Transactions of Nanjing University of Aeronautics & Astronautics
Volume 36,Issue 4,2019 Table of Contents
2019, 36(4):537-544.
DOI: 10.16356/j.1005-1120.2019.04.001
Abstract:
In this paper, the performance analysis of cooperative space shift keying (SSK) system with dual-hop amplify and forward (AF) in receive-correlated Rayleigh channel is presented. By means of the performance analysis, a closed-form approximate expression of the average bit error rate (BER) is derived for the performance evaluation. With this expression, in a high signal-to-noise-ratio (SNR) region, a tight closed-form asymptotic BER of the system is also derived. It can simplify the calculation of average BER and provide effective evaluation for asymptotic performance. By minimizing this asymptotic BER expression, a suboptimum power allocation (PA) scheme is developed, and the closed-form PA coefficients are obtained. Simulation indicates that the suboptimal PA scheme outperforms the conventional equal PA scheme, and its performance is very close to that of the exhaustive search based optimal PA scheme but with low complexity. Moreover, the system performance under the spatially correlated channel is worse than that in spatially independent channel due to the effect of spatial correlation.
In this paper, the performance analysis of cooperative space shift keying (SSK) system with dual-hop amplify and forward (AF) in receive-correlated Rayleigh channel is presented. By means of the performance analysis, a closed-form approximate expression of the average bit error rate (BER) is derived for the performance evaluation. With this expression, in a high signal-to-noise-ratio (SNR) region, a tight closed-form asymptotic BER of the system is also derived. It can simplify the calculation of average BER and provide effective evaluation for asymptotic performance. By minimizing this asymptotic BER expression, a suboptimum power allocation (PA) scheme is developed, and the closed-form PA coefficients are obtained. Simulation indicates that the suboptimal PA scheme outperforms the conventional equal PA scheme, and its performance is very close to that of the exhaustive search based optimal PA scheme but with low complexity. Moreover, the system performance under the spatially correlated channel is worse than that in spatially independent channel due to the effect of spatial correlation.
2019, 36(4):545-565.
DOI: 10.16356/j.1005-1120.2019.04.002
Abstract:
Retro-reflective beamforming technique has the potential of enabling efficient wireless power transmission over long distance (on the order of meters and even kilometers). In retro-reflective beamforming, wireless power transmission is guided by pilot signal: Based upon pilot signal broadcasted by a wireless power receiver, a wireless power transmitter delivers focused microwave power beam(s) onto the location of wireless power receiver. When the wireless power receiver’s location is not fixed or when the wireless power receiver’s location is unknown to the wireless power transmitter, the microwave power beam would follow the wireless power receiver’s location dynamically as long as the wireless power receiver broadcasts pilot signal periodically. This paper reviews our research endeavors in recent years on retro-reflective beamforming technique targeting three applications: (1) wireless charging for low-power mobile/portable electronic devices, (2) space solar power satellites(SSPS)application, and (3) wireless charging in fully-enclosed space. The feasibility and potential of retro-reflective beamforming technique with applications in wireless power transmission are demonstrated by some preliminary experimental results.
Retro-reflective beamforming technique has the potential of enabling efficient wireless power transmission over long distance (on the order of meters and even kilometers). In retro-reflective beamforming, wireless power transmission is guided by pilot signal: Based upon pilot signal broadcasted by a wireless power receiver, a wireless power transmitter delivers focused microwave power beam(s) onto the location of wireless power receiver. When the wireless power receiver’s location is not fixed or when the wireless power receiver’s location is unknown to the wireless power transmitter, the microwave power beam would follow the wireless power receiver’s location dynamically as long as the wireless power receiver broadcasts pilot signal periodically. This paper reviews our research endeavors in recent years on retro-reflective beamforming technique targeting three applications: (1) wireless charging for low-power mobile/portable electronic devices, (2) space solar power satellites(SSPS)application, and (3) wireless charging in fully-enclosed space. The feasibility and potential of retro-reflective beamforming technique with applications in wireless power transmission are demonstrated by some preliminary experimental results.
2019, 36(4):566-578.
