and control strategy for early infected patients isolated for 14 days is reasonable and effective; the earlier the closure of Wuhan is, the smaller the scale of infected people will be; the larger number of tracked and isolated contacts of confirmed cases is, the smaller the size of the patients will be.

Existence of Critical Traveling Wave Solutions for a Class of Discrete Diffusion SIR Models With Nonlinear Incidence and Time Delay
ZHANG Xiaoyan
2021, 42(12): 1317-1326.   doi: 10.21656/1000-0887.420111
Abstract(64) PDF(12)
Abstract:
The existence of critical traveling wave solutions for a class of discrete diffusion SIR models with nonlinear incidence and time delay were studied. Under the condition that the total population is not a constant, the upper and lower solutions method and the Schauder fixed point theorem were used to prove the existence of the solution on a finite interval. Furthermore, the existence of critical traveling wave solutions was proved on the real number field through limit arguments. Finally, with the fluctuation lemma and the proof by contradiction, the asymptotic boundary of the critical traveling wave was obtained.
Dynamics of a Class of Stochastic SIRS Infectious Disease Models With Both Logistic Birth and Markov Switching
HE Xueqing
2021, 42(12): 1327-1337.   doi: 10.21656/1000-0887.420140
Abstract(44) PDF(21)
Abstract:
A class of stochastic SIRS infectious disease models with both logistic birth and Markov switching were investigated. The uniqueness of the existence of a globally positive solution to the stochastic infectious disease model was first analyzed through construction of suitable V functions and then by means of Itô’s formula. Afterwards, the results of the existence of an ergodic smooth distribution for the solution of the model and the sufficient conditions for the extinction of the disease were discussed. Finally, numerical examples were given to illustrate the conclusions.
Damage Identification for Bridge Structures Based on the Wavelet Neural Network Method
XIAO Shu-min, YAN Yun-ju, JIANG Bo-lan
2016, 37(2): 149-159.   doi: 10.3879/j.issn.1000-0887.2016.02.004
[Abstract](963) [PDF 5386KB](726)
摘要:
桥梁结构在服役期间会承受复杂的荷载,长期使用会不可避免地出现各种损伤。若这些损伤不能被及时发现和适当处理,将有可能造成严重的事故。因此,桥梁结构的局部小损伤识别对于其及时检修有重要意义。通常,损伤结构的全局动态特性测试可能对局部的结构损伤不敏感,特别是对小损伤,这就需要从结构动态响应信号中提取对损伤更敏感的特征量。建立了桥梁结构的有限元模型并进行动力特性分析;采用小波包分析方法处理结构动态响应信号以构造结构损伤指标,并结合结构损伤指标和人工神经网络方法进行桥梁结构的损伤定位.
The PseudoExcitation Method and Its Industrial Applications in China and Abroad
LIN Jia-hao, ZHANG Ya-hui, ZHAO Yan
2017, 38(1): 1-31.   doi: 10.21656/1000-0887.370578
[Abstract](1042) [PDF 1039KB](1413)
摘要:
《随机振动的虚拟激励法》自1985年正式发表以来,逐渐得到许多工程领域的认可和采用,解决了很多重要而困难的工程问题.该方法不但被国内某些工程规范所推荐,而且被3种国际工程手册成章刊载,在国际上亦占有了一席之地.该文是笔者参考了数百篇国内外论文,依据其中一部分在11个工程领域对虚拟激励法的应用和一些学者的评论所撰写的综述.借以让更多工程技术人员和研究者对虚拟激励法有较为全面的了解,以结合各自工程领域更有效地开展对随机振动理论和方法研究成果的应用和发展.
Uncertainty Quantification for System Identification Utilizing the Bayesian Theory and Its Recent Advances
YAN Wang-ji, CAO Shi-ze, REN Wei-xin.
2017, 38(1): 44-59.   doi: 10.21656/1000-0887.370571
[Abstract](877) [PDF 647KB](930)
摘要:
受测试误差、建模误差、数值离散化以及环境变异等因素的影响,结构系统识别过程不可避免地存在不确定性,因此有必要引入概率统计方法来提高其鲁棒性,为工程结构安全监测提供更为可靠的结果.近年来,Bayes(贝叶斯)方法因为其诸多优势在系统识别领域受到了广泛关注.该文梳理了Bayes系统识别的历史脉络和研究进展.从Bayes系统识别的理论框架出发,分析了量化系统识别不确定性两类方法的适用条件与局限性.此外,文章综述了Bayes方法在模态参数识别、有限元模型修正以及结构损伤识别方面进行不确定性分析的理论、实现及其应用.最后对基于Bayes方法进行系统识别研究的发展趋势做出了展望.
