力学学报

2020, 52(6): 1547-1547. doi: 10.6052/0459-1879-20-377

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DYNAMIC MODELING AND STABILITY CONTROL OF FOLDING WING AIRCRAFT

Song Huixin, Jin Lei

During the deformation process, the dynamic modeling of the folding-wing aircraft presents the characteristics of multi-rigid、multi-degree of freedom and strong nonlinearity. At the same time, parameters such as aerodynamics/torque, pressure center, centroid and moment of inertia will also change greatly, which will seriously affect Flight stability. Therefore, this paper will mainly study the multi-rigid dynamics modeling and deformation stability control of the folding wing aircraft. The multi-rigid dynamic model of the folding wing aircraft is established based on the Kane method with the additional force and moment expressions. The functional relationship between the aerodynamic parameters and the folding angle is fitted through aerodynamic calculations. and the longitudinal dynamic characteristics of the aircraft at different folding angular speeds are analyzed. It is shown that the speed, height and pitch angle of the folding wing aircraft will change during the deformation process by analyzing the longitudinal dynamic characteristics, and the aircraft cannot maintain stable flight. A stability control method is proposed for the deformation process of the folding-wing aircraft based on the active disturbance rejection control theory. The nonlinear terms, coupling terms and parameter time-varying terms are regarded as the total internal and external disturbances in the longitudinal nonlinear dynamic model of the folding-wing aircraft, using the extended state observer to estimate and compensate the total disturbance in real time. The PD controller is proposed for compensated systems to realize decoupling control of speed channel and height channel. The stability of the system is proved by Lyapunov stability theory, and mathematical simulation is used to verified the stability of the folding wing aircraft. The simulation results show that the stability controller based on the active disturbance rejection control theory can solve the problems of strong nonlinearity and time-varying parameters caused by aircraft deformation, and ensure the high-precision and stable control of the aircraft.

2020, 52(6): 1548-1559. doi: 10.6052/0459-1879-20-115

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SPACECRAFT EVASION STRATEGY USING ACTIVE MANEUVERS BASED ON MANEUVERING-TARGET ACCELERATION ESTIMATION

Li Haohao, Zhang Jin, Luo Yazhong

With the development of space control technology, the safety of spacecraft in orbit has been paid more and more attention. The autonomous approach of the spacecraft with active maneuverability to the target spacecraft is a serious threat to the safety of the spacecraft in orbit. In the close orbital pursuit-evasion (PE) game of spacecraft, the acquisition of relative position, velocity and acceleration is the basis of the PE game strategy of both sides. In the case of incomplete information acquisition by both sides, an evasion control strategy based on the filtering estimation of maneuvering target and the maximizing line-of-sight yaw rate is proposed. The escaper obtains navigation information such as the relative position, velocity, and acceleration of the chaser based on the current statistical model filtering algorithm, and the chaser obtains navigation information of the escaper also based on the current statistical model filtering algorithm. The chaser uses the proportional guidance law to approach the escaper autonomously. The escaper calculates the line-of-sight direction and line-of-sight yaw rate relative to the chaser, and uses an active evasion strategy based on maximizing the line-of-sight yaw rate to escape. The different evasion strategies and different operating conditions are simulated. The results show that when the maneuverability of the escaper reaches more than 60% of the chaser, the escaper can escape successfully by using the proposed evasion strategy; the evasion strategy is not sensitive to the measurement accuracy and operating frequency of observation equipment, and the effect of evasion strategy is related to the response time, the earlier the escaper receives the warning information, the better the evasion strategy will be.

2020, 52(6): 1560-1568. doi: 10.6052/0459-1879-20-113

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DYNAMICS AND CONTROL OF RIGID-FLEXIBLE COUPLING FLEXIBLE SPACECRAFT WITH JOINT CLEARANCE

Sun Jie, Sun Jun, Liu Fucheng, Zhu Dongfang, Huang Jing

There are still lots of joint clearances that cannot be eliminated for large-scale flexible spacecraft in post-lock phase. Joint clearance directly affects the attitude maneuver of the flexible spacecraft as well as the pointing accuracy and stability of the payload, which has a great influence on the dynamic characteristics of the spacecraft. Aiming at this issue, a dynamic modelling and control method for the rigid-flexible coupling spacecraft with joint clearance is proposed in this paper. The accurate dynamic model of the joint with clearance is established firstly, thus the dynamic model of flexible structure with joint clearances is built. Then the discrete rigid-flexible coupling nonlinear dynamic model of the spacecraft with clearances is obtained by Hamilton principle and modal discrete method. The Newmark algorithm is used to solve the nonlinear equation. Based on macro fiber composite (MFC) actuator, the rigid-flexible-electrical coupling dynamic equation of the spacecraft is obtained and the control law is designed by the optimum control. The influences of joint parameters, moment of inertia of central rigid body, clearance size and clearance number on the dynamic characteristics of the spacecraft are analyzed. The effects of joint clearance on the attitude maneuver and structural vibration of the spacecraft are emphatically studied. Finally, the active control is applied to the spacecraft using MFC actuator. The results reveal that the joint parameters and moment of inertia of the central rigid body affect the natural frequency of the spacecraft. With the increase of the size of joint clearance and number of clearances, the overall stiffness of the spacecraft decreases gradually, while the attitude angle and vibration displacement response of the spacecraft increase. Through the active control based on MFC, the cooperative control of the attitude maneuver and structural vibration of the spacecraft with clearance can be realized, and the effects of clearance on the dynamic characteristics of the spacecraft can be alleviated.