DOI: 10.16356/j.1005-1120.2019.04.003
Abstract:
A 60 GHz phased array system for mm-wave frequency in 5G is introduced and a 5 bit digitally controlled phase shifter in 40 nm CMOS technology is presented. In a phased array system, the signal to noise ratio (SNR) of the receiver is improved with the beaming forming function. Therefore, the communication data rate and distance are improved accordingly. The phase shifter is the key component for achieving the beam forming function, and its resolution and power consumption are also very critical. In the second half of this paper, an analysis of phase shifter is introduced, and a 60 GHz 5 bit digitally controlled phase shifter in 40 nm complementary metal oxide semiconductor (CMOS) technology is presented. In this presented phase shifter, a hybrid structure is implemented for its advantage on lower phase deviation while keeping comparable loss. Meanwhile, this digitally controlled phase shifter is much more compact than other works. For all 32 states, the minimum phase error is 1.5°, and the maximum phase error is 6.8°. The measured insertion loss is -20.9±1 dB including pad loss at 60 GHz and the return loss is more than 10 dB over 57—64 GHz. The total chip size is 0.24 mm2 with 0 mW DC power consumption.
A 60 GHz phased array system for mm-wave frequency in 5G is introduced and a 5 bit digitally controlled phase shifter in 40 nm CMOS technology is presented. In a phased array system, the signal to noise ratio (SNR) of the receiver is improved with the beaming forming function. Therefore, the communication data rate and distance are improved accordingly. The phase shifter is the key component for achieving the beam forming function, and its resolution and power consumption are also very critical. In the second half of this paper, an analysis of phase shifter is introduced, and a 60 GHz 5 bit digitally controlled phase shifter in 40 nm complementary metal oxide semiconductor (CMOS) technology is presented. In this presented phase shifter, a hybrid structure is implemented for its advantage on lower phase deviation while keeping comparable loss. Meanwhile, this digitally controlled phase shifter is much more compact than other works. For all 32 states, the minimum phase error is 1.5°, and the maximum phase error is 6.8°. The measured insertion loss is -20.9±1 dB including pad loss at 60 GHz and the return loss is more than 10 dB over 57—64 GHz. The total chip size is 0.24 mm2 with 0 mW DC power consumption.
2019, 36(4):579-588.
DOI: 10.16356/j.1005-1120.2019.04.004
Abstract:
With targets of cost reduction per bit and high energy efficiency, 5G and beyond call for innovation in the mmWave transmitter architecture and the power amplifier (PA) circuit. To illustrate these points, this paper firstly explains the benefits and design implications of the hybrid beamforming structure in terms of the mmWave spectrum characteristics, energy efficiency, data rate, communication capacity, coverage and implementation technology choices. Then after reviewing the techniques to improve the power amplifier (PA) output power and efficiency, the design considerations and test results of 60 GHz and 90 GHz mmWave PAs in bulk complementary metal oxide semiconductor (CMOS) process are shown.
With targets of cost reduction per bit and high energy efficiency, 5G and beyond call for innovation in the mmWave transmitter architecture and the power amplifier (PA) circuit. To illustrate these points, this paper firstly explains the benefits and design implications of the hybrid beamforming structure in terms of the mmWave spectrum characteristics, energy efficiency, data rate, communication capacity, coverage and implementation technology choices. Then after reviewing the techniques to improve the power amplifier (PA) output power and efficiency, the design considerations and test results of 60 GHz and 90 GHz mmWave PAs in bulk complementary metal oxide semiconductor (CMOS) process are shown.
2019, 36(4):589-598.
DOI: 10.16356/j.1005-1120.2019.04.005
Abstract:
For electromagnetic scattering of 3-D complex electrically large conducting targets，a new hybrid algorithm, MoM-PO/SBR algorithm, is presented to realize the interaction of information between method of moment(MoM) and physical optics(PO)/shooting and bouncing ray(SBR). In the algorithm, the COC file that based on the Huygens equivalent principle is introduced, and the conversion interface between the equivalent surface and the target is established. And then, the multi-task flow model presented in this paper is adopted to conduct CPU/graphics processing unit(GPU) tests of the algorithm under three modes, i.e., MPI/OpenMP, MPI/compute unified device architecture(CUDA) and multi-task programming model (MTPM). Numerical results are presented and compared with reference solutions in order to illustrate the accuracy and the efficiency of the proposed algorithm.
