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## 2022 Vol. 54, No. 9

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In recent years, with the rapid development of deep learning in image processing, speech recognition, automatic driving, natural language processing, and other fields, this technology is also more and more widely used to process fluid mechanics direction with the characteristics of complex non-linearity, high latitude and a large amount of data. Traditional methods can not effectively deal with these huge data. Due to its powerful function fitting ability, deep learning can mine useful information from a large amount of data. At present, the deep learning technology of fluid mechanics has some preliminary research results, it has important engineering value in flow information feature extraction, multi-sensor data information fusion and intelligent reconstruction of flow field, and its potential of application has been gradually confirmed. How to use the data obtained from ground wind tunnel test, numerical simulation and flight test to carry out in-depth mining, fast intelligent perception and reconstruction of flow field can provide important guidance for active flow control. Starting from different types of network structures of deep learning, this paper discusses the research progress of convolutional neural network in flow field reconstruction. Firstly, In this paper, we introduce some basic concepts and basic network structure of convolutional neural network, and then we briefly introduce the basic structure and theory of flow field super-resolution reconstruction network, end-to-end mapping network and short-term memory network (LSTM), a series of research progress and achievements of their improved forms in the field of flow field reconstruction are summarized in detail. Finally, we summarize the article and discuss the challenges and prospects of deep learning technology of flow field reconstruction.
2022, 54(9): 2343-2360. doi: 10.6052/0459-1879-22-130
In recent years, various large space structures are gradually implemented in the aerospace industry of China. Thus, the corresponding thermally induced vibration problems are drawn more and more attentions. Under this background, it is necessary to clarify the underling mechanism of the thermally induced vibration phenomenon and the corresponding critical issues in the analysis and design. Based on the research work of the authors, this article gives a comprehensive review of the related problems and mainly focuses on some special aspects in the thermally induced vibration analysis of complex engineering structures, which are compose of many thin-walled bars. Firstly, this article introduces a Fourier finite element that decomposes the temperature into the average part and the perturbation part. In this way, the thermal conduction equation under thermal radiation can be decoupled into the corresponding two parts due to the orthogonal property of the Fourier series. Thus, the transient temperature field of closed-section or open-section thin-walled bars can be efficiently analyzed. Based on this kind of element, both linear and nonlinear methods for the thermally induced vibration analysis are presented with the emphasis on the thermal-dynamic coupling effect. In order to give the analytical form of the necessary condition of the thermally induced vibration, this paper analyzes the properties of the transient temperature and the oscillation displacement in the mode space, and thus it obtains a general criterion to evaluate the intensity of the thermally induced vibration. Based on these work, the dynamic stability of the thermally induced vibration is further discussed by not only the mechanism reflected in the thermal flutter criterion of a cantilever bar, but also the thermal flutter analysis of complex engineering structures. Finally, the conclusion part briefly addresses some important factors in the underground testing and the method of suppressing the thermally induced responses. Some research topics need further investigating in the future are also envisaged.
2022, 54(9): 2361-2376. doi: 10.6052/0459-1879-22-171
The solid-liquid phase change process in the presence of the magnetic field has extensive and important applications in industrial engineering, i.e. the electromagnetic metallurgy and additive manufacturing, where the melting process and flow mechanisms have not been fully explored. The cavity melting model, as a basic problem, has good universality to study the solid-liquid phase change process, and it can also provide some basic information for the magnetohydrodynamics influence on the phase change problems. In this paper, the solid-liquid phase change process is simulated based on the enthalpy method, and the physical model of the cavity heated from the left wall is considered, with a transverse magnetic field perpendicular to the main circulation direction. The flow field, heat transfer and melting processes are investigated, focusing to the influences of different factors. At first, for the melting problem of a square cavity without a magnetic field, we compared our numerical solution with the experimental results reported by some other literatures, and it is confirmed that the influence of the cavity width on the profile and position of the solid-liquid interface cannot be ignored. Subsequently, we use the 3D model to simulate the cases in the presence of small magnetic fields, and it is found that the Lorentz force mainly acts as a rectification effect on the chaotic 3D flow, making the flow tend to be quasi-2D (Q2D). Meanwhile owing to the existence of the solid-liquid interface, the velocity field in the mainstream region tends to be more uniform under the external magnetic field, and thus the shape of the solid-liquid interface also transforms into the 2D structure correspondingly. Finally, the Q2D model is used to study the cases under greater magnetic fields, and the influences of different parameters on the heat transfer efficiency and interface shapes are discussed. Moreover, the scaling law to describe the relation between the max vertical velocity and other dimensionless parameters is also proposed, in order to quantitatively characterize the melting process under the transverse magnetic field.