2020, 52(6): 1569-1580. doi: 10.6052/0459-1879-20-109

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A COLLISION-AVOIDANCE CONTROL ALGORITHM FOR SPACECRAFT PROXIMITY OPERATIONS BASED ON IMPROVED ARTIFICIAL POTENTIAL FUNCTION

Xu D, an

Aiming at the proximity operation of spacecraft, a collision-avoidance control algorithm based on improved Artificial Potential Fields (APF) method is proposed. According to the real-time state between the spacecraft and the target and obstacles, the APF method is used to calculate the real-time acceleration of the spacecraft, and the trajectory of the spacecraft is planned. In order to improve the applicability of the artificial potential function method, three improvement measures are proposed. First, in order to improve the accuracy of collision warning and reduce additional maneuvers, the collision probability combined with the relative distance, instead of only the relative distance, is used to evaluate the collision. Second, in order to increase the docking safety and slow down the approaching relative velocity, the safety boundary and control margin of relative velocity are used to calculate the target repulsion force. Third, in view of the fact that most spacecraft cannot provide any continuously varying thrust, two practical thrust forms, including the thrust with upper limit and constant variation rate and the bang-bang thrust, are used to substitute for the continuously variable thrust form. Numerical simulations are executed to validate the proposed method. The effects of the major mission parameters, such as the collision warning method, the target repulsion acceleration and acceleration forms, are successfully revealed by the comparison between different examples. The results show that the proposed method can improve the safety and efficiency of the spacecraft proximity operations, and has simple structure and strong real-time performance.

2020, 52(6): 1581-1589. doi: 10.6052/0459-1879-20-112

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DYNAMIC SIMULATION ANALYSIS OF CAPTURE AND BUFFER SYSTEM BASED ON CLAW-TYPE DOCKING MECHANISM

Shen Tao, Zhang Chongfeng, Wang Weijun, Feng Wenbo, Qiu Huayong

The existing docking mechanism for on-orbit service cannot provide strong support for our country's follow-up lunar exploration project due to its large size, complex structure and single docking target. Lightweight docking mechanism is also an essential link due to the limit of carrying capacity. In order to study the docking mechanism that can serve the high-orbit missions such as future Moon Space Station and manned lunar landing, a new claw-type docking mechanism was designed, which adopted androgynous configuration and can realize the interchange between active vehicle and passive vehicle, the V-shaped slot and claw hook and other structural components are used to realize the capture and energy consumption functions in the docking process of aircraft, so as to realize the stable connection between two vehicles. The docking mechanism has the advantages of small size, light weight, simple structure and easy realization of functions. The dynamic analysis of the capture buffer system was carried out, and the influence of the parameters of buffer components on its capture performance was calculated, the establishment of the digital virtual prototype was completed in ADAMS software, and the simulation research was carried out in combination with the actual two typical initial docking conditions. The results show that the energy consumption in the docking process under the two working conditions meets the design requirements, and the capture can be completed with a smaller impact force of the V-shaped slot. The results prove the feasibility of the capture buffer system, and verify the capability of the docking mechanism with this configuration has better ability to complete tasks.

2020, 52(6): 1590-1598. doi: 10.6052/0459-1879-20-108

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ATTITUDE CONTROL TECHNOLOGY FOR MASS MOMENT NANO-SATELLITE IN LOW EARTH ORBIT

Hu Yu, , Lu Zhengliang

Due to the high aero to inertia ratio and the presence of strong aerodynamic forces, the low Earth orbit nanosatellites are not very appropriate to depend on a set of momentum wheels for attitude controlling. A method of utilizing aerodynamic disturbance torque as control input based on mass moment technology is innovatively proposed for the Nano-satellite in the low Earth orbit to solve the problem of the external aerodynamic force. The exclusive use of moving mass actuator would lead to an underactuated as the aerodynamic torque was perpendicular to the relative flow vector. To achieve full three-axis stabilization, a three-axis magnetorquer is used to complement the moving mass system to generate a torque along the orbital velocity. The whole dynamic equations are derived, which describes the system with two actuators, the movable mass and the magnetorquer, actuating simultaneously. According to the influence of disturbance items, the equations are simplified. Considering the uncertainty of the aerodynamic forces, the error of system parameters, and unknown environmental disturbance, a sliding mode control scheme based on disturbance observer is designed for ideal control input. An optimal torque allocation strategy is designed in order to generate the torque determined by the aforementioned nonlinear control law by moving the masses and commanding the magnetotorquer, and therefore combining the subspace of two actuators. Finally, a semi-physical simulation platform was built for two actuators and the results indicate that, additional inertia torque, related to the mass acceleration, is the main disturbance torque during the attitude maneuver and can be significantly reduced by optimal torque decomposition strategy. Meanwhile, during the attitude maintenance, the disturbance observer can effectively observe the system disturbances and improve the attitude control accuracy. The error of attitude angle is less than $\pm $0.1$^\circ$. The results verify the feasibility of the use of the moving mass actuator to actively control the aerodynamic torque.

2020, 52(6): 1599-1609. doi: 10.6052/0459-1879-20-116

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FAST OPTIMIZATION METHOD OF REENTRY TRAJECTORY CONSIDERING AERODYNAMIC PARAMETER PERTURBATION

Yang Ben, Lei Jianchang, Wang Yuhang

In view of the limitations of the traditional reentry trajectory optimization method, which has slow convergence speed and high sensitivity to initial values, a fast algorithm for reentry trajectory based on sequential convex optimization is proposed. The method takes the change rate of inclination angle as the control variable which improves existing convex strategy and uses B-spline curve to discretize the control variable, which can effectively suppress the sawtooth phenomenon in the process of numerical optimization due to the numerical discrete method. At the same time, to avoid the problem that the algorithm appears pseudo-infeasible near the initial guess value, additional virtual control and a "backtracking straight line" search method are added to improve the stability of the algorithm, these can improve the stability, rapidity and smoothness of the algorithm. In order to study the aerodynamic parameter perturbation in the reentry process of aircraft, a generalized polynomial chaotic theory research method with few sampling points, easy implementation and high computational efficiency is proposed. A robust optimization model of reentry trajectory based on the combination of generalized polynomial chaos and convex optimization is established. The model considers the effect of aerodynamic parameter disturbance on the optimization results during the optimization process, which can avoid the complex iterative design of conventional trajectory and guidance law. What's more, it can effectively reduce the sensitivity of optimal trajectory to aerodynamic parameter perturbation, and under the disturbance of uncertain aerodynamic parameters, which still can ensure the safety of the aircraft smooth completion of the mission. At the end,taking the reentry mission of a reusable aircraft in the United States as an example, the rapidity of reentry trajectory optimization method based on sequence convex optimization and the anti-interference ability of robust optimization model to aerodynamic parameter perturbation are verified and it shows that this method has certain engineering application.

