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2022 Vol. 54, No. 1

Research Review
Fang Hongbin, Wu Haiping, Liu Zuolin, Zhang Qiwei, Xu Jian
Recently, due to the infinite design space, outstanding capability in changing shape, dimension, and topology, as well as the folding-induced extraordinary mechanical properties, origami structures and origami metamaterials have rapidly become the research frontiers and hot spots in the fields of mathematics, physics, and engineering. Origami structures and origami metamaterials have extensive application prospects in various fields, including aerospace, medical, and robotic engineering. Typical examples are the large-scale deployable aerospace structures, reconfigurable self-folding robots, and micro-scale foldable devices. As the scope of engineering applications continues to expand, the dynamics of origami structures and origami metamaterials become increasingly prominent, which not only involves dynamic modeling and parameter identification but also relates to the dynamic mechanism analyses and experimental tests. The origami dynamics research is facing many new challenges and opportunities brought by the complex spatial geometric relations, the rich deformation modes, and the folding-induced global strong nonlinear constitutive profiles. In this review, the research background and significance of origami structures and origami metamaterials are firstly surveyed, followed by a brief introduction to the fundamental definitions, assumptions, and categorization of origami. The geometric design, kinematic and static properties of the origami structures and origami metamaterials are also summarized in brief. Afterward, the recent research progress on the dynamics of origami structures and origami metamaterials are systematically reviewed, from the following aspects: (1) dynamic modeling and parameter identification methods; (2) theoretical, finite element, and experimental approaches for dynamic analysis; (3) folding-induced dynamic behaviors, including bi-stable and multi-stable dynamic behaviors, transient dynamic behaviors, and wave propagation dynamic behaviors, etc.; (4) typical dynamic applications. Finally, several open problems are addressed for future studies.
2022, 54(1): 1-38. doi: 10.6052/0459-1879-21-478
Fluid Mechanics
Liu Pengxin, Sun Dong, Li Chen, Guo Qilong, Yuan Xianxu
When flying in low or medium attitude at very high Mach number, the surface of new hypersonic vehicles will encounter the interaction between turbulence and chemical non-equilibrium, which makes the flying environment more complicated. Generation mechanism of skin friction in such high enthalpy turbulent boundary layer is the fundamental scientific problem. The clarification of this mechanism can serve guidance for the drag reduction design, which has a significant engineering practical value. This work chose the flow condition after the leading shock of a cone in hypersonic flight, and performed direct numerical simulation (DNS) of turbulent boundary including chemical non-equilibrium effect. The low enthalpy case under the same boundary condition was set as a comparison. The RD (Renard & Deck) decomposition was utilized to analyse the dominant generation process of skin friction. The profiles of the integrand functions of main contributors were compared in detail. The influence of chemical non-equilibrium on the generation mechanism of skin friction was investigated. Furtherly, quadrant analysis technique was utilized to analyse the dominant flow events of turbulence kinetic energy production term in RD decomposition. The results show that the steaks scales of skin friction fluctuation are reduced both in streamwise and spanwise directions due to the chemical non-equilibrium effect. The molecular viscous dissipation term and the turbulence kinetic energy production term are the two main contributors to the generation of skin friction. The former mainly works in the near wall region, and the influence of high enthalpy is applied through its average portion. The profile of the integrand function of the molecular viscous dissipation term is different between high- and low enthalpy cases. The results of quadrant analysis show that the ejection and sweep events are the dominant processes for the latter term.
2022, 54(1): 39-47. doi: 10.6052/0459-1879-21-490
Yuan Chaokai, Jiang Zonglin
The heat flux measurement results of point sensors cannot fully reveal the detailed heat flux distribution characteristics, especially for the areas with large heat flux gradient and complex heat flux distribution. Measurement methods of heat flux field are needed to meet the demand. The method of temperature sensitive paint has been widely used to measure heat flux field. However, the stagnation temperature of the test condition is much lower than the real flight condition. The radiation effect under hypersonic high enthalpy conditions seriously limits the application of temperature sensitive paint. To solve this problem, the embedded temperature sensitive paint method is proposed. The heat flux field is determined by the solution of the inverse heat conduction problem with inner wall temperature history measured by temperature sensitive paint. In this paper, the measurement principle, system composition, data processing method, design principle and advantages of the embedded temperature sensitive paint method are introduced in detail. The feasibility of this method is verified by numerical simulation with typical heat flux distribution. Also, the influence of temperature measurement accuracy and noise on the measurement results are analyzed. The embedded temperature sensitive paint method can be applied in the hypersonic real flight condition to reveal the detailed characteristics of the heat flux field. This method extends the application of temperature sensitive paint and solves the problem of heat flux field measurement under hypersonic high enthalpy conditions.