2022, 54(9): 2377-2386. doi: 10.6052/0459-1879-22-155
The objective of this paper is to investigate the transient evolution and dynamic characteristic of liquid nitrogen single bubble. In the experiment, electric spark transient discharge (EDM) was used to stimulate the evaporation of liquid nitrogen to form a single bubble, and the evolution process of the single bubble was captured by a high-speed camera with high resolution. In order to further reveal the unique physical properties of low-temperature media and the strong thermodynamic effects on the evolution of the single bubble, the unsteady evolution process and dynamic characteristics of single bubble in liquid nitrogen at 77.41 K and water at 298.36 K under the same ambient pressure were analyzed. And quantitative data such as the radius of bubble and interfacial velocity were obtained experimentally to elucidate the unsteady characteristics of the spherical and non-spherical evolution of liquid nitrogen single bubble. The results show that (1) the size of a single bubble in liquid nitrogen is smaller than that of ambient water at the same input voltage. The maximum radius of the liquid nitrogen bubble is about 0.69 times that of the ambient water bubble, when the input voltage is 400. The evolution of a single bubble in liquid nitrogen experiences an expansion stage, a contraction stage, an oscillation stage, and a up phase, respectively. (2) The shrinkage stage of liquid nitrogen vacuoles is mainly dominated by the heat conduction at the phase interface, and there is no obvious collapse phenomenon. The minimum radius of liquid nitrogen bubble is about 5.5 times bigger than that of the ambient water bubble during the shrinkage stage. (3) The heat transfer at the phase interface is enhanced during the early stage of the oscillation stage, the surface roughening effects is amplified over the bubble surface resulting from Rayleigh-Taylor instability coupled with the thermal effects. And small broken bubbles exist near the bubble surface during the oscillation stage. When the input voltage is higher, the number of small bubbles at the bottom of the vacuole increases significantly. (4) Due to the large buoyancy coefficient of the liquid nitrogen bubble, the overall upward migration of liquid nitrogen bubble is significant in the late stage of liquid nitrogen. The bottom of the liquid nitrogen vacuole shrinks more quickly to create a depression, driving the vacuole to into a ring shape.
2022, 54(9): 2387-2400. doi: 10.6052/0459-1879-22-144
The research on the behavior and influencing factors of bubble collision has always been one of the focuses of scientific circles. Its application in industrial fields such as mineral flotation and gas film drag reduction is also of great scientific research value. This paper focuses on the influence of curved wall on bubble impact behavior. The impact process of bubbles colliding with hydrophilic and hydrophobic curved wall under different radius of curvature was recorded by high-speed camera technology, and the effects of wettability and radius of curvature of curved wall on bubbles colliding with solid curved wall were analyzed. The results show that when the bubble collides with the hydrophilic curved wall, it will bounce many times until it leaves the curved wall; The larger the radius of curvature, the less the number of jumps, and the closer the farthest distance of the first rebound, the smaller the speed of hitting the wall again. In addition, aiming at the phenomenon of liquid film extrusion rupture, a theoretical model is established to deduce the prediction formula of liquid film induction time, which is mainly related to the thickness of liquid film, the critical rupture thickness of liquid film and the compression speed of liquid film, and the prediction error is less than 5.0%.
2022, 54(9): 2401-2408. doi: 10.6052/0459-1879-22-116
The transitional critical characteristics refer to the change of physical properties of flow field caused by the change of different flow states, which is amid the transitional stages. For instance, when flow evolves from steady to unsteady periodic. It fundamentally determines physical laws, like evolution mode and flow characteristics, deep inside the corresponding flow field, which is of great importance and necessity to understand the formation mechanism of flow phenomena. In this paper, the numerical simulations and flow stability analysis are carried out for the mirror symmetric lid driven cavity flow. The flow bifurcations, such as Hopf bifurcation and Neimark-Sacker bifurcation, are captured and their influence on the flow characteristics is discussed. The flow evolution mode is analyzed as well, it is found that with the increase of Reynolds numbers, the flow evolves from a steady state to a unsteady periodic state, then to a quasi-periodic state and finally into chaos. It is explained that the formation mechanism of various flow phenomena, for example, flow hysteresis, symmetry loss, energy cascade, etc. The flow topology is analyzed and the relation between mirror symmetry and stability is clarified. The conclusions of the present study is helpful to better understand the physics of this internal flow field, further completing the corresponding research of on this research direction, such as the classic lid driven cavity flow. Based on the findings of present study, we have found that the unsteadiness of flow field always starts as the Hopf bifurcation appears, the flow symmetry breaks as soon as the flow unsteadiness shows up. It is found that the flow evolves as the classic Ruelle-Takens mode and the flow hysteresis is observed when flow evolves from a steady state to an unsteady periodic state.
