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Chinese Journal of Theoretical and Applied Mechanics was founded in 1957, is a comprehensive bimonthly academic periodical, administrated by the Chinese Academy of Sciences(CAS), sponsored by the Chinese Society of Theoretical and Applied Mechanics and undertaken by the Institute of Mechanics, CAS. The current Editor-in-Chief is academician Wei Yueguang. Previous editor-in-chiefs in chronological order: Prof. H. S. Tsien, Prof. Y. H. Kuo, Prof. Zheng Zhemin, Prof. Lin Tongji, Prof. Huang Kezhi, Prof. Wu Chengkang, Prof. Wang Ziqiang, Prof. Yang Wei, Prof. Zheng Quanshui....... More>>
 Author:Sun Jiao, Zhou Wei, Cai Runze, Chen Wenyi Abstract: By using high speed photography technology combined with shadow method, the motion of a single rising bubble near a vertical wall in stationary water is experimentally studied. The effects of bubble size and the initial dimensionless distance between the nozzle and the wall ($S^{\ast})$ on the rising motion characteristics of bu. . . More>>
• 18 January 2020, Volume 52 Issue 1
Fluid Mechanics
THE BOUNCE DYNAMICS OF A RISING SINGLE BUBBLE NEAR A VERTICAL WALL 1)
Sun Jiao, Zhou Wei, Cai Runze, Chen Wenyi
2020, 52(1):  1-11.  doi:10.6052/0459-1879-19-228
Abstract ( 37 )   HTML( 25 )   PDF (17585KB) ( 25 )

By using high speed photography technology combined with shadow method, the motion of a single rising bubble near a vertical wall in stationary water is experimentally studied. The effects of bubble size and the initial dimensionless distance between the nozzle and the wall ($S^{\ast})$ on the rising motion characteristics of bubbles were compared. The wall effect, bubble dynamic mechanism and energy variation rule before and after the collision between bubbles and the walls are analyzed. The results show that for the Reynolds number $Re \approx 580\sim 1100$, and the initial dimensionless distance between the nozzle and the wall $S^{\ast } < 2\sim 3$, the bubbles collide with the wall surface and the bubble trajectory changes from three-dimensional spiral under unconstrained conditions to two-dimensional zigzag periodic motion. However, when $S^{\ast } > 2\sim 3$, the wall effect weakens, and the movement characteristics of the bubble with wall constraint tends to be consistent with that without constraint. Before and after the bubble collides with the wall, the wall effect causes the peak value of transverse velocity to drop to 70% of the original peak value, and vertical velocity drop to 50%. Before the bubble collides with the wall, the vertical velocity variation rule can be predicted by the distance between the bubble center and the wall ($x/R)$ and the modified Stokes number correlation formula. In the process of collision between the rising bubble and the wall surface, the deformation energy of the bubble surface is transmitted to the transverse kinetic energy of the bubble in one direction, so that the deforming bubbles can maintain a relatively constant bouncing motion. The prediction model of the average resistance coefficient of bubbles in the repeated bouncing with the wall surface is proposed, which can describe the dimensionless parameters of Reynolds number, Weber number and Eo number reflected by the experimental data.

MECHANISM INVESTIGATION OF WATER INJECTION ON SUPPRESSING HYDROFOIL CLOUD CAVITATION FLOW 1)
Wang Wei, Zhang Qingdian, Tang Tao, An Zhaoyang, Tong Tianhao, Wang Xiaofang
2020, 52(1):  12-23.  doi:10.6052/0459-1879-19-282
Abstract ( 13 )   HTML( 5 )   PDF (28189KB) ( 5 )

In order to understand the development mechanism of cloud cavitation and investigate the influence of jet flow on the suction surface of hydrofoil, the unsteady evolution process of cloud cavitation of the original NACA66(mod) hydrofoil and the hydrofoil with jet flow is simulated and compared by using density modified RNG $k$-$\varepsilon$ turbulence model and Schnerr-Sauer cavitation model. Monitoring lines of the hydrofoil suction surface are adopted and then spatiotemporal evolution of the vapor phase volume fraction, re-entrant jet flow, pressure and pressure gradient near the hydrofoil wall is obtained. The flow field characteristics of the cloud cavitation are analyzed by vortex dynamic. The suppression mechanism of active jet is analyzed. The results show that the first retraction of the attached cavity is caused by the strong local high pressure when the dissociated cavity collapse downstream, and the second retraction is affected by the re-entrant jet. The re-entrant jet zone is limited to higher pressure gradient. High pressure gradient always exists, but the initial occurrence of re-entrant jet in a time period needs the accumulation of time. Jet flow on the suction surface of hydrofoil can reduce cloud cavitation. The suppression mechanism is that injected jet makes the pressure rise near jet holes, making up for the pressure drop caused by cavitation and circumfluence, so as to increase the pressure gradient and enhance the anti-pressure ability. On the other hand, the re-entrant jet strength is decreased. The vortex structure contour of Q criterion shows complex flow structure compared to the vapor phase volume fraction contour. Vortex cores are existed in the front attached cavity and dissociated cavity, while shear may be present in re-entrant jet zone. The shear function of the injected jet suppresses the development of cavitation and re-entrant jet.

EXPERIMENTAL STUDY ON DRAG REDUCTION CHARACTERISTICS OF SUPERHYDROPHOBIC GROOVE SURFACES WITH VENTILATION 1)
Feng Jiaxing, Hu Haibao, Lu Bingju, Qin Liping, Zhang Mengzhuo, Du Peng, Huang Xiao
2020, 52(1):  24-30.  doi:10.6052/0459-1879-19-279
Abstract ( 23 )   HTML( 16 )   PDF (6108KB) ( 16 )