2022, 54(1): 48-58. doi: 10.6052/0459-1879-21-279
Du Xiangbo, Chen Shaoqiang, Hou Jingyao, Zhang Fan, Hu Haibao, Ren Feng
Wake structures of different blunt bodies with identical characteristic length are similar, this is quite challenging to be distinguished using solely human eyes. Here, we propose a blunt body wake recognition method based on the convolutional neural network (CNN), which is then verified to be highly accurate with various types of blunt bodies models in vertical soap-film water tunnel experiments. The experimental platform is composed of a self-built vertical soap-film device, three typical blunt body models (square cylinder, circular cylinder, and triangle cylinder), and an image acquisition system. Based on the optical interference method, this image processing modulus can realize continuous high-fidelity photography of blunt body wakes with different incoming velocities. The CNN recognition model is built up with input layer, convolutional layer, pooling layer, fully-connected layer, and classification layer. Among them, the convolutional layer and the pooling layer are used to extract the deep feature information of wakes, while the fully-connected layer and the classification layer together can finally determine the category or Reynolds numbers of the input wake image. By importing a data set with 9000 wake images into the CNN model, a wake feature recognition model capable of classifying various body shapes is established in a data-driven manner. Results show that the shape recognition accuracy is 97.6% at the same Reynolds number (300 wake images), and 96% at different Reynolds numbers (1200 wake images). Even when wake images with different shapes and Reynolds numbers are mixed together, the recognition accuracy in terms of both shape and Reynolds number can still reach 91% (1500 mixed wake images). The proposed method provides a solid reference for future applications of artificial intelligence in extracting physical information from blunt body wakes.
2022, 54(1): 59-67. doi: 10.6052/0459-1879-21-404
Tu Jiahuang, Huang Linxi, He Yongkang, Lü Haiyu, Liang Jingqun
Based on the four-step semi-implicit characteristic line splitting operator finite element method, the vortex-induced vibration problem of two-degree-of-freedom tandem arrangement of double cylinders is numerically simulated, and the spacing ratio, shear ratio, natural frequency ratio and reduced velocity are analyzed. The influence of four parameters on the dynamic response of cylindrical structure.The study found:natural frequency ratio and shear ratio have a greater impact on the vibration amplitude of upstream cylinder. However, the impact of the natural frequency ratio and shear ratio on the downstream cylinder is small.The upstream cylinder reaches the maximum reduction speed in the two degrees of freedom direction is different, but the downstream cylinder is basically synchronized. The resonance area of the upstream cylinder is significantly wider than that of the downstream cylinder. Meanwhile, the time of upstream cylinder enter and exit the resonance area is earlier than that of the downstream cylinder. On the other hand, the two cylinders mainly complete the phase transition in the in-lock region. With the increase of the frequency ratio, the rate of the energy transfer from the fluid to the cylinder slow down, resulting in the slower rate of the cylinder complete the transition of in-phase to anti-phase. In the shear flow case, the phase difference between lift and displacement will appear “platform period” at the space ratio is more than 3.5. When the spacing ratio further increases beyond the critical value, with the increase of the reduced velocity, the more clutter frequency appears in the fluid force power spectral density curve, which leads to the phenomenon of energy “feedback”. Finally, in the uniform flow case, the main frequency value in the lift-drag power spectral density curve is twice the relationship, but as the shear rate increases, the fluid force power spectral density curve will basically coincide.