2020, 52(6): 1610-1620. doi: 10.6052/0459-1879-20-117

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AN ALGORITHM FOR SOLVING SPACECRAFT REACHABLE DOMAIN WITH SINGLE-IMPULSE MANEUVERING

Du Xiangnan, Yang Zhen

The spacecraft reachable domain (RD) is an effective method to present the possible position boundary of a spacecraft in a future time, which is of great significance for maintaining the safety of spacecraft and improving the ability of space situational awareness. However, previous research efforts on solving RD still have some disadvantages, e.g. some RD models are relatively complicated, and some other solving methods are highly sensitive to the initial values thus result in poor computational accuracy. Therefore, it is necessary to develop a more concise and efficient RD solving algorithm. This paper develops an innovative model to solve the RD based on the extremum condition of the predicted position vector, in the pericenter coordinate frame. First, a vector description method is defined to express the spatial orientation and the criterion of accessibility for an arbitrarily given position vector. Second, the maneuvering azimuth angle in the transfer-orbit plane is used to transform the reachable domain problem to the univariate extreme value problem, at the current accessible position vector. The value of the maneuvering azimuth is determined by considering that the gradient of the describing function at the surface of RD envelope is zero, following this, the maneuvering reachable domain of the spacecraft with a single impulse can be obtained. In addition, the symmetry of the RD envelope under two-body dynamical assumption is used to reduce the computational complexity. Finally, the RD solving algorithm proposed in this paper is verified by Monte Carlo simulation. The numerical results show that the new RD algorithm proposed in this paper provides good agreement with the Monte Carlo simulation on computational accuracy. Moreover, the new RD algorithm is more concise and more accurate than the existing RD solving methods.

2020, 52(6): 1621-1631. doi: 10.6052/0459-1879-20-111

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EXPERIMENTAL STUDY ON PROPERTIES OF TURBULENT/NON-TURBULENT INTERFACE OVER RIBLETS SURFACES AT LOW REYNOLDS NUMBERS

Li Sicheng, Wu Di, Cui Guangyao, Wang Jinjun

The turbulent/non-turbulent(T/NT) interface usually refers to the thin layer that separates turbulent flow from irrotational flow. The research of T/NT interface is of great importance to deepen the understanding of matter, momentum and energy transfer between the turbulent and irrotational flow. The geometrical and dynamical properties of the T/NT interface at different Reynolds numbers over smooth and riblets surfaces with zero-pressure-gradient at different Reynolds numbers are experimentally investigated using two-dimensional time-resolved particle image velocimetry (2D-TRPIV). The Reynolds number range is about $Re_{\tau } \approx $ 400 $\sim$ 1000 in the present experiment. The T/NT interface is detected with the turbulent kinetic energy criterion. The probability density function of the interface position, fractal characteristics and the conditional averaged velocity and vorticity near the interface are analyzed. It is shown that the mean heights of the interfaces are around 0.8 $\sim$ 0.9$\delta_{99} $ under different Reynolds numbers for both smooth and riblets surfaces. The probability density function of the interface position over drag reduction riblets surface is kept the same with the smooth surface, whose distribution agrees well with normal distribution. While for the drag increment riblets surface, the distribution of interface position deviates from the normal distribution and presents positive skewness. The fractal dimension of the interface and the velocity jump across the interface will gradually increase with the Reynolds number under the present experiment condition. Moreover, the dimensionless conditional averaged vorticities have similar distributions in the vicinity of the interface over both smooth and riblets surfaces when $Re_{\tau } $ is less than 1000, correspondingly, the maximum gradient of dimensionless conditional average streamwise velocity is approximately constant.

2020, 52(6): 1632-1644. doi: 10.6052/0459-1879-20-211

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DIRECT NUMERICAL SIMULATIONS ON THE TURBULENT FLOW PAST A CONFINED CIRCULAR CYLINDER WITH THE INFLUENCE OF THE STREAMWISE MAGNETIC FIELDS

Hao Le, Chen Long, Ni Mingjiu

The flow around a cylinder is a typical flow pattern in the liquid metal blanket in Tokomak fusion device, which reveals significant influence on the relevant flow and heat transfer. In the present work, three-dimensional direct numerical simulations (DNSs) are performed to study the turbulent flows past a circular cylinder at $Re=3900$ under magnetic fields. For the case without magnetic fields, the DNS results are in good agreement with the available experimental and numerical results. With the increase of the flow distance in the downstream wake of the cylinder, the mean streamwise velocity profile varies from U-shaped to V-shaped and flattens out, indicating that the influence of cylinder on the flow structures weakens gradually. Within the shear layers, because of the Kelvin-Helmholtz instability, the shedding of the small-scale shear vortices can be observed clearly through the flow visualization. Taking the results of non-magnetic field as the initial condition, the magnetic fields along the streamwise direction are applied, where the corresponding Hartmann numbers (Ha) are 20, 40 and 80. When the magnetic field is weak, the three-dimensional turbulent properties are still clear, although the magnetic field inhibits the velocity field. As the magnetic field increases, the recirculation zone behind the cylinder is elongated. The shear layers near the cylinder become smoother and the corresponding destabilizing position shift downstream. Since the vortices in the wake are squeezed by Lorentz force in the vertical direction, the Karman vortex street gradually gets narrow with the increase of magnetic field. Meanwhile, the scale of the vortex structures becomes smaller compared with those without magnetic fields because of the dissipation effect of magnetic fields. This research not only extends the parameter range of turbulence under magnetic fields, but also shows important theoretical guiding value and engineering application value for the design and safe operation of the blanket.