Drag reduction is one of the main technical approaches to solve the enhancing speed and extending voyage of the vehicle under water, which is extremely crucial to alleviate the increasingly severe energy crisis all over the world. In the gravity pipeline experimental system, drag reduction characteristics with ventilation and gas film spreading state on superhydrophobic groove surfaces are tested and raised in the turbulent state. The variation laws of drag reduction rate with Reynolds number and dimensionless spacing of grooves at different ventilation rates are obtained. In addition, it is the diffierence of ventilation drag reduction that is compared and analyzed between merely superhydrophobic surfaces and superhydrophobic groove surfaces. The material of the experimental plate is colorless acrylic. The groove structure is processed via mechanical method and is sprayed by superhydrophobic coating. Results reveal that continuing ventilation can settle the issue of easy loss of gas film on superhydrophobic groove surface, and the gas film can achieve perennial stabilization. As ventilation rate adds, the gas film spreads more uniformly and drag reduction rate rises under the constant Reynolds number, which result in the notable drag reduction effect. As ventilation rate affects the capability of scaling out of gas film, drag reduction presents two modes with Reynolds number under the constant ventilation rate. When the ventilation rate and the Reynolds number are unchanging, the drag reduction rate firstly increases and then decreases with the expansion of the groove size, and the maximum reduction rate is obtained when $S^{+}\approx 76$. The inherent mechanism on drag reduction characteristics of superhydrophobic groove surfaces with ventilation is that not only the spreadability and stability of gas film layer is enhanced significantly but also the wetted area is increased obviously due to groove structures, meanwhile, the maximum value of drag reduction is larger than both the groove surface and the superhydrophobic surface.

NUMERICAL SIMULATION ON BUBBLE RINSING BEHAVIORS UNDER ELECTRIC FIELD 1)
Wang Yuerou, Wang Junfeng, Liu Hailong
2020, 52(1):  31-39.  doi:10.6052/0459-1879-19-193
Abstract ( 8 )   HTML( 3 )   PDF (8884KB) ( 3 )

Employing an electric field to control bubble morphology and motion, and enhance heat and mass transfer between gas and liquid are one of the important research contents of electrohydrodynamics (EHD). However, most of the current researches focus on the dynamics of bubbles under non-electric fields. Further research is needed on the behaviors of bubbles and the mechanism of electric fields under electric fields. In the present study, the dynamic behaviors of a single bubble rising in a fluid under an external electric field are numerically simulated. Based on the model established on two-dimensional, the equation of electric field and Navier-Stokes are solved, and the level set method is used to accurately capture the position and morphology of the rising bubble. The accuracy and validity of the present simulation results are verified by comparing with previous experiments and numerical results. The effects of liquid viscosity, surface tension and electric field force on bubble motion and deformation under electric field are examined by employing the Reynolds ($Re$), Bond ($Bo$) and electrical bond ($Bo_{\rm e}$) numbers. The calculation results show that the electric field has a significant influence on the dynamic characteristics of the bubble. In the case of a non-electric field, the bubble basically maintains a spherical shape when the viscosity of the liquid and the surface tension are large. Instead, the bubbles deform and gradually reach a steady state. Additionally, the bubble is strongly deformed at the initial rising stage by attributing to the electric field. With the bubble further rising, the deformation weakened, and both of the bubble velocity and aspect ratio are oscillated. The effect of vertical electric field causes a greater increase in the velocity of rising bubble. As the number of $Bo_{\rm e}$ increases, the bubble has an intense oscillation, making it more difficult to achieve a relatively stable state.

GRAVITY-CAPILLARY WAVES SLOWLY MODULATED BY UNIFORM FLOW IN FINITE WATER DEPTH 1)
Li Shaofeng, Song Jinbao
2020, 52(1):  40-50.  doi:10.6052/0459-1879-19-268
Abstract ( 7 )   HTML( 4 )   PDF (2143KB) ( 4 )

The higher harmonics are produced by the nonlinear terms, which react on the original low order harmonics, making the amplitude of waves changes slowly with space and time, thus producing slow modulation phenomenon. Based on the basic equations of water waves which are influenced by a uniform flow, under the assumptions of the fluid motion is inviscid, incompressible and irrotational, a nonlinear Schr?dinger equation (NLSE) for gravity-capillary waves in finite water depth is derived by using the multiple scale analysis method. The modulational instability of the NLSE is analyzed, the conditions of modulational instability for gravity-capillary waves and the generation of bell solitary waves are proposed. The trend of dimensionless maximum instability growth rate with dimensionless water depth and surface tension is analyzed. At the same time, the dimensionless instability growth rate as a function of dimensionless perturbation wave number is also analyzed, it is shown that it increases from zero and then decreases to zero with the increase of the dimensionless perturbation wave number. In addition, it is found that uniform down-flow decreases the dimensionless growth rate and maximum growth rate, on the contrary, uniform up-flow increases them. Capillary waves generated by the surface tension and gravity-capillary waves generated by the gravity and surface tension which are modulated by uniform flow can change the surface roughness and the structure of the upper ocean flow field, and then affect the exchange of momentum, heat and water vapor at the air-sea interface. Hence, Understanding these short-waves dynamic mechanisms of the sea surface is of great significance to the accurate measurement of satellite remote sensing, the study of sea-air interaction and the improvement of sea-air coupling model.

QUANTITATION STUDY OF INFLUENCE OF WIND SPEED UNCERTAINTY ON AERODYNAMIC FORCES OF WIND TURBINE 1)
Tang Xinzi, Wang Xiaoyu, Yuan Keren, Peng Ruitao
2020, 52(1):  51-59.  doi:10.6052/0459-1879-19-214
Abstract ( 16 )   HTML( 19 )   PDF (346KB) ( 19 )

Wind turbine aerodynamics has been one of the hottest research topics at home and abroad. At present, most relevant researches are based on deterministic working conditions. However, since wind turbine works in the complex environment of natural flow in the atmosphere all the year round, wind speed fluctuates and changes randomly, the power output of wind turbine is uncertain. The uncertainty of wind power system brings great challenges to the stability of national grid. It is important to study the aerodynamics of wind turbine under uncertain wind speed conditions. In order to reveal the influence mechanism of uncertainty on wind turbine flow field and to determine its influence on loads, this paper proposes an uncertain aerodynamic analysis method for wind turbine. Based on the blade element momentum theory and the non-intrusive probabilistic collocation, the uncertainty aerodynamic response model of horizontal axis wind turbine was established. Taking the NREL Phase VI S809 wind turbine rotor as the research object, the random output response information of wind turbine was extracted, and the influence of uncertain wind speed on turbine power, thrust, blade flapwise bending moment and edgewise moment of wind turbine were quantified. Based on the uncertain analysis of the flow induction factors in the length direction of the blade, the uncertainty propagation mechanism in the wind turbine field was revealed, which provides a reference for the wind power system design and application. Results show that, the wind speed fluctuation has a significant influence on the wind turbine power and aerodynamic forces. The standard deviation of random Gaussian wind speed range increases from 0.05 to 0.15 times average speed, the maximum fluctuation ranges of power and thrust increase from 13.34% and 8.00% to 35.11% and 22.02%, respectively; the maximum fluctuation ranges of blade flapwise bending moment and edgewise moment increase from 7.20% and 12.84% to 19.90% and 33.49% respectively. The uncertainty of the incoming wind speed leads to the obvious fluctuation of the local flow at the blade root sections, which indicates that flow control techniques can be applied in this part of the blade to reduce the sensitivity to the uncertainty of wind speed.