2022, 54(1): 68-82. doi: 10.6052/0459-1879-21-381
Luo Jian, Wang Zhihui
Most of the new-generation hypersonic cruise vehicles have sharp leading edges and thin wings, and the flow and heat transfer downstream the stagnation point are characterized by the strong shear effects and significant nonequilibrium effects. Because of the demand on the total heat load prediction and the experimental data identification, there is an increasing engineering interest in the strongly sheared nonequilibrium flow and aerodynamic heating problems. In this paper, the theoretical modeling method, as well as the direct simulation Monte Carlo (DSMC) method, is used to study the aerodynamic force and heating performance of the compressible Couette flow under the vibrational nonequilibrium effects. Firstly, based on the reference temperature method, a theoretical formula of the reference temperature for the compressible Couette flow is deduced under the calorically perfect gas model. Then, analyses are conducted of the vibrational nonequilibrium effects on the reference temperature and the Reynolds analogy. The dimensionless criterion for the vibrational nonequilibrium effects is proposed, and the criterion is further employed to design formulas for prediction of the skin-friction and heat transfer. Finally, the theoretical results are validated and calibrated by the DSMC results. Both the analytical and numerical results in this study indicate that, the vibrational nonequilibrium effects reduce the skin-friction of the compressible Couette flow, but meanwhile, the Reynolds analogy is still valid as long as the analogy ratio is corrected to take into account of the vibrational energy transfer. The present study could enrich our understanding of the vibrational nonequilibrium shear flow, and specifically, the nonequilibrium flow criterion could be extended to investigate more practical aerodynamic heating problems which significantly involve the thermal nonequilibrium effects.
2022, 54(1): 83-93. doi: 10.6052/0459-1879-21-414
Tong Ying, Xia Jian, Chen Long, Xue Haotian
When the immersed boundary-lattice Boltzmann (IB-LB) model with the direct-forcing scheme is used to analyze the viscous fluid dynamics of the flow around a moving boundary, the interaction interface and the boundary force format directly affect the numerical accuracy and computational efficiency of the flow solver. Based on the implicit diffuse interface, an improved IB-LB model with the direct-forcing scheme was presented. The boundary force expression is derived based on Eulerian/Lagrangian variable identities. The interaction interface described by the transfer matrix couples the asynchronous movement between Lagrangian points. Use Richardson iteration to numerically solve the linear equations related to the boundary force and the non-slip velocity constraint. It not only overcomes the calculation efficiency problem caused by matrix inversion in the traditional velocity correction scheme, but also gets rid of the dependence of algorithm stability and Lagrangian point distribution. According to the Taylor-Green flow with analytical solution, the numerical accuracy of the present model is evaluated. The results show that the improved IB model can retain the second-order numerical accuracy of the background LB model. The numerical results of the flow over a stationary cylinder and an oscillating cylinder show that the model can provide reliable numerical predictions in the flow simulation involving complex geometries and moving interfaces. The IB-LB model yielded the force identity can effectively suppress the non-physical oscillation of the predicted hydrodynamic forces. The simulation of the flow around the undulating airfoil verifies the practicability of the current model, and can be further popularized in the fluid-structure coupling simulation of large-deformation flexible bodies.
2022, 54(1): 94-105. doi: 10.6052/0459-1879-21-315
Jiang Changwei, Xie Yunfeng, Shi Er, Liu Daifei, Li Jie, Hu Zhangmao
At present, the research of fluid flow and heat transfer problems is mostly based on deterministic working conditions, but there are a large number of uncertain factors in real fluid flow and heat transfer problems. The uncertainty quantification of computational fluid dynamics provides an ability to understand the influence of uncertain factors such as fluid physical properties, boundary conditions and initial conditions on simulations results. In order to reveal the propagation law and evolution characteristics of thermomagnetic convection of paramagnetic fluid in random porous media, a mathematical model and algorithm program of uncertainty quantification for thermomagnetic convection were developed based on intrusive polynomial chaos expansion method. In this method, the input random parameters and output response were expressed by Karhunen-Loeve expansion and polynomial chaos expansion respectively. At the same time, the Galerkin projection method was adopted to decouple the stochastic control equations into a set of deterministic control equations which can be solved by finite element correction method, and each polynomial chaos of output response was solved. Finally, the stochastic projection method was used to solve the chaos coefficients in the corresponding deterministic control equations, and the statistical characteristics and chaos effect of the output response are obtained. The uncertainty quantification of thermomagnetic convection shows that the porosity uncertainty of porous media affects the thermomagnetic convection of paramagnetic fluid in a square cavity through the evolution of governing equations, and the thermomagnetic convection of paramagnetic fluid presents a significant chaos effect. The output response shows the characteristics of rapid convergence. The output response values in the first-order mode are at least one order of magnitude lower than the corresponding average values, while the output response values in the second-order mode are much smaller than those in the first-order mode. Compared with the Monte Carlo method, the two results agree well, but the computational cost of the intrusive polynomial chaos expansion method is significantly reduced.