2022, 54(9): 2409-2418. doi: 10.6052/0459-1879-22-218
In order to reveal the evolution of droplet propulsion, deformation, and fragmentation in supersonic and hypersonic environment, a conservative sharp-interface multiphase method is used to simulate the shock-droplet interaction with high-Mach and extremely high-Mach numbers. The numerical results are in good agreement with the experimental results, which indicates the accuracy of the numerical method and the corresponding computer code. The grid independence study demonstrates that the grid resolution used in this paper can capture the main features of the flow field and interface. The numerical results verify the shear-induced entrainment (SIE) breaking mechanism followed by the droplet deformation and fragmentation under high-Weber number, including two main features, i.e. the flattening of droplets and the shearing of the sheet at the droplet equator. The recently discovered recurrent breakup mechanism under the SIE mechanism has also been verified in this paper. The initial spherical-droplet is deformed, and breaks into smaller sub-droplets via recurrent rupture stages. And the fragmentation of droplets for high-Weber number is indeed not the result of one single shearing process, but rather occurs recurrently. The effect of the Mach number on the shock-droplet interaction is also investigated here. Our results indicate that the droplet fragmentation process for different Mach numbers is highly analogous, following the general SIE mechanism. The time evolution of the dimensionless center-of-mass drift, velocity, acceleration, and drag coefficient reveal the unified acceleration tendency for droplet under shock impact. In addition, the droplet does not propel with a constant acceleration rate for the whole stage. Instead, when the flattening effect is absent in early stage, the droplet accelerates at a constant acceleration. As the flattening occurs, the increase of the upwind area leads to an increase in the drag coefficient, which in turn increases acceleration rate of the droplet movement.
2022, 54(9): 2419-2434. doi: 10.6052/0459-1879-22-191
In the underwater launch process, the wake of the first projectile has flow interference with the hydrodynamic characteristics of the second projectile. Therefore, the research on the evolution mechanism of the wake vortex is of great significance to solve the problem of flow interference in the single launcher and multiple vehicles launched successively. In this paper, the improved delayed detached eddy simulation model and energy equation, VOF (volume of fluid) multiphase flow model, and overlapping grid technology is used to simulate the wake vortex of the projectile launched underwater. Simulation results are in good agreement with the experiment, which verifies the effectiveness and accuracy of the numerical method. Taking the wake region of the projectile as the key research object, the transient flow field distribution in the wake area is analyzed, the wake vortex is identified and its evolution is analyzed by using the vortex identification method, and the effects of the crossflow intensity and Reynolds number on the evolution of wake vortex and fluctuating pressure distribution are discussed. The results show that the interaction between the high-speed fluid core and the low-speed free flow in the wake region causes obvious Kelvin-Helmholtz instability in the wake. Under the effect of crossflow, the vortex rings shed at the vehicle tail and the vortex leg form a hairpin arc-shaped hairpin vortex. At the same time, a plurality of hairpin vortices is arranged at intervals along the axial direction to form a hairpin vortex package, which exists in the wake. With the increase of crossflow intensity, forming a multi-stage hairpin vortex package. The main reason for the appearance of the secondary peak of fluctuating pressure is the evolution of wake flow. With the increase of Reynolds number, the secondary vortex structure composed of the cylindrical vortex and U-shaped vortex in the wake becomes more and more obvious, and the instability increases.
2022, 54(9): 2435-2445. doi: 10.6052/0459-1879-22-245
The low-noise, high-speed and high-efficiency swimming ability of marine life is unmatched by any artificial underwater vehicle. With the help of time-resolved particle image velocimetry (TR-PIV), the fine flow field measurement of the zebrafish straight acceleration swimming process was carried out, and its kinematic behaviour characteristics and dynamic mechanism were analyzed. Meanwhile, bi-orthogonal decomposition (BOD) is applied to modal decomposition of the vorticity field, and the flow field's time evolution and spatial distribution characteristics are obtained. From the perspective of flow mechanism, the flow structure characteristics and the dynamic evolution characteristics of vortices during zebrafish swimming are explored. The results showed that: The flow visualization shows the structure distribution of the overall vortex wake, which is convenient to explore the coupling relationship between the motion characteristics and the vortex wake. From the beginning of the movement, all points on the body trunk of zebrafish maintain the wavy movement law. The first few large tail swings mainly provide kinetic energy during swimming, and the subsequent tail swings mainly adjust the direction and posture. Two tail swings in different directions will form a pair of vortices in opposite directions, and the vortices will gradually fall off under the timing sequence. Meanwhile, the change of the wake vorticity reflects the change of the swimming direction of the fish to a certain extent. Based on the time evolution results after BOD decomposition, it is verified that the vorticity field in this experiment has a reasonable constant amplitude in time. The spatial distribution indicates that the low-order spatial modes characterize the main vortex structure of zebrafish swimming, and the higher-order spatial modes characterize the detailed structure of the vortex flow. The research on the tail-swinging propulsion mechanism and the dynamic characteristics of fish during swimming can provide certain scientific value for designing high-efficiency fish-like propulsion devices.