Solid Mechanics
COMPARATIVE STUDY OF STOCHASTIC AND INTERVAL NON-HOMOGENEOUS LINEAR HAMILTONIAN SYSTEMS AND THEIR APPLICATIONS 1)
Qiu Zhiping, Jiang Nan
2020, 52(1):  60-72.  doi:10.6052/0459-1879-19-348
Abstract ( 14 )   HTML( 36 )   PDF (1852KB) ( 36 )

With the rapid development of computer technology, there is an urgent need for more efficient and more stable numerical algorithms with more powerful long-term simulation capabilities. Compared with the traditional algorithms, the symplectic algorithms of Hamiltonian systems have significant advantages in stability and long-term simulation. However, a variety of different degrees of uncertainties exist inevitably in the dynamic system, and the impacts of these uncertainties need to be considered in the dynamic analysis to ensure the rationality and effectiveness. Nevertheless, there has been very little research considering parameter uncertainties on the dynamic response analysis of Hamiltonian systems. For this reason, two kinds of uncertain non-homogeneous linear Hamiltonian systems are studied and compared in this paper breaking through the limitations of traditional Hamiltonian systems, where stochastic and interval parameter uncertainties are taken into account, and applied to the evaluation of structural dynamic response. Firstly, for the deterministic non-homogeneous linear Hamiltonian systems, a parameter perturbation method considering deterministic perturbations is proposed. On this basis, the parameter perturbation methods of stochastic and interval non-homogeneous linear Hamiltonian systems are proposed respectively, and the mathematical expressions of the bounds of their response are obtained. Then, the compatibility conclusion that the region of the dynamic response obtained by the interval method contains that obtained by the stochastic one is derived theoretically. Finally, two numerical examples verify the feasibility and effectiveness of the proposed method in structural dynamic response in a smaller time step, and reflect the envelope relationship between the numerical results of the response of stochastic and interval Hamiltonian systems. Also, in a larger time step, the numerical advantages of the symplectic algorithms of Hamiltonian systems are highlighted compared to the traditional algorithms and the accuracy of the proposed method is verified by comparison with the Monte Carlo simulation method.

EXACT SOLUTION OF CIRCULAR INCLUSION PROBLEMS BY A BOUNDARY INTEGRAL METHOD 1)
Guo Shuqi
2020, 52(1):  73-81.  doi:10.6052/0459-1879-19-283
Abstract ( 23 )   HTML( 23 )   PDF (208KB) ( 23 )

As an excellent numerical method, boundary element method (BEM) has been widely applied in various scientific and engineering problems. In this paper, a new boundary integral method is obtained based on Somigliana's equation and the properties of Green's function by referring to the idea of boundary element method. It can be used to find the analytic solution of linear elastic problems. The boundary integral method can also be obtained from Betti's reciprocity theorem. By using this new method, the classical problem of elastic circular inclusion under a uniform tensile field at infinity is solved. Firstly, the perfect bonding between inclusion and matrix is set up, and the displacement and stress at interface are expanded according to Fourier series. According to the symmetry of the problem and the orthogonality of trigonometric function, the hypothesis is simplified and the number of undetermined coefficients is reduced. Secondly, the appropriate trial functions are selected (these trial functions satisfy the condition of displacement single value and the control equation of linear elasticity without body force). And the boundary integral method is used to calculate the displacement and stress at the interface. Then the displacement and stress in the domain are solved using similar tricks. The exact analytical solution of the problem is obtained, which is exactly the same with the results in literatures. When the elastic modulus of the inclusion is zero or tends to infinity, it degenerates to the analytical solution of the problem of circular hole or rigid inclusion. The solution process shows that if the problem has boundary conditions at infinity, trial functions should meet the boundary condition at infinity. If the domain of the problem contains the coordinate origin, the displacement and stress of trial functions at the origin should be limited. The results show that the method is effective.

DETERMINATION OF ELASTOPLASTIC PROPERTIES OF IN-SERVICE PIPELINE STEEL BASED ON BP NEURAL NETWORK AND SMALL PUNCH TEST 1)
Song Ming, Li Xuyang, Cao Yuguang, Zhen Ying, Si Weishan
2020, 52(1):  82-92.  doi:10.6052/0459-1879-19-297
Abstract ( 16 )   HTML( 26 )   PDF (7251KB) ( 26 )

In order to obtain the elastoplastic mechanical properties of in-service pipeline materials without shutting down transportation, this paper presents a method of combining artificial intelligence back-propagation (BP) neural network, small punch test and finite element simulation to obtain the elastic-plastic mechanical properties of materials by determining the true stress-strain curve of materials. Elastoplastic mechanical properties of X80 pipeline steel was obtained by this novel method. First, 457 groups of hypothetical material constitutive relations with different elastoplastic mechanical properties are obtained by systematically changing the parameters $K$ and $n$ in the Hollomon formula. The load-displacement curves of 457 groups of different materials were obtained by using the two-dimensional axisymmetric finite element model of small punch test with Gurson-Tvergaard-Needleman (GTN) damage parameters verified by experiments. The two groups of data are substituted into BP neural network and the corresponding relationship between the load-displacement curve of small punch test and the true stress-strain curve of the conventional uniaxial tensile test is established by the method proposed. This relationship can be used to obtain the true stress-strain curve of in-service pipeline steel based on the results of small punch test, so as to determine its elastic plastic mechanical properties. The accuracy and wide applicability of the BP neural network model are verified by comparing the true stress-strain curve of X80 pipeline steel obtained by BP neural network with the results of uniaxial tensile test and the experimental data of materials in the literature.