Convergence Results on Heat Source for 2D Viscous Primitive Equations of Ocean Dynamics
LI Yuanfei
2020, 41(3): 339-352.   doi: 10.21656/1000-0887.400176
[Abstract](521) [FullText HTML](61) [PDF 405KB](286)
摘要:
考虑了在一个柱形区域上的海洋动力学中二维黏性方程组解的收敛性.在此模型中存在一个关键的参数就是热源,众多周知,它的存在可能会使流体内层之间出现共振从而导致不稳定.因此,通过推导方程组的先验界,得到了方程组的解对热源自身的收敛性.
Detached-Eddy Simulation of Flow Past Tandem Cylinders
ZHAO Wei-wen, WAN De-cheng
2016, 37(12): 1272-1281.   doi: 10.21656/1000-0887.370546
[Abstract](618) [PDF 3862KB](608)
摘要:
主要开发了SST-DES和SST-DDES两种分离涡方法,并集成到基于开源代码平台OpenFOAM开发的CFD求解器naoe-FOAM-SJTU中.选用高Reynolds(雷诺)数下串列双圆柱绕流问题作为标准算例来验证所开发的分离涡方法.该标准算例此前在美国国家航空航天局兰利研究中心的两个不同风洞做过物理试验.该研究将数值模拟得到的时均流场信息和一些其他物理量同物理试验结果比较,同时讨论分析了三维瞬态流场结构.结果表明该文开发的SST-DES和SST-DDES分离涡方法能够解决高Reynolds数下有大量流动分离的复杂流动问题.
Simulation of Multi-Hydrofracture Horizontal Wells in Shale Based on the Extended Finite Element Method
CHEN Jun-bin, WEI Bo, XIE Qing, WANG Han-qing, LI Tao-tao, WANG Hao
2016, 37(1): 73-83.   doi: 10.3879/j.issn.1000-0887.2016.01.006
[Abstract](874) [PDF 1871KB](681)
摘要:
页岩储层水平井分段多簇压裂簇间距优选是压裂技术的关键,建立了水力压裂流固耦合数学模型,基于扩展有限单元法模拟多条裂缝的扩展过程,研究多条裂缝同时扩展的转向规律,以及应力干扰、水平主应力差、裂缝间距等因素与裂缝转向角度的关系.结果表明:应力干扰作用对裂缝宽度具有限制作用,单条裂缝张开宽度比两条裂缝的大;裂缝转角随应力差的减小而增大,随压裂时间的增加而增大.簇间距越小,应力干扰越强,转角越大,综合主缝均匀扩展、支撑剂填充以及复杂裂缝网络形成等条件,确定最优簇间距为30~40 m.多条裂缝同时扩展时,中间裂缝会受到两边裂缝的限制作用,簇间距越小,限制作用越强,裂缝发育时间越长,扩展速度越慢.
Analysis on Shear Deformation and Shear-lag Effects on Twin-Cell Box Girders
ZHANG Hui, ZHANG Yu-yuan, ZHANG Yuan-hai, LI Wei
2016, 37(8): 791-803.   doi: 10.21656/1000-0887.370056
[Abstract](703) [PDF 589KB](823)
摘要:
基于各个翼板选取不同的最大剪切转角差为剪力滞广义位移,应用能量变分原理分别推导出了考虑和不考虑剪切变形时单箱双室截面控制微分方程组,结合边界条件给出了箱梁纵向应力和竖向挠度的初参数解,从力学、数学角度上证实了剪切变形和剪力滞效应是两个相对独立的力学行为,进一步阐述了二者对箱梁的影响,即剪切变形对箱梁截面纵向应力无影响,但是对竖向挠度有很大的影响.数值算例表明,利用该文解和数值解分析跨中截面剪力滞系数横向分布规律,二者吻合程度良好,其横向分布规律与单室箱梁类似,唯独不同之处是边腹板处的剪力滞效应比中腹板处的剪力滞效应略微大一些;挠度计算表明,剪切效应使得该箱梁在集中和均布荷载作用下跨中挠度分别增大4.6%和2.7%.