For electromagnetic scattering of 3-D complex electrically large conducting targets，a new hybrid algorithm, MoM-PO/SBR algorithm, is presented to realize the interaction of information between method of moment(MoM) and physical optics(PO)/shooting and bouncing ray(SBR). In the algorithm, the COC file that based on the Huygens equivalent principle is introduced, and the conversion interface between the equivalent surface and the target is established. And then, the multi-task flow model presented in this paper is adopted to conduct CPU/graphics processing unit(GPU) tests of the algorithm under three modes, i.e., MPI/OpenMP, MPI/compute unified device architecture(CUDA) and multi-task programming model (MTPM). Numerical results are presented and compared with reference solutions in order to illustrate the accuracy and the efficiency of the proposed algorithm.
2019, 36(4):599-608.
DOI: 10.16356/j.1005-1120.2019.04.006
Abstract:
This paper presents a low-complexity method for the direction-of-arrival (DOA) estimation of noncircular signals for coprime sensor arrays. The noncircular property is exploited to improve the performance of DOA estimation. To reduce the computational complexity, the rotational invariance propagator method (RIPM) is included in the algorithm. First, the extended array output is reconstructed by combining the array output and its conjugated counterpart. Then, the RIPM is utilized to obtain two sets of DOA estimates for two subarrays. Finally, the true DOAs are estimated by combining the consistent results of the two subarrays. This illustrates the potential gain that both noncircularity and coprime arrays provide when considered together. The proposed algorithm has a lower computational complexity and a better DOA estimation performance than the standard estimation of signal parameters by the rotational invariance technique and Capon algorithm. Numerical simulation results illustrate the effectiveness and superiority of the proposed algorithm.
This paper presents a low-complexity method for the direction-of-arrival (DOA) estimation of noncircular signals for coprime sensor arrays. The noncircular property is exploited to improve the performance of DOA estimation. To reduce the computational complexity, the rotational invariance propagator method (RIPM) is included in the algorithm. First, the extended array output is reconstructed by combining the array output and its conjugated counterpart. Then, the RIPM is utilized to obtain two sets of DOA estimates for two subarrays. Finally, the true DOAs are estimated by combining the consistent results of the two subarrays. This illustrates the potential gain that both noncircularity and coprime arrays provide when considered together. The proposed algorithm has a lower computational complexity and a better DOA estimation performance than the standard estimation of signal parameters by the rotational invariance technique and Capon algorithm. Numerical simulation results illustrate the effectiveness and superiority of the proposed algorithm.
2019, 36(4):609-616.
DOI: 10.16356/j.1005-1120.2019.04.007
Abstract:
A sufficient sample size of monitoring data becomes a key factor for describing aircraft engines state. Generative adversarial nets (GAN) can be used to expand the sample size based on the existing state monitoring information. In the paper, a GAN model is introduced to design an algorithm for generating the monitoring data of aircraft engines. This feasibility of the method is illustrated by an example. The experimental results demonstrate that the probability density distribution of generated data after a large number of network training iterations is consistent with the probability density distribution of monitoring data. The proposed method also effectively demonstrates the generated monitoring data of aircraft engine are in a reasonable range. The method can effectively solve the problem of inaccurate performance degradation evaluation caused by the small amount of aero-engine condition monitoring data.
A sufficient sample size of monitoring data becomes a key factor for describing aircraft engines state. Generative adversarial nets (GAN) can be used to expand the sample size based on the existing state monitoring information. In the paper, a GAN model is introduced to design an algorithm for generating the monitoring data of aircraft engines. This feasibility of the method is illustrated by an example. The experimental results demonstrate that the probability density distribution of generated data after a large number of network training iterations is consistent with the probability density distribution of monitoring data. The proposed method also effectively demonstrates the generated monitoring data of aircraft engine are in a reasonable range. The method can effectively solve the problem of inaccurate performance degradation evaluation caused by the small amount of aero-engine condition monitoring data.
2019, 36(4):617-627.