RIB MESHLESS OPTIMIZATION OF STIFFENED PLATES RESTING ON ELASTIC FOUNDATION BASED ON GENETIC ALGORITHM 1)
Qin Xia, Liu Shanshan, Shen Yajing, Peng Linxin
2020, 52(1):  93-110.  doi:10.6052/0459-1879-19-300
Abstract ( 13 )   HTML( 7 )   PDF (3283KB) ( 7 )

Based on the genetic algorithm and the first-order shear deformation theory, a meshless method is proposed to optimize the position of ribs of the stiffened plate resting on elastic foundation. Firstly, the meshless model of the stiffened plate is obtained by discretizing the plate and ribs with a series of points and by simulating the elastic foundation with springs. Secondly, the displacement field is approximately obtained based on the first-order shear deformation theory and the moving-least square approximation, and the total potential energy of the stiffened plate resting on the elastic foundation is derived. Then, the boundary conditions are dealt with the full transformation method, and the governing equation of the structure is derived from the Hamilton principle. Finally, the genetic algorithm and the improved genetic algorithm are introduced with the location of ribs as the design variable and the minimal deflection of the center point of the stiffened plate as the objective function. The arrangement of ribs is optimized to achieve the minimum center point deflection of the stiffened plate resting on the elastic foundation. Taking some ribbed plates resting on elastic foundation with different parameters and load distribution as the numerical examples, the comparison with the finite element results given by ABAQUS is carried out. The results show that the proposed meshless model can effectively analyze the bending problem of stiffened plate on elastic foundation. Meanwhile, the meshless optimization method based on the genetic algorithm and the improved genetic algorithm both can effectively optimize the position of the ribs of the stiffened plate on elastic foundation, the latter is relatively efficient, and the stable optimal solution can be obtained after only three iterations. Additionally, when the position of the rib changes during the optimization process, only the displacement transformation matrix needs to be recalculated, and the mesh reconstruction is totally avoided.

TRANSITION RADIATION IN ELASTIC MEDIUMS COUPLED BY AN INCLINED INTERFACE 1)
Yao Shan, Li Su, Shunhua Zhou
2020, 52(1):  111-123.  doi:10.6052/0459-1879-19-246
Abstract ( 10 )   HTML( 4 )   PDF (4013KB) ( 4 )

A NOVEL FAST ALGORITHM BASED ON MODEL ORDER REDUCTION FOR ONE CLASS OF TRANSIENT NONLINEAR HEAT CONDUCTION PROBLEM 1)
Zhu Qianghua, Yang Kai, Liang Yu, Gao Xiaowei
2020, 52(1):  124-138.  doi:10.6052/0459-1879-19-323
Abstract ( 9 )   HTML( 14 )   PDF (7431KB) ( 14 )

The proper orthogonal decomposition (POD) is known as an effective model order reduction method to solve the transient nonlinear heat conduction problems. Although the execution-time economy in the solution of the equations coming from the significant drop in the number of degrees of freedom (DOFs) of the original finite element discretized system, the expected reduction in the overall computational times are not generally realized. The reason is that the solution of the nonlinear reduced order model involves an iterative procedure for which the global stiffness matrix needs to be reassembled in the original high dimensional space and then to be multiplied by the POD mode matrix at every time step. In order to mitigate this problem, a new and efficient algorithm is proposed in this paper to improve the computational efficiency of the POD-based reduced order model for a kind of transient nonlinear heat conduction problem in which the thermal conductivity of material is not a constant due to the change of temperature. Firstly, the element pre-conversation method (EPM) is used to compress the time for calculating the stiffness matrix of low dimensional system. Secondly, the multi-level linearization method (MLM) is used to eliminate the time-consuming procedure of iteration. Lastly, a hypothetical element matrix is constructed to effectively combine the EPM and the MLM for reducing the overall computational time to a great extent. Both 2D and 3D numerical examples are conducted to verify the accuracy and effectiveness of the proposed new algorithm by comparing its results with those of the finite element full order model. It is quite clear that significant savings in computational time can be achieved by this algorithm while maintaining an acceptable level of accuracy. The results show that: (1) the root mean square error (RMSE) of POD solutions decreases rapidly and stabilizes below 0.01% after a slight fluctuation in the initial short time, and the computational efficiency can be improved by 2~3 orders of magnitude when the DOFs of the problem under consideration is less than 6000; (2) the new algorithm works out the problem of poor acceleration of the conventional algorithm in solving nonlinear reduced order model, the computational effort saving can be seen clearly even for small problems and more pronounced for larger problems; (3) the truncated POD modes determined under simple constant thermal boundary conditions can be directly applied to obtain the reduced order model of the transient nonlinear heat conduction problems with the same geometric domain but a variety of complex smooth/unsmooth time-varying thermal boundary conditions and to predict the corresponding temperature fields quickly and accurately, which is valuable for engineering application.

Dynamics, Vibration and Control
DUALITY RELATIONS OF BEAMS IN NATURAL VIBRATIONS 1)
Hu Haiyan
2020, 52(1):  139-149.  doi:10.6052/0459-1879-20-019
Abstract ( 31 )   HTML( 66 )   PDF (4803KB) ( 66 )

The duality relations are studied in the paper for the Euler-Bernoulli beams with homogeneous boundaries in natural vibrations. A pair of beams is first defined as a dual of different cross-sections if they have the same natural frequencies, but different variations of cross-sections. The duals of different cross-sections are analyzed via a dual of displacement description and bending moment description, and the non-uniform beams with homogeneous boundaries can be classified as the following seven duals. They are (1) the dual of a free-free beam and a clamped-clamped beam, (2) the dual of a slipping-free beam and a slipping-clamped beam (and their mirrors), (3) the dual of a hinged-free beam and a hinged-clamped beam (and their mirrors), (4) the dual of two hinged-slipping beams, (5) the dual of two slipping-slipping beams, (6) the dual of two hinged-hinged beams, and (7) the dual of a clamped-free beam and a free-clamped beam. Then, a pair of beams is defined as a dual of identical cross-sections if they have the same natural frequencies and the same variations of cross-sections. It is proved that the first four duals of different cross-sections become the duals of identical cross-sections if and only if the area of cross-section and the inertial moment of cross-section of any beam in those duals take a specific form of exponential function. Afterwards, the first three duals of identical cross-sections are verified to keep the dual relations for uniform beams, whereas the fourth dual is degenerated to a pair of mirrors. Based on the dual of displacement description and slope description, a new dual of uniform beams is found for a slipping-slipping beam and a hinged-hinged beam. Finally presented is an important feature of all the duals of uniform beams. That is, one uniform beam in a dual has statically determinate constraints while the other uniform beam in the same dual has statically indeterminate constraints.