2022, 54(1): 106-118. doi: 10.6052/0459-1879-21-427
Solid Mechanics
Du Chaofan, Zheng Yanlong, Zhang Dingguo, Zhou Xiaoting
The radial point interpolation method (RPIM) is proposed for dynamic analysis of rotating hub-Mindlin plates. Considering the shear deformation and non-linear coupling deformation which means the in-plane longitudinal shortening terms caused by transverse deformation, retaining all of the high-order terms related to the non-linear coupling deformation in the kinetic energy, the high-order rigid-flexible coupled (HOC) dynamic model is established via employing Lagrange’s equations of the second kind with floating coordinate system and the first-order shear deformation theory which means Mindlin plate theory. This model can avoid the shear locking issue by constructing high-order shape functions. And it can not only deal with thin plate problems but also thick plate problems. The high-order shape functions can be constructed easily by adding high-order polynomial basic functions in RPIM. The static results show that it is enough to avoid shear locking issue by adding 15 polynomial basic functions for RPIM. The simulation results for dynamic analysis of a rotating hub-rectangular plate are compared with those obtained by using first-order approximation coupled (FOAC) dynamic model and zero-order approximation coupled (ZOAC) dynamic model. The results show that the ZOAC dynamic model can only be applied to the case with low rotating speed because of its theoretical defects (neglecting the non-linear coupling deformation), the FOAC and HOC dynamic models can be applied to both low rotating speed and high rotating speed cases. It also shows the results using HOC are more accurate and have wider scope of application, especially in the situation of large deformation. The results are also compared with those obtained by assumed mode method (AMM) and finite element method (FEM), which shows the accuracy of RPIM. It is also demonstrated that the RPIM as a flexible discrete method has more advantages in the same computational condition and can be extended in the field of multibody system dynamics.
2022, 54(1): 119-133. doi: 10.6052/0459-1879-21-362
Xu Shipeng, Ding Xiaohong, Duan Pengyun, Zhang Heng
Fracture is a common orthopedic disease, and internal fixation implants are often used in the treatment of fractures. In the process of tissue healing or repair at the fracture, the structure mechanical properties of ideal fracture internal fixation implants need to meet different biomechanical requirements of different fracture healing stages. A microstructure topology optimization design method for regulating and designing the time-changeable stiffness characteristics of the biodegradable composite microstructure is proposed to meet the special time-changeable stiffness characteristics requirements of the ideal fracture internal fixation implant. Two kinds of degradable materials with different degradation rates and stiffness are used, and the relative density is used as the design variable to describe the distribution of different materials. Taking the maximum sum of the stiffness of the intermediate structure in specific degradation steps as the optimization objective, the topology optimization design of microstructure configuration of the composite is carried out to make it have a specific time-changeable characteristic in line with the law of fracture healing. Using the uniform corrosion method, the degradation process of the composite structure is described by material residual rate which is time-dependent, and the finite element model considering material degradation in the time dimension is established. The continuous degradation update formula is proposed by integrating the Heaviside function and Kreisselmeier-Steinhauser function. The mechanical properties of the intermediate structure at different degradation time steps are calculated by homogenization method, and the sensitivity of the optimization objective to the design variables is computed. Compare with the structure using only a single material and the topology optimization structure without time-changeable characteristic regulation, the effectiveness of the proposed topology optimization design method of composite material microstructure considering time-changeable stiffness characteristics is verified. And the effects of different parameters on the optimized configuration of unit cell and time-changeable stiffness characteristics are also studied.
2022, 54(1): 134-146. doi: 10.6052/0459-1879-21-395
Deng Ya, Zhang Yumin, Zhou Yufeng
Residual stress will be generated during its preparation, processing and service of silicon carbide single crystal, which destroys its integrity and restricts the excellent performance and reliability of devices. In order to accurately evaluate the crystal quality and improve device performance, research on the measurement of residual stress in single crystal silicon carbide was carried out in this manuscript. Firstly, the relevant theory for solving the residual stress state of single crystal silicon carbide with a hexagonal crystal structure was deduced by improving the original multiple regression analysis method. Secondly, the residual stresses in 6H-SiC single crystal wafer grown along the $[10\overline 1 0]$ orientation was detected by this method. And {214} crystal plane family of silicon carbide single crystal wafer was selected as the measured diffraction plane. Finally, error analysis of the measurement results calculated by applying the data for different numbers of (hkl) reflections was investigated to illustrate the influence of the number of lattice planes on residual stress results. The results indicated that the in-plane stress components of single crystalline 6H-SiC can be determined by multiple regression analysis; the standard deviation was higher than those calculated based on more than five sets of (hkl) crystal planes for stress calculation when given the value of the stress-free lattice spacing d0. And if the unstressed interplanar spacing was unknown, as the number of crystal planes increases, the error results of plane residual stress gradually decreased. Besides, the error results changed slowly and even tended to steady state when at least six crystal planes were used in the stress calculation. This phenomenon suggests that the experimental residual stress results have high accuracy and high precise. In addition, six or more crystal planes should be selected to solve the residual stress state of silicon carbide single crystal wafer to ensure the reliability of the experimental results.
