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2021 Vol. 53, No. 11

Theme Articles on Vibrational Energy Capture
Preface of theme articles on vibration energy harvesting
Zhou Shengxi, Tao Kai, Qin Weiyang
2021, 53(11): 2891-2893. doi: 10.6052/0459-1879-21-552
Yang Tao, Zhou Shengxi, Cao Qingjie, Zhang Wenming, Chen Liqun
With the rapid development of low-power electronic equipment and self-powered wireless sensor networks in engineering, vibration energy harvesting has been widely used in aerospace engineering, mechanical engineering, biomedical engineering, and sustainable energy engineering. Vibration energy harvesting can not only convert vibration energy into usable electrical energy to power microelectronic equipment, but also reduce harmful vibrations to protect instruments and equipment. According to the different conversion mechanisms of vibration energy, the vibration energy harvesting system can be divided into electrostatic type, electromagnetic type, piezoelectric type, magnetostrictive type, triboelectric type and their hybrid type. Among them, piezoelectric and electromagnetic vibration energy conversion mechanisms have been widely used in various engineering fields due to their simple structure, easy assembly, and high energy conversion performance. Due to extreme environmental interference, broadband, low frequency and other vibrations are easy to occur in the engineering. It forces the rapid development of vibration energy harvesting technology in the direction of nonlinearity, which further attracts many scholars to study the optimal design of the structure and circuit of vibration energy harvesting. Firstly, this article summarizes the research progress of nonlinear vibration energy harvesting technology in the past ten years. It mainly includes the research status of design technology basis, nonlinear structure design, dynamic analysis and so on. Secondly, it focuses on the main research results of the integration of vibration energy harvesting and vibration suppression, including the application of nonlinear quasi-zero stiffness and nonlinear energy sink in the field of vibration energy harvesting. Finally, the optimized design of external vibration energy harvesting circuit and active control strategy are summarized, and effective methods to further improve the efficiency of nonlinear vibration energy harvesting are analyzed.
2021, 53(11): 2894-2909. doi: 10.6052/0459-1879-21-474
Li Shenfang, Wang Junlei, Wang Zhonglin
The fluid mechanical energy including air kinetic energy and liquids kinetic energy in the environment is one of the most abundant and important clean energy. Through different energy harvesting technologies such as electromagnetic power generation technology and piezoelectric energy harvesting technology, the aforementioned clean fluid energy can be successfully converted into electrical energy and used by human. Since the triboelectric nanogenerator (TENG) was invented in 2012 year from the research lab leaded by Zhonglin Wang, the triboelectric nanogenerator has become one of the most important energy harvesting technology and has been applied to fluid mechanical energy harvesting. This paper comprehensively reviews the current research status of energy harvesting by fluidic energy harvesting TENG (FEH-TENG). The principle of charge transfer between triboelectric materials in FEH-TENG and the basic working mode is introduced. On harvesting air kinetic energy, as the mechanism of Flow induced vibrations (such as vortex-induced vibration, gallop, flutter, and wake galloping, etc.) can effectively transfer fluidic energy into mechanical energy, which is quite proper in designing the energy harvesting structure, in this work, the research progress and various energy harvesting structures of FEH-TENG in wind energy and flow-induced vibration energy harvesting are summarized. In the aspect of liquid kinetic energy harvesting, the research work of FEH-TENG utilized in wave and raindrop energy harvesting is also summarized. Furthermore, the research progress of the hybrid energy harvesting system based on FEH-TENG and optimization of triboelectric materials in improving the energy harvesting efficiency of FEH-TENG has been summarized. Then, the application of FEH-TENG in different engineering fields is introduced. Finally, the current existing problems of the FEH-TENG while collecting the fluid mechanical energy in harvesting are discussed and some perspectives for the future development of FEH-TENG are provided. This work is helpful to promote the development of FEH-TENG in the research fields of fluid mechanical energy harvesting and promote the understanding of relevant researchers in this research fields.
2021, 53(11): 2910-2927. doi: 10.6052/0459-1879-21-411
Chen Nan, Liu Jingrui, Wei Tingcun
With the rapid developments of internet of things (IoT) technology, the traditional battery-based power supplies cannot meet its requirements of power supply. Using a piezoelectric energy harvesting technology which converts the mechanical energy into electrical energy, can provide a stable and long-lasting power supply for IoTs, and has wide application prospects. Based on the discussion of the electrical characteristics of piezoelectric vibration energy harvester, this paper comprehensively summarizes state-of-the-art energy management circuits for piezoelectric vibration energy harvesters. The energy management circuits are usually composed of an AC-DC converter and a DC-DC switching converter (including the control algorithm of converters). The former is used to convert the AC voltage from the piezoelectric vibration energy harvester into DC voltage, and the latter is used to improve the efficiency of energy harvesting. Firstly, for AC-DC converters, the working principles and characteristics of full bridge rectifiers, voltage doublers, synchronized switch harvesting on inductors (SSHI) and synchronized switch harvesting on capacitors (SSHC) are analyzed. Then, the typical switching converters for piezoelectric energy harvesting are discussed, including inductor-based/ capacitor-based/ and transformer-based DC-DC switching converters and inductor-based AC-DC switching converters, besides, their characteristics and applications are analyzed. Finally, according to the characteristics of piezoelectric energy harvester, several typical control algorithms for maximum energy harvesting are analyzed, including maximum power point tracking, impedance matching and synchronous electric charge extraction (SECE). Through the comprehensive analysis and summary of the energy management circuits for the piezoelectric vibration energy harvesters, this paper reveals its bottleneck problems and future development trends, it has important reference values for the research and development of the self-powered piezoelectric energy harvesting systems.