REDUCED-ORDER MODELING FOR AEROELASTIC SYSTEMS VIA NONLINEAR STATE-SPACE IDENTIFICATION 1)
Zhang Jiaming, Yang Zhijun, Huang Rui
2020, 52(1):  150-161.  doi:10.6052/0459-1879-19-287
Abstract ( 12 )   HTML( 12 )   PDF (8683KB) ( 12 )

Reduced-order modeling for high dimensional nonlinear aeroelastic systems is one of the hot issues in the field of aeroelasticity and control. Some linear/nonlinear reduced-order modeling methodologies, such as autoregressive exogenous, auto regressive-moving-average model, Volterra series, artificial neural networks, Wiener model, and Kriging technique, were proposed for reconstructing low-dimensional aerodynamic models. However, the previous nonlinear reduced-order models, such as the nonlinear Wiener model and neural network model, still have some problems need to be addressed. For example, the identification algorithm is too complexity and the accuracy in reconstructing the dynamic behaviors needs to be improved further. In this paper, a nonlinear state-space identification-based reduced-order modeling methodology for transonic aeroelastic systems is proposed. Firstly, the unit impulse response of the transonic aerodynamic system was computed via computational fluid dynamic method. By using the snapshots of the unit impulse response, the linear dynamics part of the nonlinear state-space model is identified by using the eigensystem realization algorithm. Then, the nonlinear functions of the state variables and control input are introduced and the coefficient matrices of these nonlinear functions are optimized via the optimization algorithm. As a result, a nonlinear reduced-order aerodynamic model can be obtained. To verify the accuracy of the reduced-order modeling in predicting the transonic aeroelastic behaviors, a three-dimensional wing is selected as the testbed and the aerodynamic forces, transonic flutter computation, and limit-cycle oscillation prediction are implemented as the numerical examples. Moreover, to demonstrate the accuracy of the present reduced-order modeling method in predicting unsteady aerodynamic forces, the numerical results are also compared with other reduced-order modeling method. The numerical results show that the above three dynamic behaviors predicted via the present reduced-order model have a good agreement with the direct fluid-structure interaction method. The comparison proves that the present reduced-order aerodynamic model can be used to predict the transonic aeroelastic behaviors of aircraft with high efficiency.

STUDY ON THE INFLUENCE OF FRICTION AND ROLLING RESISTANCE ON THE GAIT OF PASSIVE DYNAMIC WALKER 1)
Zheng Peng, Wang Qi, Lü Jing, Zheng Xudong
2020, 52(1):  162-170.  doi:10.6052/0459-1879-19-216
Abstract ( 13 )   HTML( 12 )   PDF (13277KB) ( 12 )

In this paper, the influences of friction coefficient and rolling resistance coefficient on the gait of a passive dynamic walker with round feet are studied. Firstly, the normal forces and frictional forces acting on the feet of the passive dynamic walker are described based on a modified Hertz contact model and LuGre friction model, and the rolling friction resistance of the supporting foot during walking was also considered. Secondly, the dynamic equations of the passive dynamic walker are obtained by using Lagrange's equations of the second kind, and the appropriate parameters of LuGre friction model are selected by comparing with the previous studies. Finally, the influence of friction coefficient and rolling resistance coefficient on the gait of passive dynamic walker are simulated and analyzed. It is found that although the change of friction coefficient has little effect on the average speed, stride and the maximum normal contact force at the contact point of the supporting foot, the reduction of friction coefficient will change the gait types, such as periodic doubling motion or chaotic motion. However, the change of the rolling resistance coefficient will lead to a great difference on the average speed, stride and the maximum normal contact force at the contact point of the supporting foot, but it has not been found that the change of rolling resistance coefficient will cause the change of the walker's gait types.

AN INPUT LIMITED REPETITIVE LEARNING CONTROL OF FLEXIBLE-BASE TWO-FLEXIBLE-LINK AND TWO-FLEXIBLE-JOINT SPACE ROBOT WITH INTEGRATION OF MOTION AND VIBRATION 1)
Fu Xiaodong, Chen Li
2020, 52(1):  171-183.  doi:10.6052/0459-1879-19-289
Abstract ( 18 )   HTML( 15 )   PDF (1440KB) ( 15 )

In order to analyze the dynamic simulation and movement control of space robot under the influence of full flexible of base, links and joints, as well as the active vibration suppression of base, links and joints, an input limited repetitive learning controller with integration of motion and vibration is proposed. The design of the algorithm is not based on the system model information. The flexible base and the flexible joints are regarded as linear spring and torsion springs. The flexible links are analyzed by the Eulerian Bernoulli model, and the dynamic equation is established by the Lagrange equation and the assumed mode method. Based on the singular perturbation theory, the model is decomposed into a slow subsystem including the system rigid variables and the link flexible vibration, and a fast subsystem including the base and joint flexible vibration. The corresponding sub controllers are designed for the slow and fast subsystems to form the general controller with joint flexible compensation. For the slow subsystem, an input limited repetitive learning controller is proposed, which is composed of hyperbolic tangent function, saturation function and repetitive learning term. The hyperbolic tangent function and saturation function realize the requirement of limited input torque. The repetitive learning term compensates the periodic system error to complete the gradual stable tracking of the expected trajectory of base attitude and joint. However, in order to suppress the flexible vibration of the links of the slow subsystem, a hybrid trajectory reflecting the flexible vibration of the links and the rigid motion of the system is constructed by using virtual force conception, and an input limited repetitive learning controller on virtual force conception is proposed to ensure the accurate tracking of the trajectory of the base and joint, while actively suppressing the flexible vibration of the links. For the fast subsystem, the linear quadratic optimal control algorithm is used to suppress the flexible vibration of the base and joints. The simulation results show that the controller is suitable for general flexible nonlinear system, meets the requirements of limited input torque, realizes high-precision tracking of periodic signal, effectively suppresses the flexible vibration of base, links and joints, and verifies the feasibility of the algorithm.