2020, 52(6): 1645-1654. doi: 10.6052/0459-1879-20-217

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INTERFACE EVOLUTIONS AND GROWTH PREDICTIONS OF MIXING ZONE ON PREMIXED FLAME INTERFACE DURING RM INSTABILITY

Wang Yang, Dong Gang

Growth of mixing zone on premixed flame interface induced by Richtmyer-Meshkov (RM) instability occurs frequently in natural phenomena and in engineering applications. The effect of chemical reaction on the growth mechanism of mixing zone on the interface still remains unknown, and the predictions on growth rate of mixing zone on reactive interface were seldom reported. Therefore, it is necessary to study the interface evolutions and the predictions of mixing zone on the premixed flame interface during the RM instability. The present study adopted the Navier-Stokes equations with a single-step reaction and the computational scheme with high resolutions to numerically research the RM instability of flame interface with sinusoidal pattern, induced by a planar incident shock wave and its reflected shock wave. The results in present study show that during the stage after the passage of incident shock wave, besides the RM instability mechanism which leads to the "spike-cap" and "bubble" structures of the interface, the chemical reaction not only promotes the "bubble" structure growth in the form the premixed flame propagation, but also gives rise to the growth of "spike-cap" structure through the interaction with vortices structure. The more reactive the premixed gases, the rapider the growth for both "spike-cap" and "bubble" structures. The results also show that during the stage after the passage of first reflected shock wave, the chemical reaction has the same effects on the developments of both "spike-cap" and "bubble" structures in the mode of premixed flame propagation. The counteraction between both effects results in the independence of mixing zone growth on the chemical reaction. Based on above analyses, the predicted models for the stages after passages of incident shock wave and reflected shock wave are proposed, respectively, in order to provide a useful method for predictions of mixing zone growth during the reactive RM instability.

2020, 52(6): 1655-1665. doi: 10.6052/0459-1879-20-278

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EXPERIMENTAL STUDY ON QUANTITATIVE MEASUREMENT OF THREE-DIMENSIONAL STRUCTURE OF HAIRPIN VORTEX BY STEREO-PIV

Tian Haiping, Yi Xingrui, Zhong Shan, Jiang Nan, Zhang Shanying

Hairpin vortex is one of the most concerned paradigm in the study of turbulent coherent structures. The quantitative experimental measurement and hydrodynamic analysis of the three-dimensional hairpin vortex structures~is of great significance for further~applications in the turbulent flow control.~In this study, with an optimized arrangement of the synthetic jet device, a~series of~regular artificial hairpin vortex structures~are~produced in the laminar boundary layer, and then the three-dimensional shapes of~hairpin vortex structures are quantitatively revealed by stereoscopic particle image velocimetry (Stereo-PIV) using phase-locking technique. The three-dimensional flow field of the hairpin vortex within a complete period is obtained. The quality of the reconstructed three-dimensional hairpin vortex structure is reliable. The results are in line with the general knowledge of hairpin vortex, low/high~speed streaks and~ejection/sweeping~events. In addition, we acquire a more detailed understanding of the near-wall secondary vortex, the spanwise~vortex head and the area of strong shear in the spanwise~vorticity~concentration region, and the convergent/divergent flow related to the ejection~event. We also discuss the reconstruction of the three-dimensional flow field of hairpin vortice based on the fluctuating characteristics of two-dimensional flow field. It provides an idea for the quantitative study of wall turbulence coherent structure in the formation and evolution of the hairpin vortex structure, the fusion of adjacent vortex structures and the secondary induced vortex.

2020, 52(6): 1666-1677. doi: 10.6052/0459-1879-20-203

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NUMERICAL STUDY ON DYNAMIC STALL FLOW CONTROL FOR WIND TURBINE AIRFOIL USING PLASMA ACTUATOR

Zhang Weiguo, Shi Zheyu, Li Guoqiang, Yang Yongdong, Huang Minqi, Bai Yunmao

In order to solve the problem of aerodynamic performance deterioration caused by dynamic stall, based on the dynamic grid and sliding grid technology, the large eddy simulation numerical calculation is carried out, and the dynamic flow control mechanism of unsteady pulsed plasma is explored. The results show that the plasma aerodynamic actuator can effectively control the airfoil dynamic stall, improve the mean and transient aerodynamic forces, and reduce the negative peak value of the pitch moment and the area of the hysteresis loop. The negative pressure "bulge" appears in the plasma application areas, and the peak suction of the upper airfoil surface increases obviously. The two unsteady control parameters, pulsed frequency and duty cycle, have significant influence on the flow control. When the dimensionless pulsed frequency is 1.5, the plasma control effect is better, and when the duty cycle is 0.8, it is close to the aerodynamic benefits under the continuous working mode. In the deep stall state: the plasma impels the flow separation position to move backward obviously, which resists the occurrence of large-scale dynamic stall vortices. The structure of the separation vortices is broken, dissipated and reattached to the airfoil by the plasma, and the influence area of the vortices is reduced. In the light stall state: the plasma actuator has strong ability to control the shear layer, which induces the transition of the airfoil boundary layer in advance and promotes the momentum mixing with the main flow. The "vortex clusters" near the airfoil leading edge induced by plasma actuation play a role of virtual aerodynamic shape. The harmonic oscillation of aerodynamic force / moment is caused by the nonlinear and strong coupling effect between the dynamic vortex structure with different scales and frequencies and the plasma aerodynamic actuation.

2020, 52(6): 1678-1689. doi: 10.6052/0459-1879-20-090

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A DYNAMIC RESPONSE PREDICTION MODEL OF FIBER-METAL HYBRID LAMINATED PLATES EMBEDDED WITH VISCOELASTIC DAMPING CORE UNDER LOW-VELOCITY IMPACT EXCITATION

Li Zelin, Li Hui, Wang Dongsheng, Ren Chaohui, Zu Xudong, Zhou Jin, Guan Zhongwei, Wang Xiangping

A dynamic response prediction model of fiber-metal hybrid laminated plates embedded with a viscoelastic damping core under low-velocity impact excitation is established analytically for the first time in this research. Firstly, based on the classical laminates theory and von Kármán theory, the constitutive relation of elastic damage of fiber-metal hybrid laminated plates embedded with a viscoelastic damping core is established. Then, the deformation of laminated plates under impact is divided into contact and stretching areas. Within the contact areas, Von Mises failure criteria are used for metal layers, Tsay-Hill failure criteria for fiber layers and Drucker-Prager failure criteria for viscoelastic layer to determine the damage of laminated plates. Considering the contribution of different material layers to the dynamic response subjected to the impact load for modifying the displacement formula, the theoretical solutions of energy, displacement and impact contact force in each layer of such laminated plates are obtained after each failure event occurs, and gives the flow chart of structure dynamic response analysis of concrete. Finally, a TA2 titanium alloy and T300 fiber/epoxy hybrid plate embedded with the Zn33 viscoelastic core is taken as the research object to carry out the drop-weight impact test. The theoretical prediction results of the impact contact force, displacement response, and impact load-displacement curve are found to agree well with the measured ones. Besides, the maximum calculation errors of the concerned peaks are less than 9%. Thus, the effectiveness of the proposed theoretical model has been verified.