2021, 53(11): 2928-2940. doi: 10.6052/0459-1879-21-440
Zou Hongxiang, Guo Dinghua, Gan Chongzao, Tang Shuguang, Yuan Jun, Wei Kexiang, Zhang Wenming
By setting small electromechanical systems such as wireless sensors in the traffic environment to realize traffic condition monitoring, system management and facility health monitoring, etc., the traffic system can be operated in a safer, orderly and efficient manner. However, how to power these widely distributed small electromechanical systems? This paper proposes a magnetic coupling road energy harvesting design to collect vehicle rolling energy and convert it into electricity. The device transmits non-contact energy through magnetic coupling, which reduces the impact on the device and makes it have a good seal, so as to improve the robustness. The vehicle rolling excitation is converted into high-speed one-way rotation through the up-frequency gear and the ratchet mechanism, and the reversing gear mechanism can continue to collect the reset elastic potential energy, which improves the output power of the device. Based on the working principle of the system, the electromechanical coupling dynamics model is established. The numerical simulation explored the impact of key design parameters such as the limit distance of the speed bump and the stiffness of the resetting spring on the dynamics and electrical performance of the energy harvesting system. When the vehicle speed is 50 km/h, the maximum output voltage of the system is 76.28 V and the maximum power is 59.94 W. The magnetic coupling road energy harvesting device can become an important part of the intelligent traffic system in future, harvesting the energy of the traffic environment and providing sustainable green carbon-free power for small and medium electromechanical systems in the traffic environment.
2021, 53(11): 2941-2949. doi: 10.6052/0459-1879-21-374
Meng Ying, Ding Hu, Chen Liqun
Piezoelectric energy harvesting based on circular plates has great potential in replacing chemical battery to provide power for low-power electronic devices. This paper investigates the harvesting performance of a piezoelectric circular plate energy harvester with a proof mass considering its contact area via theoretical modeling and numerical simulations. Firstly, based on the Kirchhoff thin plate theory, the generalized Hamilton principle is applied to derive the electromechanical coupling equations of the piezoelectric circular plate energy harvester considering the proof mass. The equations are approximately discretized using the Galerkin method, and the discretized equations yield closed solutions of voltage, power output, and optimal load resistance. In addition, the correctness of the theoretical model is verified via the finite element simulations, and the results show that the theoretical model can successfully predict the power output of the piezoelectric circular energy harvester. Finally, the closed solutions are used to explore the effects of related parameters, such as the load resistance, the proof mass, the inner and the outer radius of the piezoelectric circular plate, on the natural frequencies, the output voltage and power of the piezoelectric circular energy harvester. The results show that when the contact radius between the proof mass and the piezoelectric composite plate is small enough (here, the contact radius is less than 1/14 of the plate radius), the contact area between the proof mass and the circular plate can be ignored. It is found that the piezoelectric plate with inner diameter between 2.5 mm and 4 mm can improve the harvesting performance of the energy harvester, compared with the piezoelectric plate without hole. As well as that the proper choice of the mass, the load resistance and the outer radius of piezoelectric circular plate can not only reduce the natural frequencies of the piezoelectric circular plate, but also improve its harvesting performance.
2021, 53(11): 2950-2960. doi: 10.6052/0459-1879-21-441
Zhao Linchuan, Zou Hongxiang, Liu Fengrui, Wei Kexiang, Zhang Wenming
The poor performance of energy harvesting under low speed excitation is the bottleneck that restricts the application of rotational energy harvesting. In this paper, a dynamic coordinated modulation mechanism is proposed to modulate the dynamic behavior of the system, which can make the device work effectively under low speed excitation and achieve an enhanced electrical performance of the rotational energy harvesting system. The coordinated modulation of centrifugal-softening-nonlinear-magnetic-force-geometric-boundary can not only increase the vibration displacement of the system and the deformation of the piezoelectric material under low speed excitation, but also modulate the maximum displacement of the system when the vibration displacement is too large, so as to make the vibration controllable and improve the reliability. Moreover, the geometric boundary can easily integrate the triboelectric nanogenerator to realize the coordinated power generation of piezoelectric and triboelectric in the process of vibration and impact, which can make effective use of space and enhance the electrical performance. Based on Hamiltonian principle, the electromechanical coupling equation of the system is established and verified by experiments. The experimental results show that the system can work effectively in the speed range of 0−250 r/min. The P-P voltage of piezoelectric unit and triboelectric nanogenerator are 132 V and 1128 V, and the total average power is 1426 μW at the speed of 250 r/min. The dynamic coordinated modulation mechanism proposed in this paper provides a new method to improve the dynamic and electrical performance of energy harvesting system, and shows potential application prospects in the self-powered internet of things.