RESEARCH ON SPONTANEOUS ACTION POTENTIAL INDUCED BY CHANNEL NOISE IN MORRIS-LECAR SYSTEM 1)
Yang Li, Xianbin Liu
2020, 52(1):  184-195.  doi:10.6052/0459-1879-19-294
Abstract ( 17 )   HTML( 13 )   PDF (5354KB) ( 13 )

There are a growing number of problems in biological physics involving the coupling between a piecewise deterministic dynamical system and a continuous time Markov process, which is more appropriate to be modeled as a stochastic hybrid system than a diffusion process. Specifically, we investigate the spontaneous action potential induced by channel noise in stochastic hybrid Morris-Lecar system without a saddle state both theoretically and numerically in the case of weak noise. The initiation phase of an action potential can be regarded as an event of noise induced escape, for which the optimal paths and then the quasi-potential are computed via an auxiliary Hamiltonian system. Due to the absence of the saddle point, the ghost separatrix is chosen as threshold for studying the transition events from the resting state. Through evaluating the quasi-potential on the threshold, we have found an obvious minimum that acts similarly as a saddle point. Prehistory probability distribution has been performed by improved Monte Carlo simulation, which confirmed the theoretical results for not only the initial phase but also the excitable phase. In addition, the contour line of quasi-potential as another choice of threshold selected by previous researchers has been introduced and their advantages and disadvantages are compared. Finally, the impacts on patterns of optimal paths and quasi-potential about various combinations of Na$^{+}$ and K$^{+}$ channel noise are studied thoroughly. The results shows that it is the fluctuation of K$^{+}$ channel that plays the dominant role in the process of spontaneous excitability and there exists an optimal ratio for the two channel noises which minimizes the fluctuation strength.

Biomechanics, Engineering and Interdiscipliary Mechanics
ANALYTICAL SOLUTION OF FROST HEAVING FORCE IN NON-CIRCULAR COLD REGION TUNNELS 1)
Li Yansong, Chen Shougen
2020, 52(1):  196-207.  doi:10.6052/0459-1879-19-226
Abstract ( 16 )   HTML( 15 )   PDF (2341KB) ( 15 )

A complex variable method is presented of stress and displacement problems for non-circular cold region tunnels. The complex variable method considers the non-circle tunnel support, the frost heaving circle and the unfrozen surrounding rock at the same time, making the problem from the single connected domain to multi connected domain problem, and can not directly apply the classical complex function theory to solve the problem of the stress and displacement of the non-circular tunnel. The analytical formula in Zeta plane orthogonal curvilinear coordinate system of non-circular tunnel lining to frozen surrounding rock to unfrozen surrounding rock system is derived by using classical complex variable method and continuity condition with power series and conformal transformation. Then, the frost heaving force and frost heaving deformation of the non-circular cold region tunnel are obtained by conformal transformation. This complex variable method is applied to Zhegushan tunnel research, and the analytical solution of Zhegushan tunnel openning frost heave stress and frost heave displacement is obtained. Comparing the analytical solution with the numerical solution to verify the correctness of the analytical solution. It can be seen from the results that frost heaving force has an obvious influence on the lining, and the additional circumferential stresses caused by frost heaving at the vault, arch foot and arch bottom are significantly increased. The additional normal stresses caused by frost heaving at the vault and both sides of arch shoulder are significantly increased. Because of the geometric configurations of lining, the frost heaving deformation is uneven, which leads to uneven distribution of frost heaving forces. Compared with previous studies, which consider the frost heaving ring as a single ring, the complex variable method is more practical. And the research results were expected to provide a referenced basis for elasto-plastic analysis of cold-region tunnel.

ADVANCES IN MULTIPHASE SEEPAGE CHARACTERISTICS OF NATURAL GAS HYDRATE SEDIMENTS 1)
Cai Jianchao, Xia Yuxuan, Xu Sai, Tian Haitao
2020, 52(1):  208-223.  doi:10.6052/0459-1879-19-362
Abstract ( 928 )   HTML( 321 )   PDF (899KB) ( 321 )

Natural gas hydrate, as a kind of clean and environmental-friendly energy, has large reserves and attract great attention in recent years. In the past 20 years, exploration and reserves prediction for natural gas hydrate reservoirs have been widely conducted within mainland and offshore areas in China. In 2017, China Geological Survey carried out the tentative production for natural gas hydrate based on depressurizing seepage theory in Shenhu Area of the South China Sea. In worldwide, the hydrate tentative production are faced with the typical problems like low gas production and sand production. One of the main reasons is that the complex mechnisams of multiphase flow in sediments during development are still unclear. In this paper, we review parallel capillary model and Kozeny particle model which are widely used in seepage analysis during natural gas hydrate development. Then we analyze the multiscale simulation methods for hydrate seepage and briefly describe experimental advances in terms of permeability measuremnts, evolutionary process for physical properties of sedimens during seepage and laboratory production simulation for hydrate production. Afterwards, we summarize the numerical simulation methods for gas production during the exploitation of gas hydrate reservoirs at the field scale. Future works and challenges are proposed for multiphase seepage model, in situ testing of hydrate samples, evolutionary process for structural and physical properties, field scale numerical simulation and horizontal well fracturing technology applications.

EXPERIMENTAL STUDIES ON THE PROPAGATION CHARACTERISTICS OF HYDRAULIC FRACTURE IN CLAY HYDRATE SEDIMENT 1)
Yang Liu, Shi Fukun, Zhang Xuhui, Lu Xiaobing
2020, 52(1):  224-234.  doi:10.6052/0459-1879-19-179
Abstract ( 20 )   HTML( 22 )   PDF (29256KB) ( 22 )

Hydraulic fracturing technology is an important oil and gas well stimulation measure, which has been widely used in commercial development of unconventional resources such as shale oil and gas. The propagation characteristics of hydraulic fracture is not well known in hydrate sediment. In this study, the hydrate sediment samples are prepared, and the influencing factors are analyzed. The experimental results show that the breakdown pressure of hydrate sediment sample and hydrate-ice sediment sample is much larger, which is related to the special stress-strain characteristics and water permeability. When the strain of silty sediment is higher than 6%, the strength rises rapidly to present the characteristics of strain hardening. It has a certain hindrance to the expansion of hydraulic tensile fractures. The silty sediment is composed of small particle and characterized by poor permeability. It is difficult for water to rapidly transfer pressure, thereby increasing the breakdown pressure. In addition, there is a significant delay effect on the fracture propagation of silty sediment sample, indicating that the fractures extend under the combined action of fluid pressure and thermal stress. Extending the injection time contributes to heating and decomposing the hydration. The research results are helpful for understanding the propagation law of hydraulic fractures in hydrate sediments. It is of great significance to explore the application of fracturing technology in the development of hydrate sediments.