DOI: 10.16356/j.1005-1120.2019.04.008
Abstract:
An adaptive prescribed performance control scheme is proposed for the drag free satellite in the presence of actuator saturation and external disturbances. The relative translation and rotation dynamics between the test mass and outer satellite are firstly derived. To guarantee prescribed performance bounds on the transient and steady control errors of relative states, a performance constrained control law is formulated with an error transformed function. In addition, the requirements to know the system parameters and the upper bound of the external disturbance in advance have been eliminated by adaptive updating technique. A command filter is concurrently used to overcome the problem of explosion of complexity inherent in the backstepping control design. Subsequently, a novel auxiliary system is constructed to compensate the adverse effects of the actuator saturation constrains. It is proved that all signals in the closed-loop system are ultimately bounded and prescribed performance of relative position and attitude control errors are guaranteed. Finally, numerical simulation results are given to demonstrate the effectiveness of the proposed approach.
An adaptive prescribed performance control scheme is proposed for the drag free satellite in the presence of actuator saturation and external disturbances. The relative translation and rotation dynamics between the test mass and outer satellite are firstly derived. To guarantee prescribed performance bounds on the transient and steady control errors of relative states, a performance constrained control law is formulated with an error transformed function. In addition, the requirements to know the system parameters and the upper bound of the external disturbance in advance have been eliminated by adaptive updating technique. A command filter is concurrently used to overcome the problem of explosion of complexity inherent in the backstepping control design. Subsequently, a novel auxiliary system is constructed to compensate the adverse effects of the actuator saturation constrains. It is proved that all signals in the closed-loop system are ultimately bounded and prescribed performance of relative position and attitude control errors are guaranteed. Finally, numerical simulation results are given to demonstrate the effectiveness of the proposed approach.
2019, 36(4):628-634.
DOI: 10.16356/j.1005-1120.2019.04.009
Abstract:
The pull test is a damaging detection method that fails to measure the actual length of a bolt. Thus, the ultrasonic echo is an important non-destructive testing method for bolt quality detection. In this research, the variational modal decomposition (VMD) method is introduced into the bolt detection signal analysis. On the basis of morphological filtering (MF) and the VMD method, a VMD-combined MF principle is established into a bolt detection signal analysis method (MF-VMD). MF-VMD is used to analyze the vibration and actual bolt detection signals of the simulation. Results show that MF-VMD effectively separates intrinsic mode function, even under strong interference. In comparison with conventional VMD method, the proposed method can remove noise interference. An intrinsic mode function of the field detection signal can be effectively identified by reflecting the signal at the bottom of the bolt.
The pull test is a damaging detection method that fails to measure the actual length of a bolt. Thus, the ultrasonic echo is an important non-destructive testing method for bolt quality detection. In this research, the variational modal decomposition (VMD) method is introduced into the bolt detection signal analysis. On the basis of morphological filtering (MF) and the VMD method, a VMD-combined MF principle is established into a bolt detection signal analysis method (MF-VMD). MF-VMD is used to analyze the vibration and actual bolt detection signals of the simulation. Results show that MF-VMD effectively separates intrinsic mode function, even under strong interference. In comparison with conventional VMD method, the proposed method can remove noise interference. An intrinsic mode function of the field detection signal can be effectively identified by reflecting the signal at the bottom of the bolt.
2019, 36(4):635-640.
DOI: 10.16356/j.1005-1120.2019.04.010
Abstract:
A method for evaluating the benign and malignant breast tumors based on radio-frequency (RF) data was explored by extracting the characteristic parameters of breast ultrasound RF signals. The breast biopsy data were used as the reference data for judging the lump benign or malignant. The extracted ultrasound RF data were reconstructed and segmented by computer aided method to obtain the breast tumor region of interest (ROI) and its characteristic parameters (entropy and standard deviation). The characteristic parameters were statistically analyzed to evaluate the relationship between characteristic parameters and benign or malignant breast tumors. The results indicate the entropy and standard deviation of normal region is much higher than that of lump region, which shows that the standard deviation and entropy characteristic parameters of ultrasonic RF signals are meaningful in the diagnosis of breast tumors. The proposed method provides a new direction for computer-aided diagnosis of benign and malignant breast tumors.