2020, 52(6): 1690-1699. doi: 10.6052/0459-1879-20-165

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PIEZORESISTIVE SENSING MECHANISM AND PIEZORESISTIVE PERFORMANCE OF IN-PLANE RANDOM STACKED GRAPHENE COMPOSITES

Li Zheng, Yang Qingsheng, Shang Junjun, Liu Xia

Many experimental researches on the in-plane random stacked graphene composites (GC) for wearable sensors have been carried out. Due to the limitation of experimental technology, its piezoresistive sensing mechanism and piezoresistive performance are still an open problem. Based on the microstructure characteristics of GC, the position and direction of graphene flakes in GC are determined by the uniformly distributed random numbers between 0 and 1, and a novel two-dimensional GC model is established. According to the uniform deformation characteristics of GC, the finite element method for piezoresistive performance of GC is developed. The relative resistance, gauge factor, morphology of graphene flakes and current density contour of GC are obtained. By connecting them, it is revealed that the substantial cause of piezoresistive effect is the change of graphene flakes density and the specific reason is the variation of the electron migration pathway and the invalid flakes number. The increase of the length of electron migration pathway caused by the relative sliding of overlapped graphene flakes leads to the linear sensing characteristics, while the cut of the number of electron migration pathway and the increase in the number of invalid flakes induced by the separation of graphene flakes bring about the non-linear sensing effect. In addition, the results show that GC with high area fraction and GC with large-scale graphene flakes have a large sensing range, while GC with low area fraction and GC with small-scale graphene flakes have a higher gauge factor. Finally, the in-plane resistivity of contact surface of overlapped graphene flakes is assumed as a function of strain and the influence of contact resistance on piezoresistive effect of the GC is investigated, to understand the mechanism of the GC piezoresistive performance. These results can contribute to the improvement or innovation of GC fabrication method and the production of the GC piezoresistive sensing devices for expected sensing performance.

2020, 52(6): 1700-1708. doi: 10.6052/0459-1879-20-197

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ORIGIN OF HEAT EFFECTS AND SHEAR MODULUS CHANGES OF A Cu-BASED AMORPHOUS ALLOY

Zhang Langting, Vitaly A Khonik, Qiao Jichao

Shear modulus is one of important parameters to control the viscous flow, diffusion and structural relaxation of amorphous alloy. Macroscopic shear elasticity determines the change of heat flow. The correlation between the mechanical properties and the heat flow during the structural relaxation and glass transition is one of the important issues to understand the origin of mechanical properties of amorphous alloy. In the framework of the interstitialcy theory, the shear modulus, heat flow and viscosity of Cu$_{49}$Hf$_{42}$Al$_{9}$ amorphous alloy were used to probe the correlation between shear modulus and heat flow. In parallel, evolution of interstitialcy defects concentration was determined by shear modulus in initial and relaxed states. From the perspective of energy, the influence of interstitialcy defects concentration on the thermodynamic properties of amorphous alloy was investigated by activation energy spectrum (AES). Dynamic mechanical analysis (DMA) was used to investigate the dynamic mechanical process of the Cu$_{49}$Hf$_{42}$Al$_{9 }$ amorphous alloy. Structural relaxation induced by physical aging and the evolution of internal friction in-situ annealing was discussed. The results demonstrated that interstitialcy theory could accurately describe the relaxation kinetics, shear softening and other phenomena induced by structural relaxation of amorphous alloy. Temperature dependence of the shear modulus in initial and relaxed states can be well predicted by the data of differential scanning calorimetry (DSC). Activation energy spectrum directly reflects the interstitialcy defects concentration, which can be activated per unit activation energy. Structural relaxation leads to a reduction of the defect concentration, which indicates the structure transforms to a more stable state. During the glass transition process, defect concentration rapidly increases, which corresponds to the shear softening accompanied by heat absorption. Structural relaxation induces decrease of both internal friction and atomic mobility of amorphous alloy. However, the atomic mobility is high enough to eliminate the influence of structural relaxation on defect concentration in the supercooled liquid region.

2020, 52(6): 1709-1718. doi: 10.6052/0459-1879-20-233

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THEORETICAL NONLINEAR ANALYSIS OF A BIOMIMETIC TUNABLE LENS DRIVEN BY DIELECTRIC ELASTOMER

Shi Huiqi, Wang Huiming

Dielectric elastomer (DE) is a class of electroactive polymer smart materials. Under the external electric field, it can produce various forms of responses. Comparing with the traditional lens with which the focus length is manipulated by the mechanical controls, the DE soft tunable lenses exhibit the distinct advantages in the tuning way of the focal length. The DE soft tunable lenses tune the focal length by mimicking the eyeball of human beings. The lens is composed of two circular DE films which are fixed on the rigid frame. The salty water is filled in the enclosed space and forms a convex lens. The top DE film is coated by the annular compliant electrodes. Under the voltage excitation, the upper film is deformed. Accordingly, the lower film is deformed due to the incompressibility of the salt water sealed in the enclosed space. Subsequently, the focal length of the tunable lens is changed. By employing the variational principle and the neo-Hookean model, we obtain the governing equations, boundary conditions and the continuity conditions of the biomimetic lens when driven by the dielectric elastomers. The nonlinear governing equations are solved by the shooting method and the continuity conditions at the interface are treated with in an effective way. The theoretical results agree well with the experimental data. The extensive parametric analysis is carried out based on the presented model. The numerical results show that the geometrical configuration, the initial focal length, the area of the coated annular compliant electrodes, the pre-stretch of the top DE film and the shear modulus of the bottom film have significant effect on the adjusting performance of the tunable lens. The presented theoretical model provides an effective tool in designing and optimizing the biomimetic adaptive focus lens.