NUMERICAL CALCULATION OF VORTEX-INDUCED VIBRATION OF REINFORCED THERMOPLASTIC PIPE 1)
Rui Xue, Chen Dongyang, Wang Guoping
2020, 52(1):  235-246.  doi:10.6052/0459-1879-19-312
Abstract ( 15 )   HTML( 13 )   PDF (11010KB) ( 13 )

The dynamic model for efficiently predicting the vibration characteristics and vortex-induced vibration (VIV) response of reinforced thermoplastic pipe (RTP) is established based on Van der Pol wake oscillator model and transfer matrix method for multibody systems (MSTMM). The simulation results are compared with that of ANSYS software and experimental data, which verified the accuracy of the model. The influence of steel joints, top tension, and different inflow distribution on the VIV response of the riser is investigated. The results show that higher flow velocity may excite higher modes. The riser vortex induced vibration is mainly controlled by low-order modes. The steel joints of the riser have less influence on the wet modal of the riser. However, the influence of the VIV amplitude distribution excited by the higher-order modes as dominant vibration modes is greater. The shear flow has a great influence on the VIV amplitude distribution along the axial direction of the riser. The VIV amplitude caused by small energy at low flow velocity is smaller. However, when the shear flow velocity is enough to excite a higher-order mode of the riser, the VIV amplitude is larger than that of the uniform flow at the same flow velocity.

A NEW SOLUTION FOR FRICTIONAL SLIP CONTACT BETWEEN SURROUNDING ROCK AND LINING IN A HYDRAULIC CIRCULAR TUNNEL 1)
Yin Chonglin, Lü Aizhong
2020, 52(1):  247-257.  doi:10.6052/0459-1879-19-238
Abstract ( 23 )   HTML( 7 )   PDF (2696KB) ( 7 )

In practical engineering, when the surrounding rock and the lining contact with each other, the interface between the lining and the surrounding rock mass is not fully smooth, nor can it bear arbitrarily large friction. The tangential sliding will occur on the contact surface between the lining and the surrounding rock when the shear stress on the interface is greater than the maximum static friction. The state of the minimum relative sliding on the interface is considered as the true working state of the lining, and this kind of contact is called frictional slip contact. Coulomb friction model is used to simulate frictional slip contact between the lining and the surrounding rock mass. Under the premise of considering the mechanical process of the support delay, the equations of stress boundary condition, stress continuous condition and displacement continuous condition are listed by the plane elastic complex variable method. Combined with the optimization theory, a general frictional slip contact solution method is established. Furthermore, in the process of solving the optimization problem by the mixed penalty function method, the optimization model is greatly simplified by reducing the number of design variables, the iteration speed of the optimization process and the precision of the optimization results are improved. On this basis, the stress analytic solutions for a lined hydraulic circular tunnel under the interaction of the lining and the surrounding rock are derived. This method can simultaneously solve the two limiting contact cases of pure bond contact and pure slip contact and has generality. At the same time, the threshold of friction coefficient satisfying the pure bond contact under different conditions are obtained by using a precise calculation method. At last, the variation laws of tangential stresses on the boundaries of the lining and the surrounding rock are obtained.

PARTITIONED HYBRID METHOD FOR SOIL-STRUCTURE INTERACTION ANALYSIS OF NUCLEAR POWER STRUCTURE 1)
Chen Shaolin, Guo Qichao, Zhou Guoliang
2020, 52(1):  258-282.  doi:10.6052/0459-1879-19-271
Abstract ( 17 )   HTML( 48 )   PDF (68569KB) ( 48 )

Soil-structure interaction analysis is an important step in seismic design and safety assessment of nuclear power structures. Material damping and non-linearity are important factors affecting the structural response in the analysis of soil-structure dynamic interaction of nuclear power structures. If the frequency-domain method is used, the damping can be easily considered, but the equivalent linearization is needed to consider the non-linearity, which is not suitable for strong earthquakes, The time-step integration method is suitable for considering non-linearity, but Rayleigh damping model is generally used for material damping. Except for a few modes with specified damping ratio, the response of other modes will be restrained by the large damping determined by Rayleigh damping model, which makes the seismic response quite different from the real situation. If the modal superposition method is used, the damping effect can be reasonably taken into account, but the non-linearity can not be taken into account in the modal superposition method. Therefore, how to reasonably consider the damping and non-linearity is an important issue in the soil-structure interaction analysis of nuclear power structures. Considering that the main structure of nuclear power plant is rigid, and it is not easy to enter the non-linearity under earthquake, a new method for soil-structure interaction analysis is proposed in this paper. The modal superposition method is used to structure analysis, and the soil and foundation is analyzed by the explicit time-step integration method, the influence of infinite domain (radiation damping) is considered through artificial boundary conditions. This partitioned algorithm of soil-structure interaction based on modal superposition and time-step integration is realized, and verified by a simple example. Then, the soil-structure interaction analysis of a CAP1400 nuclear power structure is conducted, with the modal damping and Rayleigh damping are adopted respectively. The difference between modal damping and Rayleigh damping on the structure and site response is compared and analyzed. The results show that the structural damping model has little effect on the site response, but has obvious effect on the structure response.