2022, 54(9): 2446-2459. doi: 10.6052/0459-1879-22-157
Due to the demand for lightweight materials in automotive and aerospace fields, magnesium and its alloys play an irreplaceable role due to a series of advantages such as low density and high strength. Currently, Mg-3Al-1Zn alloy is one of the most widely used commercial magnesium alloy. It is of great significance to study its deformation mechanism and shock response of Mg-3Al-1Zn alloy. In this paper, molecular dynamics method has been used to study the shock behaviors of Mg-3Al-1Zn alloy with a cylindrical void. For [0001] and ${\text{[10}}\bar {\text{1}} {\text{0]}}$oriented Mg-3Al-1Zn specimen, the nucleation and evolution of dislocations near void surface induced by shock wave are discussed. Simulation results show that the activation of slip system near the void is strongly dependent on the shock orientation. In [0001] orientation, basal dislocations preferentially nucleate near the void, and basal lattices near void are found to be rotated by ~ 21° and finally form a high-angle grain boundary. However, prismatic dislocations are observed to be the preferentially mode along the ${\text{[10}}\bar {\text{1}} {\text{0]}}$ orientation, subsequently, a large number of basal dislocations nucleated. Based on the theory of stress wave, it is found that the dislocation behaviors near the void are greatly affected by the reflected isometric wave (SV2), while the plastic deformation behaviors associated with void collapse are greatly affected by the irrotational wave (P2). Moreover, the distributions of the shear stress near the void are analyzed to predict the distributions of the nucleated dislocation under different shock orientations. In general, simulation results in this paper are in good agreement with the prediction based on stress wave theory and the distributions of the resolved shear stress, and the nucleation and evolution mechanisms of the dislocations near the void are obtained.
2022, 54(9): 2460-2471. doi: 10.6052/0459-1879-22-125
During charging and discharging of lithium-ion batteries (LIBs), lithium extraction and insertion induce inhomogeneous volume changes of storage particles, resulting in significant mechanical stresses. Dependent on the size and shape of storage particles as well as the recharging-charging rate, the diffusion-induced stress may lead to crack nucleation, propagation and even fracture of storage particles, yielding detrimental effects on the capacity and cycle life of LIBs. Aiming to simulate and predict the failure process of storage particles in LIBs, this work addresses a chemo-mechanically coupled phase-field cohesive zone model (PF-CZM) within the framework of the unified phase-field theory for damage and fracture. The numerical algorithm and computational implementation are also presented in the context of the multi-field finite element method, with applications to the modeling of mechanical failure of two-dimensional cylindrical and three-dimensional spherical storage particles in LIBs. As it intrinsically incorporates the strength-based nucleation criterion, the fracture energy-based propagation criterion and the variational principle based path chooser, the proposed PF-CZM applies not only to fracture analyses of pre-notched storage particles, but also to the simulation of the complete failure process of intact ones with no pre-defined defects. Extensive numerical results demonstrate that the proposed model is able to capture arbitrary crack configurations in storage particles due to evolution of Li-ion concentration, to predict the resulting mechanical failure of LIBs, and is useful for the optimal design of commercial LIBs.
2022, 54(9): 2472-2488. doi: 10.6052/0459-1879-22-057
In order to elucidate the influence of particle size distribution on the internal meso-mechanical behaviour of the iron powder compaction system, based on discrete element method (DEM), a compaction model was established by changing the particle size distribution of iron powder particles. Combined with the force chain extraction method, the influence mechanism of particle size distribution on the evolution of force chains was explored by analyzing the spatial distribution of force chains, the number of force chains, the length of force chains and the directionality of force chains. The findings reveal that the spatial distribution of force chains created by powders with varying particle sizes is different. The force chain distribution created is more concentrated the smaller the particle size distribution range is. On the other hand, the larger the size distribution range is, the more loose and uniform the force chain distribution is. The particle size distribution also has an effect on the number of force chains, which is manifested in that the total number of force chains gradually decreases with the increase of the particle size distribution range of the powder. The particle size distribution of the powder has a significant effect on the number of short force chains formed by the particles, but has a limited effect on the length of the force chain. With the increase of the particle size distribution range, the direction of the force chain is gradually concentrated from a uniform distribution to a specific angle direction, showing a certain anisotropy, and the formed cross force chain network structure is conducive to improving the degree of powder densification. This paper provides a basis for expanding the meso-mechanical theory of powder compaction from the influence of powder particle size distribution, and also provides guidance for further improving the powder densification behaviour by combining the powder particle size distribution and the evolution process of the internal force chain in the system.