2020, 52(6): 1719-1729. doi: 10.6052/0459-1879-20-212

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DYNAMICS ANALYSIS OF STOCHASTIC SPATIAL FLEXIBLE MULTIBODY SYSTEM

Guo Xiang, Jin Yanfei, Tian Qiang

Flexible multibody systems with light weight and high precision are widely used in practical engineering. The structural parameters (physical parameters and geometric parameters) of the flexible multibody system show randomness due to the existence of many uncertain factors such as actual design tolerance, manufacturing error and environmental temperature. The dynamic model with random structural parameters can objectively reflect the dynamic behavior of the real system, and the influence of the uncertainty of structural parameters on the dynamic response of the spatial flexible multibody system cannot be ignored. A non-intrusive calculation method is proposed based on the generalized-alpha algorithm to study the dynamic response of stochastic spatial flexible multibody system with multiple random parameters. The absolute node coordinate formulation (ANCF) is used to describe the flexible body, and the dynamic model of multibody system is established. The polynomial chaos expansion (PCE) method is used to construct the surrogate model of the stochastic dynamics equation of the system. Then, the stochastic response surface method (SRSM) is embedded into the generalized-alpha method. The regression method of improved sampling (RMIS) and the monomial cubature rules (MCR) are used to determine the sample points respectively. The numerical results are compared with those of Monte Carlo simulation (MCS), and the validity of the proposed algorithm is verified. Under the condition of the same definite integral precision, the calculation results of sample points determined by the monomial cubature rules are more stable and the calculation efficiency is higher.

2020, 52(6): 1730-1742. doi: 10.6052/0459-1879-20-273

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DYNAMICAL ANALYSIS ON A KIND OF SEMI-ACTIVE VIBRATION ISOLATION SYSTEMS WITH DAMPING CONTROL

Zhang Wanjie, Niu Jiangchuan, Shen Yongjun, Yang Shaopu, Wang Li

A series of single-degree-of-freedom semi-active nonlinear vibration isolation system with cubic stiffness based on relative velocity feedback on-off control is studied. By using the averaging method, the approximate analytical solutions of the primary resonance of the system are obtained, which is controlled by the acceleration and relative velocity based acceleration drive damping control, the velocity and relative velocity based sky-hook damping control, and the displacement and relative velocity based ground-hook damping control, respectively. A further comparison between the numerical solutions and the approximate analytical solutions under different control strategies is fulfilled. And such comparison results suggest that the approximate analytical results are quite consistent with the numerical solutions, which verifies the effectiveness of the approximate analytical solutions. Moreover, the stability conditions of the steady-state solution of the system under different control strategies are analyzed by Lyapunov theory, and the influences of system parameters on the control effect are discussed. In order to compare the control performances in the three different control approaches, the amplitude-frequency response equation is conducted. The results show that the similar expressions can be found in the switching conditions in the process of the analytical analysis of the three relative velocity feedback control strategies. In the aspect of suppressing resonance response amplitude, the sky-hook damping control strategy based on velocity and relative velocity feedback has the best damping effect in low frequency band, while the acceleration drive damping control strategy based on acceleration and relative velocity feedback has the best damping effect in high frequency band. The sky-hook damping control strategy also shows good performance in reducing the amplitude response of transient response. This analytical research method can also be applied to the system with other semi-active on-off control strategies, and it provides an effective way for the control strategy research of semi-active vibration isolation system.

2020, 52(6): 1743-1754. doi: 10.6052/0459-1879-20-147

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KINETICS ANALYSIS OF NON-SMOOTH VIBRATION-DRIVEN SYSTEM WITH THREE-PHASE CONTROL

Zhu Shihui, Zhou Zhen, Lü Jing, Wang Qi

Mobile robot has become an important branch in the domain of robotics. In order to achieve its movement in some narrow and special environments, the vibration-driven system has been proposed and researched by domestic and foreign scholars. In this paper, such a vibration-driven system consisting of an external rigid box and two internal mass blocks which are driven by three-phase control on two parallel orbits is researched. And the box is always in contact with the rough ground via three rigid support elements. This kind of vibration-driven system has simple structure, good sealing performance, and relies on the friction force between the box and the rough ground to realize its directional movement. Based on the two-dimensional LuGre friction model and Lagrange equations of the second kind, the dynamic modeling method and numerical algorithm of the vibration-driven system are presented in an isotropic friction environment. The use of the two-dimensional LuGre friction model can effectively avoid the difficulty of solving the dynamic equations caused by the discontinuity of the Coulomb friction model, and can accurately reveal the stick-slip switching phenomenon during the movement of vibration-driven systems. The numerical simulation results show that the driving parameters of the internal mass blocks can be adjusted to realize rectilinear translation, rotation about a fixed-axis and general plane motion of the rigid box. And four types of stick-slip motion with different sliding regions can occur during the translation and rotation of the rigid box, such as grazing sliding, crossing sliding, switching sliding and no stick. In addition, the translational speed and rotational speed of the box body and the radius of curvature of the box centroid trajectory can be changed by adjusting the driving parameters.