A LANE-CHANGING BML MODEL CONSIDERING THE INFLUENCE OF BOTH LANE INFORMATION AND TURN SIGNALS 1)
Gao Qingfei, Zhang Ji, Sheng Zhe, Dong Liyun
2020, 52(1):  283-291.  doi:10.6052/0459-1879-19-247
Abstract ( 8 )   HTML( 8 )   PDF (1724KB) ( 8 )

The lane-changing behaviors of vehicles are frequently adopted by drivers in order to get better driving conditions and turn signal plays an essential role in guiding vehicles' lane-changing behaviors. In this paper, based on the BML (Biham-Middleton-Levine model ) model, we proposed a lane- changing cellular automata model which takes the influence of both lane information and turn signals into account. When a vehicle cannot move forward, the driver will judge whether the vehicle meets the lane-changing conditions or not. If the driver can change his/her lane, then the lane-changing probability is calculated according to the lane information (such as average velocities and densities of those vehicles in his own and target lanes) and the state of turn signals. Finally, the driver can determine whether he/she changes lane or not by the corresponding probability. Numerical simulations were carried out to investigate the effect of lane-changing behaviors on the phase transition between the free flow phase and the global jamming phase. Two kinds of BML models were studied, one with traffic lights and the other without traffic lights. Numerical results show that the critical density of the BML model without traffic lights increases considerably due to the introduction of lane-changing rules. At a smaller scale, the critical density approximates that of the BML model with traffic light control. The effect of lane change is significant on traffic dynamics. Furthermore, a new coexisting phase of both the free flow phase and the local jamming phase was found. The underlying generation and evolution mechanism of the coexisting phase is discussed in detail. It is shown that the local congestions will result in the global congestion under higher densities. However, the lane-changing rules does not have distinct effect on the critical density of the BML model with traffic lights. But the region of phase transition becomes narrower. It indicates that lane-changing behaviors can lead to variations of local traffic features and take less effect on the global features of traffic system.

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•  RESEARCH PROGRESS IN AUXETIC MATERIALS AND STRUCTURES1) Xin Ren, Xiangyu Zhang, Yimin Xie Chinese Journal of Theoretical and Applied Mechanics. 2019 Vol. 51 (3): 656-689 doi: 10.6052/0459-1879-18-381 Abstract (950)   HTML (63)    PDF (1758KB) (724)
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 ADVANCES IN MULTIPHASE SEEPAGE CHARACTERISTICS OF NATURAL GAS HYDRATE SEDIMENTS 1) Cai Jianchao, Xia Yuxuan, Xu Sai, Tian Haitao Chinese Journal of Theoretical and Applied Mechanics. 2020 Vol. 52 (1): 208-223 doi: 10.6052/0459-1879-19-362 Abstract (928)   HTML (42)    PDF (899KB) (321)
 A REVIEW ON THE DEFORMATION AND FAILURE OF SEALS IN OILFIELD1) Zhengjin Wang, Tiejun Wang Chinese Journal of Theoretical and Applied Mechanics. 2019 Vol. 51 (3): 635-655 doi: 10.6052/0459-1879-19-061 Abstract (714)   HTML (42)    PDF (45847KB) (455)
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 RESEARCH PROGRESS OF PLASMA/MHD FLOW CONTROL IN INLET Yiwen Li, Yutian Wang, Lei Pang, Lianghua Xiao, Zhiwen Ding, Pengzhen Duan Chinese Journal of Theoretical and Applied Mechanics. 2019 Vol. 51 (2): 311-321 doi: 10.6052/0459-1879-18-290 Abstract (380)   HTML (34)    PDF (11997KB) (244)
 RESEARCH ON THE MAGNETO-MECHANICAL EFFECT IN ACTIVE AND PASSIVE MAGNETOSTRICTIVE VIBRATION ISOLATOR Muqing Niu, Bintang Yang, Yikun Yang, Guang Meng, Liqun Chen Chinese Journal of Theoretical and Applied Mechanics. 2019 Vol. 51 (2): 324-332 doi: 10.6052/0459-1879-18-254 Abstract (380)   HTML (21)    PDF (2730KB) (171)
 A GRADIENT SMOOTHING GALERKIN MESHFREE METHOD FOR THIN PLATE ANALYSIS WITH LINEAR BASIS FUNCTION1) Like Deng, Dongdong Wang, Jiarui Wang, Junchao Wu Chinese Journal of Theoretical and Applied Mechanics. 2019 Vol. 51 (3): 690-702 doi: 10.6052/0459-1879-19-004 Abstract (373)   HTML (9)    PDF (12603KB) (155)
 STUDY ON THE INFLUENCE OF COMPRESSIVE STRESS ON THE COMPRESSION SHEAR CRACK PROPAGATION1) Bo Wang, Yangbo Zhang, Hong Zuo, Houjin Wang Chinese Journal of Theoretical and Applied Mechanics. 2019 Vol. 51 (3): 845-851 doi: 10.6052/0459-1879-18-369 Abstract (343)   HTML (8)    PDF (3565KB) (181)
 PATHOGENETIC MECHANISMS OF GLAUCOMA------RESEARCH PROCESS ON THE DEFORMATION OF LAMINA CRIBROSA 1) Zhang Ting, Li Long, Song Fan Chinese Journal of Theoretical and Applied Mechanics. 2019 Vol. 51 (5): 1273-1284 doi: 10.6052/0459-1879-18-321 Abstract (341)   HTML (74)    PDF (21642KB) (372)
 A BRIEF INTRODUCTION OF COMPLETED KEY PROGRAM PROJECTS ON MECHANICS IN 2018 Kuncao Bai, Dongxing Cao, Gang Wang, Tiangang Lei Chinese Journal of Theoretical and Applied Mechanics. 2019 Vol. 51 (3): 965-969 doi: 10.6052/0459-1879-19-097 Abstract (327)   HTML (10)    PDF (171KB) (164)
 A NEW ELASTIC MODEL FOR RUBBER-LIKE MATERIALS Zhigang Wei, Haibo Chen Chinese Journal of Theoretical and Applied Mechanics. 2019 Vol. 51 (2): 473-483 doi: 10.6052/0459-1879-18-303 Abstract (318)   HTML (18)    PDF (5862KB) (130)
 A QUASI-ZERO STIFFNESS VIBRATION ISOLATOR BASED ON HYBRID BISTABLE COMPOSITE LAMINATE Hao Li, Fagang Zhao, Xubin Zhou Chinese Journal of Theoretical and Applied Mechanics. 2019 Vol. 51 (2): 354-363 doi: 10.6052/0459-1879-18-266 Abstract (312)   HTML (9)    PDF (12298KB) (107)
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Former Editors-in-Chief
11th' Editorial Committee

Editor-in-Chief
Wei Yueguang
Editor-in-Chief
Wei Yueguang

Associate Editor-in-Chief
Chen Liqun　　Feng Xiating 　　　 Lu Xiyun
Wang Yuesheng　　　Wang Guangqian