2022, 54(9): 2489-2500. doi: 10.6052/0459-1879-22-204
There are a large number of naturally formed joints in natural rock mass, which lead to changes in the mechanical properties, vibration, permeability, energy transfer and other properties of rock mass. The propagation and attenuation of blast stress waves in the rock mass with joints also change, which affects the effect and safety of engineering blasting. The explosion crack propagation and explosion stress wave propagation law of the jointed rock mass are studied, and the effective stress and vibration velocity of the rock mass on both sides of the joint are obtained by establishing the explosion numerical model of the jointed rock mass. The transmission and reflection coefficient and the transmission and reflection energy ratio of the joint are calculated by using the stress wave wave theory and energy density theory. On this basis, the effects of joint geometric parameters (joint filler thickness D, normal distance R from blast source to joint, vertical distance H from blast source to joint, joint inclination $\theta$) on the expansion of blast cracks at different positions of the joint were studied. And the relationship between the above-mentioned joint geometric parameters and the joint's transmission and reflection coefficient and transmission and reflection energy ratio. The results show that when the joint is located in the crack area and the ratio H/R of the vertical distance H from the blast source to the joint to the normal distance R is equal to 1, the reflection coefficient and reflected energy ratio of the joint are at the maximum value, and shear stress becomes the main factor affecting the damage of joint surface within this range. The fracture area of the rock mass near the explosion side of the joint is positively correlated with the thickness D of the joint filler. The fractured area of the rock mass near the blast side of the joint is negatively correlated with the normal distance R from the blast source to the joint and the vertical distance H from the blast source to the joint. When the joint is located in the crack area, the joint has the greatest impact on the blasting effect of the rock mass.
2022, 54(9): 2501-2512. doi: 10.6052/0459-1879-22-237
Fluid-solid coupling seismic wave motion problems are aimed at investigating the characteristics and laws of seismic wave propagation in the complex system composed of fluid and solid media. In traditional simulation methods, numerical solutions of acoustic and elastic wave equations are generally used to describe the waves in ideal fluid and elastic solid respectively, and the coupling between the two media with different properties is dealt with in real time. Consequently, traditional methods suffer from complex numerical schemes, relatively low numerical simulation accuracy and computational efficiency. Based on spectral element method and multi-transmitting formula artificial boundary condition, a high order explicit numerical method for fluid-solid coupling seismic wave motion problems is developed in this paper. This method uses a unified computational framework, in which Biot’s equations for saturated porous media can degenerate to acoustic and elastic wave equations for ideal fluid and elastic solid respectively. Three numerical examples of ideal fluid-saturated porous medium-elastic solid system are given: the horizontal layered site model with vertical incidence of P wave, the irregular layered interface model under obliquely incident P wave and arbitrary shape interface model under obliquely incident P wave. The accuracy and efficiency of the proposed method are verified in comparison with the results of transfer matrix method and lumped mass finite element method. The numerical simulation results show that compared with the traditional finite element method, this method can obtain higher numerical accuracy with much less nodes, and can reliably simulate the dynamic response of fluid-solid coupling problems in a wider frequency range. The proposed method fully represents the characteristics of high precision, high efficiency and flexibility to handle complex sites.