2021, 53(11): 2961-2971. doi: 10.6052/0459-1879-21-410
Zhao Long, Lu Zeqi, Ding Hu, Chen Liqun
Integration of vibration isolation and energy harvesting is a dynamic mechanism, in which the harmful vibration could be isolated and converted into electrical energy. In this paper, the dynamic behavior of dual-functional metamaterials for vibration isolation and energy harvesting is studied based on the low frequency band gap characteristics of local resonance metamaterials. A spherical pendulum resonator with energy harvesting function is placed in the spherical cavity by fixing the pendulum of the induction coil. The vibration in the range of band gap frequency can be harvested in the resonator, with the aiming at the dual-functions of vibration isolation and energy harvesting. The dynamic equation of dual-functional metamaterial beam under transverse excitation is established, the energy band structure of metamaterial is obtained by using Bloch’s theorem, and the band gap characteristics of metamaterial beam under different parameters are studied. The theoretical model and research method are verified by finite element simulation. Furthermore, the vibration isolation and energy harvesting characteristics of dual-function metamaterial plates are studied. Finally, a dual-functional metamaterial dynamic experimental platform for vibration isolation and energy harvesting is designed and constructed. The analytical, numerical and experimental results demonstrate that the vibration of the metamaterial beam matrix is significantly suppressed in the frequency range of the local resonant band gap. Simultaneously, the vibration is sinked in the resonator, so that the harvested voltage reaches the maximum. The comparison of the energy band structure and amplitude frequency response between with and without the additional resonator reveals that the addition of the spherical pendulum resonator can generate a local resonant band gap in the low frequency range, which can effectively improve the vibration isolation and energy harvesting performance of the metamaterial beam at the low frequency.
2021, 53(11): 2972-2983. doi: 10.6052/0459-1879-21-471
Zhang Ying, Wang Wei, Cao Junyi
Chaos and bifurcation make the nonlinear dynamic response sensitive to structural parameters for multi-stable energy harvesting system, so that it is difficult to design the nonlinear characteristics directly from structural parameters. In order to acquire the relationship between the nonlinear restoring force and the structural parameters quantitatively, an accurate modelling method of magnetic force for multi-stable energy harvesting system is proposed. The relative distance and the rotational angle between the end magnet and the external magnet are calculated to determine the relative spatial position between magnets, and the magnetic charge theory is adopted to deduce the model of the nonlinear magnetic force in multi-stable energy harvesting system. Then, the experimental platform is carried out to measure the nonlinear magnetic force under different structural parameters for multi-stable energy harvesting system. The comparative analysis shows that the magnetic force calculated by the proposed method is in a better agreement with the experimental result than other methods. The effectiveness of the proposed method for magnetic force prediction is verified by the peak values errors of 4.3% and 6.49% for bi-stable energy harvesting system and tri-stable energy harvesting system respectively. In addition, the influence mechanism of structural parameters on potential wells is investigated to obtain the steady states critical positions of multi-stable energy harvesting system based on the proposed method, and also the influence of different structural parameters on voltage response is analysed for bi-stable and tri-stable energy harvesting systems. After parameters optimization, the maximal RMS voltage response for bi-stable system is 10.22 V in case of the vertical distance 34 mm, while for tri-stable system the maximal RMS voltage response is 12.7 V in case of the vertical distance 28 mm and horizontal distance 8 mm. This research is expected to provide the guidance for the output performance optimization of multi-stable energy harvesting system.
2021, 53(11): 2984-2995. doi: 10.6052/0459-1879-21-446
Zhang Xuhui, Chen Luyang, Chen Xiaoyu, Xu Dongmei, Zhu Fulin, Guo Yan
Vibration energy harvesting technology can convert the vibration energy of equipment working conditions into electrical energy, which provides a new idea for realizing self-powered wireless monitoring nodes in coal mines. In this paper, we design a linear-arch composed beam tri-stable piezoelectric energy harvester by introducing nonlinear magnetic force, and analyse the influence of the horizontal distance, vertical distance and excitation acceleration on dynamic characteristics. The nonlinear magnetic force model is established by the magnetic dipole method, the nonlinear restoring force of the linear-arch composed beam is measured experimentally, and the restoring force model is obtained by polynomial fitting. The dynamic model of the system is established based on Euler-Bernoulli beam theory and Lagrange’s equations. From the perspective of time domain, we analyse the influence of the horizontal distance, vertical distance of the magnets, and excitation acceleration on the dynamic characteristics of the system. A prototype of a linear-arch composed beam tri-stable piezoelectric energy harvester was fabricated, and an experimental platform was built for experimental research, by collecting the response speed data at the end of the composite beam after being excited, the speed-displacement data at the end of the composite beam was obtained, which verified the correctness of the theoretical simulation. The results show that the introduction of a nonlinear magnetic field can make the potential of the system have single potential well, double potential well or triple potential well. When we keep the excitation is constant, adjusting the horizontal and vertical spacing of the magnets can enable the system to achieve monostable, bi-stable or tri-stable motion, and the response displacement is relatively large during tri-stable motion. Increasing the excitation acceleration is beneficial for the system to across the barrier and achieve a large response. The research provides theoretical guidance for the design of linear-arch composed beam tri-stable piezoelectric energy harvester.