Some New Advances in the Probability Density Evolution Method
LI Jie, CHEN Jian-bing
2017, 38(1): 32-43.   doi: 10.21656/1000-0887.370336
[Abstract](869) [PDF 683KB](2037)
摘要:
介绍了随机动力系统中概率密度演化理论的基本方程与求解方法〖CX4〗.〖CX〗在此基础上,论述了广义概率密度演化方程求解的若干新进展,包括群演化方程及其求解、概率空间剖分的理性准则、点集加密技术与信息拓展方法等.
Chaos Control for the Duopoly Cournot-Puu Model
DU Lin, ZHANG Ying, HU Gao-ge, LEI You-ming
2017, 38(2): 224-232.   doi: 10.21656/1000-0887.370256
[Abstract](806) [PDF 890KB](505)
摘要:
基于非线性动力学的基本原理,研究了经济系统中的双寡头垄断Cournot-Puu模型及其混沌控制方法.Cournot-Puu模型具有双曲线形需求函数和彼此不同的不变边际成本,离散化的差分系统显示出其复杂的非线性、分岔和混沌行为.在此基础上,结合Cournot-Puu模型的基本特征,应用延迟反馈控制方法以及自适应控制方法对该系统的混沌行为进行了研究.在结合实际经济意义的条件下,对该模型的输出进行调整并实现混沌控制.
Investigations of Self-Propulsion in Waves of Fully Appended ONR Tumblehome Model
WANG Jian-hua, WAN De-cheng
2016, 37(12): 1345-1358.   doi: 10.21656/1000-0887.370525
[Abstract](889) [PDF 3993KB](547)
摘要:
采用基于重叠网格技术的CFD方法数值研究了全附体ONRT船模在迎浪工况中自航的水动力特性.文中数值计算采用自主开发的面向船舶与海洋工程的CFD求解器naoe-FOAM-SJTU.自航计算中船体运动及螺旋桨转动等通过重叠网格技术完成,波浪环境则采用求解器中的三维数值造波和消波模块实现.计算中自航船模的螺旋桨转速通过静水自航数值计算得出,波浪工况计算采用东京2015 CFD会议中标准算例进行设置.数值计算结果,如船体运动、实时航速变化等,与试验数据进行了对比分析.此外,给出了数值预报的推力和扭矩系数,并且通过详细的流场信息来分析和解释了船模在波浪中自航过程中的水动力变化情况.数值预报结果同试验值吻合较好,说明采用当前结合重叠网格技术和CFD的数值方法可以很好地预报波浪中自航问题.
Study of Stress Field Near Interface Crack Tip of Double Dissimilar Orthotropic Composite Materials
LI Jun-lin, ZHANG Shao-qin, YANG Wei-yang
2008, 29(8): 947-953.  
[Abstract](2874) [PDF 460KB](19)
Abstract:
A study of double dissintilar orthotropic composite materials interfacial crack was made by constivcting new stress functions and employing the method of composite material complex.In the case that the characteristic equations' discriminants are all more than zero,the theoretical fonmula of the stress field and the displacement field near the mode Ⅰ interface crack tip,without oscillation and inter-embedding between the interfaces of the crack were delved.
Second Order Approximation Solution of Nonlinear Large Deflection Problem of Yongjiang Railway Bridge in Ningbo
CHIEN Wei-zang
2002, 23(5): 441-451.  
[Abstract](5117) [PDF 395KB](85)
Abstract:
The solution and computational aspects on nonlinear deflection of Yongjiang Railway Bridge in Ningbo were investigated.An approximate iteration algorithm on nonlinear governing equation was presented,and the obtained results show that,if altitude difference and span of the riverbanks are taken as 5 meters and 100 meters,respectively,the maximum gradient in the middle of the bridge exceeds 5%,much larger than maximum allowance gradient in railway design code.Therefor,a new solution scheme for decreasing gradient of the bridge is put forward,that is,the altitude difference between two riverbanks can be decreased to about 1/10 of the initial magnitude by building roadbeds with 0.5% gradient and 1 kilometer length at two riverbanks.As a direct result,the deflection gradient of the railway bridge is much reduced and the value is between 0.5%~0.6%.