2022, 54(9): 2513-2528. doi: 10.6052/0459-1879-22-068
As a basic structural member, elastic beam structures are widely used in architecture, aviation, aerospace, shipbuilding, and other engineering fields. To suppress the vibration level of elastic beam structures effectively, it is of great significance to understand their vibration characteristics and dynamic responses. This manuscript establishes the vibration analysis model of the axially loaded beam structure with the nonlinear support and elastic boundary constraints. Dynamic behavior of the beam structure is predicted by applying the Galerkin truncated method. Mode functions of the axially loaded beam structure with elastic boundary constraints are selected as the trial and weight function in Galerkin truncated method. Firstly, the influence of the truncated number on the stability of the Galerkin truncated method is studied and the reliability of the Galerkin truncated method is verified by the harmonic balance method. On this basis, the influence of the sweep direction of the harmonic excitation and the parameters of the nonlinear support on the dynamic responses of the axially loaded beam structure with nonlinear supports and elastic boundary constraints is studied. The results show that dynamic responses of the axially loaded beam with the nonlinear support and elastic boundary constraints are sensitive to the initial values of calculation. Parameters of the nonlinear support significantly affect the dynamic responses of the axially loaded beam with the nonlinear support and elastic boundary constraints. In certain parameters of the nonlinear support, the complex dynamic behavior of the beam structure with the nonlinear support and elastic boundary constraints appears. Appropriate parameters of the nonlinear support can suppress the complex dynamic behavior of the axially loaded beam structure with the nonlinear support and elastic boundary constraints. Meanwhile, appropriate parameters of the nonlinear support can also suppress the vibration level at both ends of the axially loaded beam structure with the nonlinear support and elastic boundary constraints.
2022, 54(9): 2529-2542. doi: 10.6052/0459-1879-22-088
Modern spacecraft usually carry large amounts of liquid propellant. In the process of attitude change, the liquid fuel may slosh violently due to the action of inertial force and gravity, resulting in additional sloshing force, which will have an important impact on the spacecraft. In order to obtain the law of liquid sloshing and meet the requirements of on-board computer real-time calculation, a dynamic model for equivalent liquid sloshing is studied and verified in this paper. Firstly, the moving pulsating ball model (MPBM) of large liquid sloshing motion is extended to the gravity environment. Based on the Newton-Euler dynamic equation of the moving pulsating ball and the energy relation in the process of "breathing movement", the expression of the normal component of the sloshing force is derived. In addition, the equivalent model of liquid not involved in sloshing is introduced to make the calculation of liquid centroid position more accurate. Compared with the experimental data in the references and the calculation results of computational fluid dynamics (CFD) software, the effectiveness of the improved MPBM under large amplitude sloshing and zero momentum maneuver is verified. Also, based on the equivalent model, the effects of different time series of impulse excitation on liquid sloshing response in spacecraft are studied. Finally, an experimental platform for precise measurement of liquid sloshing force is designed and built to verify that the MPBM can also well reflect the variation trend of sloshing force in the liquid sloshing of equivalent non spherical tank. The research work of this paper has important reference value for the further study of rigid-liquid coupling dynamic behavior of liquid filled spacecraft in gravity environment.
2022, 54(9): 2543-2551. doi: 10.6052/0459-1879-22-187
Due to the advantages of large storage ratio, high controllability, reconfigurability, easy assembly and diversified design, the origami structure has broad application prospects in the fields of aerospace, biomedicine, architecture, robotics, material science, etc. With the development of origami structure engineering, the dynamic research for the origami structure with low stiffness becomes more important. In this paper, a general bar-and-hinge dynamics model is developed, in which a non-rigid origami structure is equivalent to a spatial truss structure with rotational spring. Considering the geometric nonlinearity of the material, a bar element based on Ogden hyperelastic constitutive model is used to simulate the creases and virtual creases of the non-rigid origami structure, which can deal with the non-rigid origami structure with large overall motions and large deformations. A nonlinear rotational spring is introduced to reflect the bending resistance of the crease. Compared with the traditional rotational spring constitutive model, the modified nonlinear rotational spring constitutive model proposed in this paper has stronger versatility and robustness, and can effectively avoid the mutual penetration between the folding surfaces in contact-impact dynamics. Based on the principle of virtual work, the dynamic equations of the non-rigid origami multibody system considering the damping effect are established, which are solved by the variable-step generalized-α method. Finally, a series of numerical examples of three classical origami structures are presented to verify the accuracy and efficiency of the bar-and-hinge dynamics model proposed in this paper. Furthermore, by adding virtual creases and correcting the initial configuration, the locking problem of the unfolding and folding process in the rigid origami model is effectively resolved. Compared with the rigid origami model, the bar-and-hinge dynamics model can continue to perform further calculation and provide the fully deployed configuration with large deformation. On this basis, the complex dynamic behaviors of the non-rigid origami structure are revealed, and the mechanics characteristics of multi-stable, transient dynamics and wave dynamics are analyzed.