2021, 53(11): 2996-3006. doi: 10.6052/0459-1879-21-392
Li Haitao, Cao Fan, Ren He, Ding Hu, Chen Liqun
Flow-induced vibration contains considerable energy, which can be converted into electrical energy through energy harvesting. To improve the energy conversion efficiency in low-speed flow fields, the influence of bluff body and the ratio between width and thickness (W/T) on flow-induced vibration energy harvesting performance under different cross-sections was investigated experimentally, and the wake characteristics were analyzed by computational fluid dynamics (computational fluid dynamic, CFD) simulation. The energy harvesting device consists of a piezoelectric cantilever beam and a bluff body with various cross-sections. Firstly, according to the flow-induced vibration theory, a wind tunnel experimental platform for flow-induced vibration energy harvesting was built. The section of the bluff body is set to be rectangular, triangular and D-shaped, and the ratio of width to thickness is set to 1, 1.3, 1.8 and 2.5, respectively. The influence of W/T of the bluff body on the flow-induced vibration energy harvesting was analyzed experimentally. Finally, the insight mechanism of the experimental results is revealed through the computational fluid dynamics simulation. If the section of bluff body is rectangular, increasing the value of W/T will significantly increase the maximum output voltage. However, if the section of bluff body is triangular and D-shape, the vortex-induced vibration (VIV) will occur in the low flow speed region with the increase of W/T, which could improve the energy harvesting effect for low wind speed. The experimental results can be revealed by the related CFD simulation. As the CFD simulation at U = 3 m/s shows, with the increase of W/T, the configuration will lead to more powerful vortex streets, which can significantly enhance the energy harvesting performance of flow-induced vibration. This study can provide a theoretical and experimental basis for the structure optimization of flow-induced vibration energy harvesters and improve the energy conversion efficiency for the low-speed wind.
2021, 53(11): 3007-3015. doi: 10.6052/0459-1879-21-438
Tian Haigang, Shan Xiaobiao, Zhang Jubin, Sui Guangdong, Xie Tao
Piezoelectric energy harvesters can persistently drive the low-power micro-electromechanical systems in the natural environment. For simulating two degrees of freedom plunge-pitch motions of the airfoil and harvesting effectively the aeroelastic vibration energy, this paper proposes a novel airfoil-based flutter piezoelectric energy harvester. Based on the unsteady aerodynamic model, the mathematical model of the fluid-structure-electric coupling fields of the airfoil-based flutter piezoelectric energy harvester is derived. The finite element model is established to simulate the two degrees of freedom plunge-pitch motions of the airfoil and obtain the vortex shedding and flow field characteristics around the airfoil. A wind tunnel experimental system is designed and the prototype of the piezoelectric energy harvester is fabricated. The correctness of the mathematical and simulation models is verified by using the experimental method, and the determined effects of structural parameters of the piezoelectric energy harvester on its aeroelastic vibration response and harvesting performance are analyzed numerically. The obtained results show that the output voltage obtained from theoretical analyses, simulation analyses and experimental investigation demonstrate the good consistency, which verifies the correctness of the mathematical and simulation models. The simulation analyses demonstrate that the changed pressure fields around the airfoil can be obtained, which indicate that the alternated pressure difference drives the airfoil to take place two degrees of freedom plunge-pitch motions. When the airflow velocity exceeds the flutter onset of one, the piezoelectric energy harvester takes place the flutter and occurs the limit cycle oscillations. When the eccentricity is 0.3 and the airflow velocity is 16 m/s, the maximum output voltage is up to 17.88 V and the corresponding output power is 1.278 mW. The power density is up to 7.99 mW/cm3, which achieves the superior harvesting performance over other. The research results provide an important guidance for further designing more efficient airfoil-based flutter piezoelectric energy harvesters.