A method for evaluating the benign and malignant breast tumors based on radio-frequency (RF) data was explored by extracting the characteristic parameters of breast ultrasound RF signals. The breast biopsy data were used as the reference data for judging the lump benign or malignant. The extracted ultrasound RF data were reconstructed and segmented by computer aided method to obtain the breast tumor region of interest (ROI) and its characteristic parameters (entropy and standard deviation). The characteristic parameters were statistically analyzed to evaluate the relationship between characteristic parameters and benign or malignant breast tumors. The results indicate the entropy and standard deviation of normal region is much higher than that of lump region, which shows that the standard deviation and entropy characteristic parameters of ultrasonic RF signals are meaningful in the diagnosis of breast tumors. The proposed method provides a new direction for computer-aided diagnosis of benign and malignant breast tumors.
2019, 36(4):641-651.
DOI: 10.16356/j.1005-1120.2019.04.011
Abstract:
To gain high efficiency for the simulation of the aerodynamic characteristics of the rotor in hover, body-fitted momentum source (BFMS) method is proposed. In this method, the actual blade geometry is represented by the single layer of volume grid surrounding the blade. Aiming at correctly simulating the aerodynamic characteristics of the discrete cells along the chordwise of blade airfoil section, a new distributed force model is proposed. For comparison, the RANS method with S-A turbulence model and the steady rotor momentum source (SRMS) method based on embedded grid systems are established， respectively. And the grid connecting methodology is improved to embed the blade into the background grids for the three methods. Then, simulations are performed for the hovering Caradonna-Tung rotor by these methods, and the calculated results are compared with the available experimental data. Moreover, the pressure distributions along the blade are compared with the conventional momentum source methods. It is demonstrated that the BFMS method can be employed as an effective approach to predict rotor aerodynamic characteristics with a low computational resource and reasonable accuracy.
To gain high efficiency for the simulation of the aerodynamic characteristics of the rotor in hover, body-fitted momentum source (BFMS) method is proposed. In this method, the actual blade geometry is represented by the single layer of volume grid surrounding the blade. Aiming at correctly simulating the aerodynamic characteristics of the discrete cells along the chordwise of blade airfoil section, a new distributed force model is proposed. For comparison, the RANS method with S-A turbulence model and the steady rotor momentum source (SRMS) method based on embedded grid systems are established， respectively. And the grid connecting methodology is improved to embed the blade into the background grids for the three methods. Then, simulations are performed for the hovering Caradonna-Tung rotor by these methods, and the calculated results are compared with the available experimental data. Moreover, the pressure distributions along the blade are compared with the conventional momentum source methods. It is demonstrated that the BFMS method can be employed as an effective approach to predict rotor aerodynamic characteristics with a low computational resource and reasonable accuracy.
2019, 36(4):652-662.
DOI: 10.16356/j.1005-1120.2019.04.012
Abstract:
In order to investigate the elastic properties of directionally solidified (DS) superalloys, an elasticity model called boundaries elastic model (GBE model), considering grain boundaries and tensile orientations, is proposed in this paper. Two assumptions are adopted in the GBE model: (1) The displacement of grains, which moves along the perpendicular direction, is restricted by the grain boundaries; (2) Grain boundaries influence region (GBIR) is formed around the grain boundaries. Based on the single crystal (SC) calculation method of elastic properties, the GBE model can well predict macroscopic equivalent elastic modulus (Young’s modulus) of DS superalloys under different tensile orientations effectively. To demonstrate the correctness of the GBE model, 3D finite element simulation is adopted and tensile experiments on a Ni3Al-base DS superalloy (IC10) along five tensile orientations are carried out. Meanwhile, the grain boundaries are observed by light microscopy and transmission electron microscope (TEM). Therefore, the GBE model is proved to be feasible by comparing the simulated results with the experiments.
In order to investigate the elastic properties of directionally solidified (DS) superalloys, an elasticity model called boundaries elastic model (GBE model), considering grain boundaries and tensile orientations, is proposed in this paper. Two assumptions are adopted in the GBE model: (1) The displacement of grains, which moves along the perpendicular direction, is restricted by the grain boundaries; (2) Grain boundaries influence region (GBIR) is formed around the grain boundaries. Based on the single crystal (SC) calculation method of elastic properties, the GBE model can well predict macroscopic equivalent elastic modulus (Young’s modulus) of DS superalloys under different tensile orientations effectively. To demonstrate the correctness of the GBE model, 3D finite element simulation is adopted and tensile experiments on a Ni3Al-base DS superalloy (IC10) along five tensile orientations are carried out. Meanwhile, the grain boundaries are observed by light microscopy and transmission electron microscope (TEM). Therefore, the GBE model is proved to be feasible by comparing the simulated results with the experiments.