2022, 54(9): 2552-2566. doi: 10.6052/0459-1879-22-176
As a kind of good damping material, viscoelastic material is widely used in machinery, aviation, civil engineering and other fields. A new viscoelastic nonlinear energy sink is proposed by replacing the damping element with a viscoelastic Maxwell element in the traditional nonlinear energy sink, and the vibration damping performance of the model under harmonic excitation is investigated. Firstly, the dynamic equation of the system is established according to Newton's second law. The harmonic balance method is adopted to obtain the system amplitude-frequency response curves, and the Runge-Kutta numerical method in MATLAB is applied to verify the correctness of the analytical solution, and it is found that the results are in good agreement. Then, the damping performance of the viscoelastic nonlinear energy sink and the influence of parameters are analyzed. Finally, the variation trend of vibration reduction effect are analyzed when the nonlinear stiffness ratio and damping ratio change at the same time under different mass ratios, and the optimal value range of viscoelastic nonlinear energy sink is discussed. The results show that the maximum amplitude of the primary system first decreases and then increases with the increase of nonlinear stiffness. When the parameters are selected properly, the damping effect of viscoelastic nonlinear energy sink is better than that of traditional nonlinear energy sink. In addition, with the increase of the mass ratio, the minimum value of the maximum amplitude of the primary system first decreases and then tends to remain unchanged, and the optimal range of nonlinear stiffness ratio and damping ratio is greater. The above conclusions provide a theoretical basis for the practical application of the viscoelastic nonlinear energy sink.
2022, 54(9): 2567-2576. doi: 10.6052/0459-1879-22-193
Time integration algorithm is a key issue in solving dynamical system. An unconditionally stable Hamel generalized α method is proposed to solve the instability issue arising in the time integration of dynamic equations and to eliminate the pseudo high order harmonics incurred by the spatial discretization of finite element simultaneously. Therefore, the development of numerical integration algorithm to solve the above-mentioned problems has important theoretical and application value. The algorithm proposed in this paper is developed based on the moving frame method and Hamel’s field variational integrators along with the strategy to construct an unconditionally stable Hamel generalized α method. It is shown that a new numerical formalism with higher accuracy can be derived under the same framework of the unconditional stable algorithm established through a special variational formalism and variational integrators. The above-mentioned formalism can be extended from general linear space to Lie group by utilizing the moving frame method and the Lie group formalism of the Hamel generalized α method has been obtained. Both the convergence and stability of the algorithm are discussed, and some numerical examples are presented to verify the conclusion. It is demonstrated by the theoretical analysis that the Hamel generalized α method proposed in the paper is unconditionally stable, second-order accurate and can quickly filter out pseudo high-frequency harmonics. Both conventional and proposed methods have been applied to numerical examples respectively. Comparisons between results of numerical examples show that the aforementioned advantages of the proposed method in terms of accuracy, dissipation and stability are tested and verified. At the same time, it can be developed that new numerical integration algorithms with even higher order accuracy. The scheme can also be proposed, which is suitable for both general linear space and Lie group space. A new way for constructing variational integrators is also obtained in this paper.
2022, 54(9): 2577-2587. doi: 10.6052/0459-1879-22-131
Under the impacted of solar heat flux, the satellite antenna in orbit is prone to thermally induced vibration or inaccurate pointing, which will lead to spacecraft failure in serious cases. In this study, a modeling and model order reduction method for rigid flexible thermal coupling multibody system based on the improved component mode synthesis method is proposed. First of all, the displacement and temperature field of the flexible antenna are discretized by the unified element shape function of the absolute node coordinate formulation (ANCF), which can avoid the mapping error and efficiency problems caused by the mismatching of the two physical fields. The ANCF reference node is used to describe the central rigid bodies. In addition, the solar heat flux input and the surface emitting radiation are considered in the system equation. According to the highly nonlinear characteristics of the tangent stiffness matrix of the ANCF, the first-order Taylor expansion is used to linearize the dynamic and heat transfer equations. The tangent stiffness matrix in the linearized horizon is a constant matrix, which avoids the iteration of the elastic force and its Jacobian matrix in each time step, and makes the model order reduction method could be applied. Afterwards, the improved component mode synthesis method is used to divide the substructure and reduce the degrees of freedom of the system. The substructures are connected by constraint equations to ensure the accuracy and continuity between the structures. At last, four numerical examples such as the pure heat conducting semicircular thin plate, the thermal expansion of thin plate, the flexible solar panel and the rigid flexible thermal coupling parabolic antenna are given to verify the effectiveness of the proposed method. The results show that the proposed method can reduce the scale of the system and improve the efficiency of simulation calculation without losing accuracy.