2021, 53(11): 3016-3024. doi: 10.6052/0459-1879-21-377
Guo Jiyuan, Fan Kangqi, Zhang Yan, Yang Yusen, Ma Xiaoyu
Harvesting the ubiquitous low-frequency mechanical energy for power generation can reduce the number of expired batteries, achieve self-sustained sensors, and cut down the costs for deploying and maintaining the sensor networks. However, the conventional vibrational energy harvesters (VEHs) perform poorly in exploiting low-frequency mechanical energy due to the mismatch between the excitation frequency and the working frequency of the conventional VEHs. To effectively harvest the low-frequency mechanical energy from the surrounding environment, we report herein a rope-driven electromagnetic harvester with a magnetic gear for enhancing the rotation speed and then improving the output power. By transforming low-frequency vibrations to bi-directional rotation via a rope-driven shaft and then converting the bi-directional rotation of the shaft to uni-directional rotation of a driven wheel with enhanced speeds through a stiffness-variable plectrum and a magnetic gear, the proposed motion-transmission system can achieve high-speed rotation under low-frequency vibrations. Based on the motion-transmission system, an electromagnetic energy harvester was designed and fabricated by embedding magnets into the driven wheel and arranging coils in the proximity of the wheels. A theoretical model for the proposed harvester was developed and then validated by experimental test. When excited at 2 Hz with an amplitude of 40 mm, the maximum output power of the proposed harvester reaches 7.82 mW with the aid of the magnetic gear with a transmission ration of 10:4, corresponding to 143% improvement as compared with that of the harvester without the magnetic gear (3.22 mW). Under the same excitation condition, the proposed harvester can increase the voltage of a 220 μF capacitor from 0 V to 1.5 V in 1.2 s via a standard rectifier to convert its alternating current (AC) output into direct current (DC) output. In addition, the proposed harvester can provide 0.35 mW electric power under low-frequency and irregular vibration excitation. Therefore, the proposed design may be a feasible strategy for developing high-performance low-frequency energy harvesters.
2021, 53(11): 3025-3034. doi: 10.6052/0459-1879-21-469
Zhao Xiang, Li Siyi, Li Yinghui
This paper established dynamic model of forced vibration of the curved piezoelectric energy harvesters with cracks. The Green’s function of piezoelectric curved beam with cracks is obtained based on analytical solutions of vibration equation of the electromechanical coupled Prescott models and continuity conditions at crack sections. The system equation of the electromechanical coupled model with cracks is decoupled and the output voltage of the forced vibration of the damaged curved piezoelectric energy harvester under forced vibration is acquired by the linear superposition principle. The damaged conditions of the piezoelectric curved beam can be detected by inverse method, which is proposed in this paper and suitable for the structure in vibration.In the numerical simulations, the analytical solutions of damaged piezoelectric curved beam that have zero crack depth are compared with results in the previous references. The validity of solutions in this paper is verified. The influence of the crack depth, crack location, material geometric parameters and damping on frequency responses of the voltage is investigated separately. The results show that the effect of cracks on the curved piezoelectric energy harvester is more complicated than that of the straight beam model. The voltage response of damaged piezoelectric curved beam is proportionally decrease at the first order frequency that is the first order frequency of heathy curved beam. And the damaged piezoelectric curved beam is excited out the second-order frequency, which is the first order frequency value of healthy piezoelectric curved beam in an short-circuit. The depth of cracks and the range of cracked positions in the piezoelectric curved beam can be determined by monitoring the change of voltage response, which verifies the feasibility of the inverse method. It is feasible and accurate to use the solution of vibration problem to detect the health condition of damaged piezoelectric curved beams.
2021, 53(11): 3035-3044. doi: 10.6052/0459-1879-21-452
Liu Xuan, Wu Yipeng, Qiu Jinhao, Ji Hongli
Piezoelectric materials have good application prospects in the fields of vibration energy harvesting and structural vibration control due to their good electromechanical coupling characteristics. The piezoelectric interface control circuits based on synchronous switch and inductance can adjust the piezoelectric voltage amplitude and phase according to the working principle of oscillation circuit, optimizing the electromechanical energy conversion in piezoelectric vibration systems. The optimized synchronous electric charge extraction technique based on the interface control circuit mentioned above has realized the efficient piezoelectric energy conversion from vibration to electrical energy. This paper proposed a semi-active piezoelectric damping control circuit derived from the optimized synchronous electric charge extraction circuit. The energy conversion phenomenon between the primary and secondary sides of flyback transformer was unitized, the structure vibration suppression was then realized by transferring the electrical energy into the mechanical energy in piezoelectric vibration control systems. The new circuit which combines the piezoelectric electric charge energy extraction and the semi-active damping control approach realized the bidirectional control of piezoelectric vibration system, with a core of flyback transformer. The corresponding control circuit and its working principle were introduced, the piezoelectric vibration damping model under the new synchronized switch damping technology was also established. An experimental platform for the vibration control of a piezoelectric cantilever beam was built and the theoretical model is verified through experiments, the stability problem of the vibration control system was also solved through a simpler control approach.