2022, 54(1): 147-153. doi: 10.6052/0459-1879-21-426
Yin Yaode, Zhao Demin, Liu Jianlin, Xu Zengyao, Hou Wei
Acrylic elastomer VHB 4910 is one of the most significant categories of dielectric elastomer and has the promising applications in the field of soft robotics, actuators, energy harvesters and intelligent vibration isolation. But the nonlinear viscoelasticity of elastomer affects the mechanical behavior of the material dramatically. Recently fractional order models have received much successes in modeling complex material. In the work, a 3D tensorial constitutive model of elastomer based on the fractional Kelvin-Voigt model at finite deformation is formulated. And then the constitutive relation of uniaxial stretches is also derived. Subsequently a series of uniaxial experiments of VHB 4910 elastomer under different stretch rates are conducted. Based on the additive structure of the constitutive model, the parameters of the hyperelastic spring and the fractional viscoelastic element are identified, respectively. The material parameters of hyperelastic spring in the model are identified by the Neo-hookean, Mooney-Rivlin and Gent model at first. Then the parameter identifications for both variable order and constant order fractional viscoelastic element are conducted in order to investigate the rate dependency of fractional viscoelastic elastomer. The results show that the Mooney-Rivlin model can give a better fitting result for the hyperleastic spring element. Both of the variable order and constant order fractional viscoelastic model can simulate the rate dependency of the viscoelastic elastomer well. Constraining the order of the fractional model influents the accuracy of fitting results non-significantly. The relationship between viscosity of fractional element and stretch rate is observed to be nonlinear, which indicates the non-Newtonian fluid feature of the elastomer. Then a modified power law is developed to quantitatively describe this nonlinear relationship. The fitting curve of the modified power law is compared with the Cross non-Newtonian fluid model. The result shows that the developed model can lead to a better fitting results than Cross fluid model.
2022, 54(1): 154-162. doi: 10.6052/0459-1879-21-445
Di Honggui, Guo Huiji, Zhou Shunhua, Wang Binglong, He Chao
In the actual foundation-tunnel system, the properties of soil and structures often change longitudinally along the tunnel line. In order to consider the longitudinal variation characteristics of structures, a multi coupling periodic finite element method for dynamic response analysis of unsaturated soil-structure system is proposed in this paper. Firstly, based on the practical wave equation of unsaturated soil, the finite element expression of ub-pl -pg scheme for unsaturated soil with 5 degrees of freedom at a single node is derived by Galerkin method, which can save the computing efficiency compared with the finite element expression of ub-v-w scheme with 9 degrees of freedom at a single node. Then, by introducing the stretching function with complex number, the perfectly matched layer boundary element is constructed to truncate the infinite domain. Finally, multi periodicity is used to simulate the longitudinal variation characteristics of the structure. By introducing the free wave propagation theory and combining the continuity conditions between periodic structures, the coupling between periodic structures can be realized. The results of the proposed method are compared with the results obtained by the existing 2.5 dimensional coupled FE-PML model and analytical method respectively, which verified the reliability of the proposed method. Compared with the existing analytical methods or numerical methods, the proposed method has the advantage of considering the longitudinal variation characteristics of the structure efficiently. Based on the proposed method, taking unsaturated soil-tunnel-isolation pile system as an example, the vibration reduction and isolation effect of isolation pile is discussed. The results show that compared with gnawing piles, the regular of surface dynamic response changes after considering the spacing between isolated piles. Therefore, in order to accurately predict the vibration response of subway tunnel system, the longitudinal variation characteristics of the system structure should be taken into consideration.