2020, 52(6): 1755-1764. doi: 10.6052/0459-1879-20-177

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NOETHER QUASI-SYMMETRY AND APPROXIMATE NOETHER CONSERVATION LAWS FOR WEAKLY NONLINEAR DYNAMICAL EQUATIONS

Zhang Yi

There are a lot of nonlinear problems in nature and engineering technology, which need to be described by nonlinear differential equations. Conservation laws play an important role in solving, reducing and qualitative analysis of differential equations. Therefore, it is of great significance to study the approximate conservation laws of nonlinear dynamical equations. In this paper, we apply the Noether symmetry method to the study of approximate conservation laws of weakly nonlinear dynamical equations. Firstly, the weakly nonlinear dynamical equations are transformed into the Lagrange equations of general holonomic system. Under the Lagrangian framework, the definition of Noether quasi-symmetry and the generalized Noether identities are established, and the approximate Noether conservation laws are obtained. Secondly, the weakly nonlinear dynamical equations are transformed into the Hamilton equations of general holonomic system in phase space. Under the Hamiltonian framework, the definition of Noether quasi-symmetry and the generalized Noether identities are established, and the approximate Noether conservation laws are obtained. Thirdly, the weakly nonlinear dynamical equations are transformed into the generalized Birkhoff's equations. Under the Birkhoffian framework, the definition of Noether quasi-symmetry and the generalized Noether identities are established, and the approximate Noether conservation laws are obtained. Finally, taking the famous Van der Pol equation, the Duffing equation and the weakly nonlinear coupled oscillators as examples, the computation of Noether quasi-symmetries and approximate conservation laws for weakly nonlinear systems under three different frameworks is analyzed. The results show that the same weakly nonlinear dynamical equation can be reduced to different general holonomic systems or different generalized Birkhoff systems. The result under the Hamiltonian framework is a special case of the Birkhoffian framework, while the result under the Lagrangian framework is equivalent to that under the Hamiltonian framework. Using Noether symmetry method to find approximate conservation laws of weakly nonlinear dynamical equations is not only convenient and effective, but also has great flexibility.

2020, 52(6): 1765-1773. doi: 10.6052/0459-1879-20-242

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HOVERING ORBITS DESIGN FOR PERTURBED ASTEROIDS WITH PARAMETRIC EXCITATION RESONANCE

Si Zhen, Qian Yingjing, Yang Xiaodong, Zhang Wei

In this paper, the solar gravitational perturbation is considered as a part of the asteroid system instead of treating it as perturbation. Based on the concept of parametric excitation resonance in nonlinear vibration theory, a novel stable parametric resonance orbit near the equilibrium point is designed. In order to consider the gravitational field of an irregular asteroid and the gravitational force of the Sun, the perturbed particle-linkage model is adopted. By analyzing the equilibrium points and the natural frequencies of the unperturbed system, the preconditions that the parametric resonance periodic orbit can exist are given. Taking the second principal resonance and 1:3 internal resonance as examples, the steady-state solutions of parametric resonance orbit are obtained by using multi-scale method. The stability of the steady-state solution is determined. The nonlinear dynamic behaviors of the system are analyzed by the amplitude-frequency response curve. In addition, parametric excitation effect caused by solar gravitational perturbation and the energy transfer phenomenon between long and short periodic motions are analyzed. The proposed method of this paper can expand the existing periodic orbit families near asteroids.

2020, 52(6): 1774-1788. doi: 10.6052/0459-1879-20-141

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COMPLICATED BURSTING BEHAVIORS AS WELL AS THE MECHANISM OF A THREE DIMENSIONAL NONLINEAR SYSTEM

Ma Xindong, Jiang Wenan, Zhang Xiaofang, Han Xiujing, Bi Qinsheng

Bursting oscillation behavior induced by multiple time-scale coupling effect is one of the important topics in nonlinear dynamics research. In this paper, complicated bursting oscillation behaviors as well as their generation mechanism of a three-dimensional nonlinear dynamo system with slowly changing parametric excitation are revealed when the excitation frequency is much smaller than the natural frequency. The system can be used to describe the dynamic behaviors of two kinds of self-exciting homopolar dynamo systems, which are mathematically equivalent. By treating the parametric excitation as a slow-varying parameter, the generalized autonomous system corresponding to the nonautonomous system as well as the fast subsystem and the slow variable are got based on the fast-slow analysis method. Then, the stabilities and bifurcations of the fast subsystem are investigated theoretically, and the correctness of the theoretical analysis is verified by a one-parameter bifurcation diagram related to a typical parameter. With the help of the overlapping of the transformed phase diagram and bifurcation diagram, the mechanism of the symmetric delayed subHopf/fold cycle bursting oscillation as well as its dynamic transitions, i.e. delayed subHopf/fold cycle bursting oscillation, symmetric delayed pitchfork bursting oscillation of focus/focus type and delayed pitchfork bursting oscillation of focus/focus type are analyzed. The result shows that, two different forms of bifurcation delay phenomenon will appear under different parameter conditions, one is the subcritical Hopf bifurcation delay, and the other one is the pitchfork bifurcation delay. In addition, our research indicates that the stabilities of the equilibrium points and the width of the pitchfork bifurcation delay interval are both influenced by the control parameter. Meanwhile, we also find that the symmetry of the dynamic behaviors is affected by the choice of the initial values. The study of this paper further deepens the understanding and the comprehending of the different bursting patterns induced by bifurcation delay phenomenon.

2020, 52(6): 1789-1799. doi: 10.6052/0459-1879-20-231

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STABILITY AND MODE EVOLUTION CHARACTERISTICS OF A CANTILEVERED FLUID-CONVEYING PIPE ATTACHED WITH THE LUMPED MASS

Yi Haoran, Zhou Kun, Dai Huliang, Wang Lin, Ni Qiao

This work mainly investigates evolutions for the dynamic characteristics of a cantilevered pipe conveying fluid by regulating a lumped mass along the pipe's length, for the purpose of controlling the stability and vibration behaviors of the pipe. Firstly, on the base of the extended Hamilton principle, a nonlinear dynamic model for the cantilevered fluid-conveying pipe attached with the lumped mass is established. In the following, a linear analysis is performed to explore the evolution of critical flow velocity varying with the placed position of lumped mass, which is substantiated by experimental measurements showing that transition of the flutter mode occurs. In addition, it is significant that the attached lumped mass ratio has a great impact on the critical flow velocity based on the linear dynamic analysis, which is dependent on the placed positions and mass ratio. Subsequently, a nonlinear analysis is conducted to investigate the effect of lumped mass on vibration amplitude of the pipe. It is indicated that the vibration amplitude is first increased and then decreased with the lumped mass varying from the fixed end to the free end, which is well compared to those of experimental measurements. The vibration mode of the pipe conveying fluid is transferred from the second mode to the third mode with varying the placed position of lumped mass, which is also observed in the experiments. The present study is expected to be beneficial for designing an underwater driven system based on flutter of pipes conveying fluid. In this way, the pipe's vibration mode can be adjusted through adding and adapting the lumped mass.