2021, 53(11): 3045-3055. doi: 10.6052/0459-1879-21-453
Fluid Mechanics
Wang Haoxiang, Li Guangli, Yang Jing, Xiao Yao, Wang Xiaoyong, Xu Yingzhou, Xu Xiangui, Cui Kai
In order to study the flow characteristics of the high-pressure capturing wing (HCW) configuration at subsonic, transonic and supersonic regime, the conceptual configuration of the conical-cone airframe combined HCW was selected, and the typical state points were selected in the range of Mach number 0.3 to 3. The numerical simulation and analysis were carried out under zero angle of attack condition. The results show that in the speed range studied, since the vertical distance between the airframe and HCW at the symmetry plane was the smallest, the aerodynamic interference was the most obvious and gradually weakened along the span. As the Mach number increased, the flow field structure between the airframe and HCW was obviously different. The specific performance were as follows: when the Mach number was less than 0.5, no flow separation occurred, and when the Mach number was greater than 0.5, the obvious flow separation in the back section of the airframe began to appear. Since HCW and the airframe formed an equivalent channel that first contracted and then expanded, the pressure on the lower surface of HCW and the upper surface of fuselage both decreased first and then increased. After entering the transonic speed domain, under the influence of the HCW, the flow separation became more obvious. The shock wave began to appear between the airframe and HCW, and interacted with the separation zone, and a shock wave train appeared which resulted in significant pressure fluctuations on the lower surface of HCW. When the Mach number was 1.5, the shock wave position between the airframe and HCW reached the tail of the airframe, and separation zone almost disappeared. When Mach number continues to increase, the entire flow field presented a shock-dominated structure and the pressure distribution on the lower surface of HCW and the upper surface of fuselage gradually became flat.
2021, 53(11): 3056-3070. doi: 10.6052/0459-1879-21-059
Xu Xiaofei, Tong Songhao, Zhang Da, Dong Chao, Liu Fengxia, Wei Wei, Liu Zhijun
Active fluids hold great potential for the development of new materials, but realizing this potential requires a quantitative understanding of the mechanical behavior that these fluids exhibit, especially the rheological behavior. The Brownian motion equation is extended to establish the kinematic model of self-propelled particles. The viscosity of active fluid is determined based on the reverse non-equilibrium molecular dynamics scheme. The effects of volume fraction, forward locomotion velocity and rotational diffusion coefficient of active particles on the rheological behavior of active fluid are investigated, and the formation mechanism of special rheological behavior of active fluid is determined. The results show that the rheological curve of the active fluid can be divided into viscosity reduction regime, transition regime and Newtonian regime. The higher the volume fraction of the active particle is, the more significant the non-Newtonian properties of the active fluid are. The forward locomotion of the active particles leads to the reduction of the viscosity of the active fluid in the low shear rate region. The coupling effect of forward locomotion and rotational locomotion leads to the non-monotonic change of the rheological curve in the moderate shear rate region, and the frequent rotational locomotion of the active particles leads to the inhibition of the non-Newtonian properties of the active fluids. The fluctuation of active particles makes the active fluids have special rheological behavior. The higher the volume fraction of active particles, the faster the forward locomotion velocity and the smaller the rotational diffusion coefficient are, the easier the active particles produce obvious fluctuations in the active fluid is. The fluctuation of active particles is obvious in the low shear rate region. With the increase of shear rate, the fluctuation of active particles is gradually weakened, and the aggregation structure of particles is constantly destroyed. Finally, the rheological behavior of the system is similar to that of the general passive fluids.
2021, 53(11): 3071-3079. doi: 10.6052/0459-1879-21-368
Solid Mechanics
Mi Sien, Liu Xiaoming, Wei Yueguang
A transition method from discrete molecular dynamics (MD) simulation to continuum elastic finite element analysis (FEA) is proposed. Firstly, the moving position and displacement of crystal material atoms is obtained by MD calculation, and then the finite element deformation model under the assumption of continuous medium is constructed according to the characteristics of crystal structure. Further, the strain and stress fields are obtained combined with the constitutive relationship of material mechanical behavior. In order to test the effectiveness of the MD-FEA method, this method is applied to analyze the tensile deformation of Al-Ni soft-hard composite nano cylinder and the nano indentation of substrate Al with spherical diamond indenter. The stress and the strain fields of the above two problems are obtained by MD-FEA method, and the calculated results are compared with the atomic strain calculated by discrete deformation gradient and the atomic potential stress in traditional MD method. The difference between the stress and strain field calculated by MD-FEA method and the traditional MD atomic strain and potential stress is discussed in detail, and the effectiveness of MD-FEA method and its advantages over traditional MD method are discussed. The result shows that the MD-FEA method and the traditional MD method are consistent when the stress and strain change softly in the volume, and in the area where stress and strain change rapidly and in the surface/interface area, the MD-FEA method can calculate the result more precise. Meanwhile, the MD-FEA method avoid the selection of the cutoff radius and weighting functions, which is necessary in traditional MD method and can lead to human error in some circumstances. When the strain is large, there are obvious difference between the small strain calculated by MD-FEA method and the Green strain calculated by traditional MD method. Thus the MD-FEA method is more suitable for the situation that the stress and strain is small.