2022, 54(1): 163-172. doi: 10.6052/0459-1879-21-367
Dynamics, Vibration and Control
Zhang Wanjie, Niu Jiangchuan, Shen Yongjun, Yang Shaopu, Liu Jiaqi
On the issues of time delay in the semi-active control system with magnetorheological fluid damper, the controllable time-delay variable is introduced into the switching conditions of semi-active control strategy. The influences of time delay in the switching conditions of sky-hook damping control system are studied. The vibration characteristics of a linear stiffness system under foundation excitation, with magnetorheological fluid damper based on fractional-order Bingham model, are analyzed by the approximate analytical method. The analytical solutions of the primary resonance of the semi-active control system with time delay are obtained through the averaging method, and the stability conditions of the steady-state solution of the system are demonstrated according to Lyapunov theory. The amplitude-frequency responses of analytical solutions show a good correlation with the numerical solutions close-by the resonance frequency, which validates the accuracy and efficiency of the analytical solutions. Furthermore, the influences of time delay on the amplitude-frequency responses of the system at fixed excitation frequency, the primary resonance amplitude responses and the corresponding resonance frequencies changed with different time-delay values are investigated by using the approximate analytical solution. The results suggest that the amplitude responses of the semi-active control system in a small time-delay range is lower than the control system without time delay near the excitation frequency corresponding to the resonance peak, and there is an optimal time delay making a significant reduction of the amplitude of the primary resonance peak. However, the vibration of the control system would be worsened with larger time delays, leading to the flutter of the control system at high frequencies. The principles of time delay introducing to linear stiffness system with fractional-order Bingham model under semi-active control of sky-hook damping are determined. It provides a reference of selecting a feasible time delay in semi-active damping control vibration system.
2022, 54(1): 173-183. doi: 10.6052/0459-1879-21-467
Bai Zhengfeng, Kong Qingfeng, Zhao Qi
Since the mass of the soft manipulator is distributed along the length of arm continuously, when Lagrange method is used to establish the dynamic modeling of the soft manipulator, it involves complex integral calculation. The discrete centralized mass model reduces the complexity, but the accuracy is limited. In this paper, in order to improve the accuracy and efficiency of dynamics modeling and simulation, of the soft manipulator, the modal method is adopted to describe the kinematics of the soft manipulator. Then, considering the dynamic characteristics of the soft manipulator from the energy point of view, it is found that the calculation of rotational kinetic energy generated by the angular velocity is complex, which affect the efficiency of solving the dynamics equation. However, the percentage of rotational kinetic energy in the process of dynamic modeling is less than 3% of the total kinetic energy on a given condition. Consequently, the effect on the dynamics results is small and it can be ignored in the modeling process. Further, a dynamics model of the soft manipulator is proposed based on the concentrated mass description of the center of mass. The continuous distribution mass of the soft manipulator is equivalent to the concentrated mass located in the center of mass. The kinetic energy equivalent coefficient is calculated based on the statistical method. Then, the kinetic energy matching between the two is realized by the kinetic energy equivalent coefficient and the calculation accuracy is improved. The simulation results show that compared with the centralized mass model which usually places the concentrated mass at any position (for example, the midpoint or end of the soft manipulator), the model takes into account the accuracy of the continuous distributed mass model and the calculation efficiency when using the centralized mass model. The model proposed in this work can obtain the dynamics characteristics of the soft manipulator accurately and efficiently, and the numerical calculation is stable.
2022, 54(1): 184-195. doi: 10.6052/0459-1879-21-481
Fan Wenliang, Sheng Xiangqian
Compared with the time-domain method, the frequency-domain method is a more efficient and easy-to- implement method for random vibration analysis. However, the existing frequency-domain methods often involve truncation for degree of mode or decomposition of the power spectrum in multi-correlation conditions, which may have impact on the computational accuracy and efficiency of the methods. To this end, an accurate and efficient auxiliary harmonic excitation generalized method is proposed for the analysis of random vibration of linear structures under stationary Gaussian excitation in the framework of the frequency domain method. First, the concepts of generalized impulse response function and generalized frequency response function are introduced, and a generalized analysis method, which is equivalent to the complete quadratic combination method of response power spectrum calculation, is derived. Secondly, replacing the product of generalized frequency response function by the product of response of auxiliary harmonic excitation, a more easily implemented auxiliary harmonic excitation generalized method is further proposed based on generalized analysis method. Third, according to the different calculation methods of response for structure under the auxiliary harmonic excitation, two generalized methods of auxiliary harmonic excitation generalized method with different applicability are proposed, namely, the auxiliary harmonic excitation generalized method based on the mode superposition and the auxiliary harmonic excitation generalized method based on the time analysis. Meanwhile, the computational performance of the above two methods and their comparative analysis with the existing methods are introduced. Finally, the computational accuracy and efficiency of the proposed method are verified by two examples. The results of the examples show that the auxiliary harmonic excitation generalized method has significant advantages of the calculation efficiency over the complete quadratic combination method and the pseudo-excitation method with the same calculation accuracy.