2020, 52(6): 1800-1810. doi: 10.6052/0459-1879-20-280

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PIV EXPERIMENTAL STUDY ON THE HEMODYNAMICS OF AORTIC VALVE UNDER VARIED TILTED ANGLES

Liu Zhaomiao, Xue Hebo, Yang Gang, Pang Yan, Fang Yongchao, Li Mengqi, Qi Yipeng, Shi Yi

Leaflet thrombosis is a typical secondary valvular disease after aortic valve replacement, and abnormal hemodynamic characteristics are crucial in its development. In this study, the effects of angle between the longitudinal axis of the aortic valve and that of the ascending aorta ($\alpha =0^\circ$, $\alpha =5^\circ$, $\alpha =10^\circ$ and $\alpha =15^\circ$) on the velocity, vorticity and viscous shear stress distribution are investigated using particle image velocimetry (PIV). It is of great significance to understand the hemodynamic mechanism of thrombosis after aortic valve replacement. The results show that the transvalvular flow in the aortic root is centrosymmetric flow when $\alpha =0^\circ$, while it tilts to the side of left coronary artery when $\alpha =5^\circ$, $\alpha =10^\circ$ and $\alpha =15^\circ$. The transvalvular flow tilts with the increasing of tilted angle and impacts on the wall of the ascending aorta, damaging the endothelial cells and causing thrombosis. In addition, the velocity within the aortic sinus increases and the vortex also moves toward the bottom of the aortic sinus with aortic valve tilted, which is unfavorable for the blood flowing from the coronary artery ostium to the myocardium for blood supply. Meanwhile, the high vorticity and high viscous shear stress area of the aortic root also tilts to the side of left coronary artery. And the high vorticity area of the aortic sinus is located at the bottom of the aortic sinus and the high viscous shear stress area is distributed at the wall of the aortic sinus. The vorticity and viscous shear stress are realy high when there is a mismatch between the ascending aorta longitudinal axis and that of the aortic valve, especially $\alpha =10^\circ$ and $\alpha =15^\circ$, providing a favorable environment for thrombosis. The results benefit to contribute theoretical bases and technical reference for the selection of clinical aortic valve replacement surgical parameters and that of the avoidance of secondary valvular disease.

2020, 52(6): 1811-1821. doi: 10.6052/0459-1879-20-229

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WIDENING AND DEEPENING OF RECIPROCAL PROGRAMMING AND ITS APPLICATION TO STRUCTURAL TOPOLOGY OPTIMIZATION

Tie Jun, Sui Yunkang, Peng Xirong

The work of this paper involves two aspects of mathematics and mechanics. In terms of mathematics: (1) The reciprocal programming newly proposed in the mathematical programming theory is developed from the s-m type (or called m-s type) to the s-s type and m-m type reciprocal programming (among which s means single goal, m means multiple goals), so that the definition of reciprocal programming is complete into three types; (2) From the KKT condition to examine the two aspects of reciprocal programming, it is obtained that the three theorems of two sides of reciprocal programming which involves quasi-isomorphism theorem and quasi-simultaneous solution theorems. Moreover, the proofs of the three theorems provide a theoretical basis for the two parties to reference and compare from each other in the solution of reciprocal programming; (3) Respectively, the solution strategies and detailed solutions are given for the case where both sides of a pair of reciprocal programming are reasonable ,and the case where one aspect is unreasonable while the other is reasonable. In terms of mechanics: (1) This paper gives the explanation of whether the structural optimization design model is reasonable or not; (2) In the application of reciprocal programming to structural topology optimization, a solution strategy for unreasonable structural topology optimization models is proposed; (3) A way to solve the MCVC model (the minimization of multiple compliances under a given volume) with the help of the MVCC model (Minimization of the volume under multiple compliance constraints), where the modeling is based on the ICM (Independent Continuous Mapping) method. At the end of this article, four numerical examples are given by Matlab codes, where two of the mathematical programming problems illustrate the relationship between the two sides of reciprocal programming, and two of structural topology optimization problems is two cases in many structural topology optimization problems. The numerical results support the reciprocal programming theory proposed in this paper.

2020, 52(6): 1822-1837. doi: 10.6052/0459-1879-20-188

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IMPROVEMENT OF EXPLICIT ALGORITHMS STABILITY WITH VISCO-ELASTIC ARTIFICIAL BOUNDARY ELEMENTS

Li Shutao, Liu Jingbo, Bao Xin

Viscoelastic artificial boundary elements are commonly applied in the analysis of semi-infinite wave propagation problems, which can accurately absorb the scattered waves generated in the calculation domain. However, the mass density, the stiffness and the damping coefficient of the viscoelastic artificial boundary element are different from those of the internal domain. Therefore, the instability often occurs in the boundary region when the explicit time-domain stepwise integration is performed in the overall model, so, the calculation efficiency of the explicit integral for the overall system is affected. Currently, there is no effective solution to this problem which remains to be settled to conduct efficient large-scale wave propagation simulation. For the two dimensional viscoelastic artificial boundary element, we establish the edge subsystem and corner subsystem which can represent the typical characteristics of the overall system, by the analysis method of transfer matrix spectral radius based on the central difference format commonly used, we derive the analytical solutions of the stability conditions of the edge subsystem and corner subsystem. After that, we analyze the influence of various physical parameters of the two dimensional viscoelastic artificial boundary element on the stability conditions, and obtain the method for improving the stability condition of the explicit algorithm by increasing the mass density of the viscoelastic artificial boundary element. The homogeneous and layered half-space examples show that, set the mass density of the internal element as the upper limit of the mass density of the viscoelastic artificial boundary element, the method proposed in this paper can effectively improve the numerical stability of the explicit time-domain integration when using the viscoelastic artificial boundary elements, without affecting the calculation accuracy, and the calculation efficiency can be significantly improved in the explicit dynamic analysis. The model size (distance from the scattered wave source to the artificial boundary) has a little effect on the stability of the explicit integral which can be ignored.

2020, 52(6): 1838-1849. doi: 10.6052/0459-1879-20-224

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