2021, 53(11): 3080-3096. doi: 10.6052/0459-1879-21-449
Kong Xijun, Xing Haojie, Li Hongjing, Zhou Zhenghua
Multi-transmitting formula (MTF, referred to as transmitting boundary for simplicity) is a kind of widely-used artificial boundary condition in the numerical simulation of near-field wave motion. It has advantages as very simple definition and formulations, adjustable accuracy and excellent versatility. However, higher-order MTFs suffer from drift problem from time to time when they are applied in finite-element simulations. There have been several ways of suppressing the drift instability of MTF, but those ways are usually accompanied by remarkable loss of accuracy. This work reports a new modified MTF scheme with a drift-elimination factor, which can effectively control the drift problem of MTF at a high level of accuracy. This approach keeps the first-order transmitting term of MTF unchanged and only modifies those terms regarding higher-order transmitting errors, thus the loss of accuracy caused by the modification is greatly reduced. Meanwhile, the added drift-elimination factor ensures the satisfaction of GKS stability criterion in the case of zero-frequency and zero-wavenumber wave energies, which gives a theoretical support for the control of drift instability. A higher-order unified expression of the proposed approach is further summarized, in which the traditional Zhou-Liao’s modified MTF with drift-elimination factor can be seen as a special case of this work. A comparison analysis of the reflection coefficient of different boundary methods shows that the proposed approach not only has superiority in accuracy, but also adapts to a much wider range of the value of drift-elimination factor. Finally, two numerical tests in the context of finite-element simulation of SH wave propagation validate the effectiveness of the proposed approach in both controlling drift problem and maintaining the accuracy of higher-order MTFs. The drift-elimination factor in the proposed approach has little influence on the absorption capacity of those waves impinging the artificial boundary under normal incidence or over small incident angles, in which most of the wave energies have been taken into account.
2021, 53(11): 3097-3109. doi: 10.6052/0459-1879-21-435
Wang Chunhui, Wang Jiaan, Wang Chao, Guo Chunyu, Zhu Guangyuan
The previous studies on the vertical penetration of structures through level ice mostly did not consider the water action, which was inconsistent with the actual application scenarios. In this paper, a numerical simulation method of ice-water-structure interaction based on structured-arbitrary Lagrange Euler (S-ALE) fluid-structure coupling method and penalty function contact algorithm is established by using LS-DYNA finite element software. Eulerian algorithm is used to describe air and water areas, Lagrangian algorithm is used to describe cylinder structure and level ice structure, and elastic-plastic strain rate model is used to characterize the mechanical properties of ice materials. Self-built test bench for vertical penetration of cylinder through level ice verified the feasibility of finite element method to calculate the interaction between structure and level ice problem. By simulating the ice-breaking process of cylinder vertical upward water breakthrough, it is compared with the ice-breaking process of cylinder vertical penetration in waterless environment. The results show that there is "water cushion effect" in the interaction between structure and level ice in water environment; The extreme value of ice breakthrough load has no significant change with the presence or absence of water; The duration of ice load when the structure breaks through level ice in water environment is obviously longer than that in waterless environment.The elastic deformation stage of level ice in water environment is longer, and the deflection change of level ice is greater than that in waterless environment. The research results of this paper provide a research basis for strength calculation and optimization design of ice-breaking structure with vertical vertical upward water breakthrough in polar ice area.
2021, 53(11): 3110-3123. doi: 10.6052/0459-1879-21-217
Dynamics, Vibration and Control
Lü Jialin, Niu Jiangchuan, Shen Yongjun, Yang Shaopu
The vibration control of linear boring bar system attached with linear dynamic vibration absorber and nonlinear energy sink under external harmonic excitation is studied. By ignoring the nonlinear factors in the boring bar system, the three degree of freedom motion equation of the boring bar system attached with linear dynamic vibration absorber and nonlinear energy sink is established, and the forced vibration of the boring bar system with combined dynamic vibration absorber is studied. The approximate analytical solution of boring bar system with combined dynamic vibration absorber is obtained by means of averaging method. The accuracy of the approximate analytical solution is verified by comparing with the numerical solution, and they are in good agreement with each other. By using the approximate analytical solution, the effects of linear dynamic vibration absorber and nonlinear energy sink parameters on the vibration suppression performance of boring bar are analyzed in detail. Based on the analysis of the influence law of the combined dynamic vibration absorber on linear boring bar system, the parameters of the combined dynamic vibration absorber with given mass are optimized, in which the linear dynamic vibration absorber parameters are optimized by using the approximate analytical solution of H optimization method, and the damping of nonlinear energy sink is optimized by the approximate analytical solution of the system. The analysis results show that the combination of linear dynamic vibration absorber and nonlinear energy sink can effectively suppress the vibration of linear boring bar system, moreover, the linear boring bar system can obtain better vibration attenuation effect by using the combined dynamic vibration absorber with optimized parameters. By adding nonlinear energy sink can not only improve the vibration suppression effect of linear dynamic vibration absorber, but also improve the robustness of vibration control system. The analysis results can provide a reference for the design of built-in damping boring bar.