2022, 54(1): 196-208. doi: 10.6052/0459-1879-21-450
Yu Xiangjie, You Bindi, Wei Cheng, Zhao Yang, Xia Bin, Liu Zhaoxu
In traditional absolute nodal coordinate formulation (ANCF) modelling method, the neutral line of the beam with variable cross-section is assumed consistent with structural median line. It will reduce predicting accuracy in flexible deformation and dynamic behaviour for the beam with variable cross-section. For solving this kind of problems, a new dynamic predicting method for slender beam with variable section is presented in this paper. The neutral line position errors of beam with variable cross-section caused by variable section structure and composite material properties are considered to establish the displacement field in this method. Combining with the strain feedback control law and the proposed method, the active vibration control strategies for this beam under space thermal load are proposed by using the sensory and actional piezoelectric patches. Meanwhile, the correctness and accuracy of the proposed method has been verified by taking the variable section solar-sail masts into numerical analysis with the proposed method. According to the numerical results, the higher prediction accuracy can be provided by the proposed method, and the flexible deformations of solar-sail mast with variable section caused by thermal load have been effectively suppressed by the strain feedback control law. For obtaining the optimized control results in flexible deformation of the beam with variable cross-section, the dynamic behaviour of it with different piezoelectric ply control strategies has been further analysed. According to the numerical results, the active vibration control will be deteriorated with the assembling distance between sensing and actuating piezoelectric plates increasing. In addition, the stability and sensitivity of the control system can be improved by raising the controller gain. However, the unsteady vibration of the beam will also be excited with the overshoot controller gain. The theoretical value and practical significance in the compositive technical performance can be provided for the beam with variable cross-section during on-orbit working process.
2022, 54(1): 209-219. doi: 10.6052/0459-1879-21-473
Biomechanics, Engineering and Interdiscipliary Mechanics
Wang Tianyu, Niu Yilong, Zhou Jianbang, Wang Xiaofei, Shao Lihua, Han Jianmin
In the field of dental implantology, the most commonly used implant materials are pure titanium or titanium alloy, however, implants composed of titanium have aesthetic defects and potential allergic problems. Zirconia ceramic implants are considered to be an ideal alternative to titanium implants due to their high strength, aesthetics and biocompatibility, but the research on zirconia implants in China is still in its start-up phase comparing with titanium-based implants. In this paper, the stress-strain conditions inside the bone tissue in which the zirconia implants were placed were analyzed by finite element modeling of zirconia ceramic implants as well as the bone tissue and simulation of the dynamic implant placement process. The finite element simulation results shows that the contact area between the implant and the bone tissue increased with the increase of the implantation depth, and the stress within the cancellous bone increased. Considering the specific structure of the bone tissue, the maximum stress and strain within the cancellous bone was taken as the main object of the analysis, then the implant model was optimized in combination with the damage analysis method. In addition, three implant models with self-tapping edge design were designed, and the optimal design was determined by stress-strain analysis. The implant models with self-tapping edge design were then simulated and analyzed for three clinical implant scenarios: thread forming, thread cutting, and thread forming and cutting. The analysis of three implant models with self-tapping edge design led to the conclusion that the thread forming and cutting implant solutions are safer in the process of clinical implant. The results of this paper can shed light on the structural design of zirconia implants and the setting of implantation conditions, and provide theoretical guidance for the independent development of zirconia implants in China and indicate the direction for their early clinical application.