2022, 54(9): 2588-2600. doi: 10.6052/0459-1879-22-207
The damper is connected to the building structure by setting braces in engineering, but in order to simplify the analysis, the bracing horizontal stiffness is regarded as infinite, that is, the influence of braces on the random response of energy dissipation structure is not considered. In fact, it is more in line with engineering practice to consider the effect of the braces with finite horizontal stiffness on the response of the energy dissipation isolated structure. To analyze the response of the generalized Maxwell energy dissipation isolated structure considering the influence of the braces under the Hu Yuxian spectrum seismic excitation considering the effect of the braces, a concise analytic solution for solving random seismic response is proposed. The non-classical damping system are composed of the equivalent constitutive relation of the generalized Maxwell damper with braces, the motion equation of the isolated structure and the Hu Yuxian spectral filtering equation. The complex modal method is used to decouple the non-classical damping energy dissipation isolated system, and the Duhamel integral expression of the series response of the energy dissipation isolated system based on white noise excitation are obtained through different response modes. Based on the properties of Dirac function, the energy dissipation isolated system series response covariance is simplified into non-integral expression. According to Wiener-Khinchin relationship between the power spectral density function and its covariance function, the energy dissipation isolation system series response power spectrum and ground acceleration power spectrum are obtained. Based on the definition of spectral moments in random vibration theory, the 0 ~ 2 order spectral moments of energy dissipation isolation system series response are obtained. The example verifies the correctness and efficiency of the proposed method in the bracing system by comparing with the pseudo excitation method, and discusses the influence of different bracing stiffness on damping effect of damper.
2022, 54(9): 2601-2615. doi: 10.6052/0459-1879-22-147
In aerodynamic shape optimization design and aircraft performance analysis, the cost of directly using numerical simulation or wind tunnel experiments to obtain aerodynamic forces is high. Building surrogate model is an important way to improve the efficiency of shape optimization and performance analysis. However, in the process of building the model, researchers only focus on the aerodynamic force and moment information after integration. In this paper, the accuracy and generalization of modeling are improved by making full use of the pressure distribution information generated in the sampling process, thereby reducing the cost of sample acquisition. In this paper, an aerodynamic modeling method integrating pressure distribution information under the framework of small sample is proposed. Firstly, the pressure distribution information and aerodynamic coefficients of airfoil surface under different flow parameters are obtained by numerical simulation or wind tunnel experiments. Secondly, the pressure distribution information is extracted by proper orthogonal decomposition technology to obtain the POD coefficients corresponding to the distribution information under different input parameters. Then, the pressure distribution information is modeled by Kriging algorithm combined with input parameters. The pressure distribution information is integrated to obtain the prediction model of low precision aerodynamic coefficients. Finally, the low precision aerodynamic coefficients are combined with the input parameters to construct a high precision aerodynamic prediction model by Kriging algorithm. The method is verified by the same-state variable airfoil example and the CAS350 airfoil variable-state example. Compared with the traditional Kriging model, this method can effectively improve the prediction accuracy of aerodynamic force and the robustness of the model, and reduce the data amount of learning samples.
2022, 54(9): 2616-2626. doi: 10.6052/0459-1879-22-170
Under the pressure of energy and environmental protection, the electric vehicle and intelligent driving have been attached great attention in recent years. The wheel vibration of the electric vehicle driven by hub motors is severe, which has the more interaction with the bridge pavement. Current studies are mainly aimed at traditional vehicles, while there are few works on the dynamic interaction between the electric wheels with highway bridge and the vibration of multi-vehicle-bridge coupling system based on intelligent driving fleets. In this paper, the researches are carried out based on the electric vehicle driven by hub motors. Considering the multi-point contact relationship between the wheel and bridge deck, the vehicle-bridge coupling dynamic characteristics of two intelligent driving electric vehicles driven by hub motors crossing the bridge are studied. The influences of motor mass, motor excitation, tire and suspension stiffness nonlinearity, vehicle distance and vehicle speed on vibration response of the coupling system, as well as the influences of bridge irregularities excitation and triple coupling excitation on ride comfort of the electric vehicle are analyzed. The results show that, the vehicle distance and vehicle speed are important factors which affecting the vibration characteristics of the vehicle-bridge coupling system. In the dynamic design of the vehicle-bridge coupling system, the influence of the vehicle distance and vehicle speed should be pay more attention. The more flat the bridge deck is, the more significant of influence of motor excitation and bridge deck secondary excitation on vehicle ride comfort and road friendliness are. When the vehicle is driving on a flat bridge deck, the influence of the two kinds of excitation on the hub motors electric vehicle should not be ignored. The proposed model in this paper is expected to provide a theoretical reference for the study of coupling vibration of the intelligent driving electric vehicles and bridge.
2022, 54(9): 2627-2639. doi: 10.6052/0459-1879-21-600