2021, 53(11): 3124-3133. doi: 10.6052/0459-1879-21-475
Zhang Liqi, Yue Chengyu, Zhao Yonghui
Establishing a parameterized aeroelastic model is one of the obstacles in aeroelastic research of the variable-sweep wing. The local modeling technology is widely known as a practical method for constructing a linear parameter varying (LPV) model. However, there has been a lack of effective methods to deal with the incoherency of the local aeroelastic models. The inconsistency of the local aeroelastic models is reflected in the discontinuity of the local structural and aerodynamic models with the change of the system parameters. To solve this problem, this paper proposed a bottom-up coherent processing method to deal with the incoherent local aeroelastic models of the variable-sweep wing. Firstly, the Hungarian algorithm was used to track the structural modes and sort them according to the modal branches. In this way, the matched modes can ensure the coherency of the structural models; Next, the incoherent problem of the aerodynamic model was solved by introducing a scaling matrix in the expression of rational functional approximation, such that the aerodynamic coefficient matrices were written in a coherent form. After the above two steps, the resulting local state-space models have a coherent form, and the aeroelastic state-space model at arbitrary swept angle can be constructed quickly by interpolating the coherent local state-space models, so the computations for the aeroelastic stability and the slow time-varying responses can be performed effectively. Simulation results demonstrated that the model obtained by interpolating on the incoherent aeroelastic models will lead to great modeling errors, while the one obtained by interpolating on the coherent local models can produce an accurate aeroelastic model at any given swept angle of the wing. This paper provides a useful, accurate and efficient modeling method of the parameter-varying aeroelastic system for the variable-sweep wing.
2021, 53(11): 3134-3146. doi: 10.6052/0459-1879-21-275
Biomechanics ,Engineering and Interdiscipliary Mechanics
Lin Weijian, Li Junyan, Chen Zhenxian, Jin Zhongmin
Knee osteoarthritis (OA), a leading cause of knee pain and chronic disability, is a common type of arthritis. The biomechanics of cartilage is an important indicator of the evaluation of knee OA. However, the biomechanics of cartilage of early knee OA remains to be elucidated. The biomechanical differences among the cartilage of healthy knee, early medial knee OA and early coexisting medial and lateral knee OA were still unknown. Therefore, three knee models with these three different OA situations were established based on fibril-reinforced biphasic cartilage finite element model. The biomechanical differences among the cartilage of healthy knee, early medial knee OA and early coexisting medial and lateral knee OA were investigated in the situation of maximum load and in the situation of maximum flexion angle of a gait cycle. When compared with the results of the healthy knee model, the fluid pressure and solid effective stress decreased while the strain increased in the medial compartment cartilage of early medial knee OA model. The results of the lateral compartment cartilage of early medial knee OA model were almost the same as that of healthy knee model. However, the fluid pressure and solid effective stress decreased and the strains increased in both compartment cartilage of early coexisting medial and lateral knee OA model. In conclusion, the changes of the degenerated cartilage in early knee OA would reduce the load support capability and increase the deformation of cartilage, thereby increasing the risk of further degeneration of cartilage. The proposed knee finite element model considering fibril-reinforced biphasic cartilage could be used to study the biomechanical differences between the cartilage of healthy knee and the cartilage of knee OA. In addition, the proposed model could also be adopted in other biomechanical studies of the joints such as hip, ankle and spine.
2021, 53(11): 3147-3156. doi: 10.6052/0459-1879-21-390
Zhao Mi, Long Pengzhen, Wang Piguang, Zhang Chao, Du Xiuli
In an array of elliptical cylinders, upon impinging on large structure, linear incident waves are scattered by bodies; the scattered waves due to linear incident waves subsequently impinge other bodies; the higher-order scattered waves are generated in the same manner as the multiple scattering problem exists. Based on the diffraction theory and elliptic cylindrical coordinates, the analytical solution for the incident and the scattered waves, say the first-order scattered wave, on an isolated elliptical body is formulated firstly; then, with the first-order scattered wave from other bodies as the excitation source, the analytical solution for second-order scattered waves is developed; Analogously, the analytical solution for higher-order scattered waves is obtained; finally, the total wave pressure on a body in an array is obtained in a form of a sum of the incident wave pressure, the first-order scattered wave pressure due to the linear incident wave and the scattered wave pressure considering multiple scattering waves. The present method is validated by a FEM and is applied to two cases in which multiple scattering problem on bodies with different parameters (wave number, separation, wave propagation direction, etc.) is discussed. It can be seen from the results that the effect of high-order scattered wave matters as the wave number is large; multiple scattering problem is reducing but still exists as the distance between bodies increasing; As the quantity of bodies growing, the multiple scattering problem is increasing and its impact is drastically undulant; the effect of high-order scattered wave on the leading structures is larger than that on the one in the downstream.
2021, 53(11): 3157-3167. doi: 10.6052/0459-1879-21-318