2022, 54(1): 220-231. doi: 10.6052/0459-1879-21-503
Nie Shaojun, Wang Yunpeng
Shock tunnel ground test is usually used to study the high-enthalpy aerodynamic characteristics of new hypersonic vehicles. As one of the basic researches of high-temperature aerodynamics, high-precision aerodynamic force measurement is the key technology of shock tunnel ground test. When a force test is conducted in the shock tunnel, the vibration of force measurement system is excited during the starting process of shock tunnel, which causes inertial interference to the output signal of the balance. The balance signals, with dynamic force and inertial-vibration, may not directly show regularity of the real dynamic force, resulting in a big error between the processed balance forces and the real loads, and making the results unreliable. Due to complex structure of the force measurement system, part of the high-frequency components of the balance signal (high-frequency interference caused by structural high-order modal vibration, unsteady aerodynamic load or other flow field interference) may not be fully attenuated within the extremely short-duration (millisecond level). At this time, traditional filter processing and Fourier transform may increase the error of results. In order to solve the problem of aerodynamic force measurement fast and accurately, wavelet transform and Hilbert-Huang transform are used in this study to carry out noise reduction and time-frequency transform analysis for the balance signal in a cone’s force test of shock tunnel, to effectively identify the different interference components and output reliable force results. In this paper, the time-frequency transform is applied to the signal processing of the step-load and balance output. The force results are compared and analyzed to verify the effectiveness and reliability of the current method in the data-processing of the shock tunnel test, and obtain good results. At the same time, the time-frequency processing method of signal in this study will be used in the sample data pre-processing of the shock tunnel balance intelligent research.
2022, 54(1): 232-243. doi: 10.6052/0459-1879-21-387
Li Jialin, Zhao Jian, Sun Zhi, Guo Xinglin, Guo Xu
The transmission frame in launch vehicles is a key structure to transfer the thrust load between the rocket body and engine. The structural lightweight design can not only ensure the thrust-weight ratio of engine, and improve the stability of rocket, also provide reference values for the reusable launch vehicles in the future research. Under the moving morphable component (MMC)-based framework, this paper proposes an approach for solving lightweight design problem of transmission frame structures. In this method, structural topology can be described by using a set of morphable components with explicit geometric information, which renders the optimized layout in terms of a small number of design variables. By analyzing the characteristics and requirements of transmission frame structures, structural stiffness maximum under volume constraint is chose as the objective function, and the corresponding problem formulation based on the MMC explicit topology optimization method can be formulated. Thus, an optimization platform is established to achieve the lightweight design of transmission frame in practical engineering. Under two different load cases (i.e., the thrust load is located at zero angle and swing, respectively), the optimized result is that the large wing plate structure between the middle thrust load area and the connection position of conical structure is constructed to enhance the structural bending capacity. Compared with the traditional frame structure, the effectiveness of the proposed method in the lightweight design is proved.
2022, 54(1): 244-251. doi: 10.6052/0459-1879-21-309
Zhang Changguang, Gao Benxian, Zhou Wei, Li Haixiang
Long-term freeze-thaw cycles of the seasonal cold region result in the deterioration of strength and deformation properties of surrounding rock, which make cold region tunnels easily reach a plastic state, and surrounding rock of a cold region tunnel displays the non-uniform frost heave mainly in radial direction. Based on the Mohr-Coulomb criterion, plastic solutions of the frost heaving force, stress and displacement for a cold region tunnel were presented. The proposed solution reasonably accounts for the deterioration of surrounding rock properties caused by freeze-thaw cycles and the non-uniform frost heave of surrounding rock. Meanwhile, the corresponding elastic solutions and a means to determine the elasto-plastic state of frozen surrounding rock were introduced. Furthermore, discussions and comparative verifications of the proposed solution were performed. Finally, the effects of freezing-thawing cycles, the non-uniform frost heave and volumetric frost heave ratio on stress distribution, plastic zone radius, wall displacement and frost heave force of cold region tunnels were investigated. It is indicated herein that the proposed solution has broad applicability and decent comparability, which is partly demonstrated by a plastic solution available in the reference. With increasing the number of freeze-thaw cycles, the frost heave force, wall displacement and plastic zone radius are increased by 20.3%, 8.44 times, and 2.16 times, respectively. It quantifies the deterioration effect of surrounding rock properties caused by long-term freeze-thaw cycles. When frozen surrounding rock is frost heaved from a uniform model to a non-uniform one, the frost heave force is increased by 42.8%, yet the radius of plastic zone is almost unchanged. Four parameters of volumetric frost heave ratio significantly affect the frost heave force, peculiarly the water-heat migration factor which leads to the increase of the frost heave force by 123.6%. The results of this study can provide some theoretical basis for the design and frost damage solving of seasonal cold region tunnels.
2022, 54(1): 252-262. doi: 10.6052/0459-1879-21-401