2019, 36(4):663-674.
DOI: 10.16356/j.1005-1120.2019.04.013
Abstract:
Conventional pneumatic tires exhibit disadvantages such as puncture, blowout at high speed, pressure maintenance, etc. Owing to these structural inevitable weaknesses, non-pneumatic tires have been developed and are investigated. A non-pneumatic mechanical elastic wheel (NPMEW) is introduced and investigated as a function of static radical stiffness characteristics and contact behavior. A bench test method is utilized to improve the riding comfort and the traction traffic ability of NPMEW based on tire characteristics test rig，and the static radical stiffness characteristics and the contact behavior of NPMEW are compared with that of an insert supporting run-flat tire (ISRFT). The vertical force-deformation curves and deformed shapes and contact areas of the NPMEW and ISRFT are obtained using a set of vertical loads. The contact behavior is evaluated using extracted geometrical and mechanical feature parameters of the two tires. The results indicate that the NPMEW appears to exhibit considerably high radical stiffness, and the numerical value is dependent on the mechanical characteristic of the flexible tire body and hinge units. NPMEW demonstrates more uniform contact pressure than ISRFT within a certain loading range, and it can efficiently mitigate the problem of stress concentration in ISRFT shoulder under heavy load and enhance the wear resistance and ground grip performances.
Conventional pneumatic tires exhibit disadvantages such as puncture, blowout at high speed, pressure maintenance, etc. Owing to these structural inevitable weaknesses, non-pneumatic tires have been developed and are investigated. A non-pneumatic mechanical elastic wheel (NPMEW) is introduced and investigated as a function of static radical stiffness characteristics and contact behavior. A bench test method is utilized to improve the riding comfort and the traction traffic ability of NPMEW based on tire characteristics test rig，and the static radical stiffness characteristics and the contact behavior of NPMEW are compared with that of an insert supporting run-flat tire (ISRFT). The vertical force-deformation curves and deformed shapes and contact areas of the NPMEW and ISRFT are obtained using a set of vertical loads. The contact behavior is evaluated using extracted geometrical and mechanical feature parameters of the two tires. The results indicate that the NPMEW appears to exhibit considerably high radical stiffness, and the numerical value is dependent on the mechanical characteristic of the flexible tire body and hinge units. NPMEW demonstrates more uniform contact pressure than ISRFT within a certain loading range, and it can efficiently mitigate the problem of stress concentration in ISRFT shoulder under heavy load and enhance the wear resistance and ground grip performances.
2019, 36(4):675-679.
DOI: 10.16356/j.1005-1120.2019.04.014
Abstract:
The morphologies and hydration properties of MgO expansive material at different curing temperatures were investigated. When the curing temperature varies from 25 ℃ to 50 ℃, the conductivity of MgO rises from 40 to 80 μs/cm, the hydration product of MgO expansive material curing in water for 28 days is from 1.5—2 mm to 2—2.5 μm in length through SEM observation, and the expansion of pastes with 5% of the magnesium oxide is from 0.36% up to 1.01%, it is increased by 2.78 times. When the content of cement paste increases to 95% and cured in water for 90 days, the brucite forms as hexaflaggy-shaped crystal, which is less than 0.1 μm and tends to aggregates. The effect of curing temperature on the hydration of MgO expansive material is obvious.
The morphologies and hydration properties of MgO expansive material at different curing temperatures were investigated. When the curing temperature varies from 25 ℃ to 50 ℃, the conductivity of MgO rises from 40 to 80 μs/cm, the hydration product of MgO expansive material curing in water for 28 days is from 1.5—2 mm to 2—2.5 μm in length through SEM observation, and the expansion of pastes with 5% of the magnesium oxide is from 0.36% up to 1.01%, it is increased by 2.78 times. When the content of cement paste increases to 95% and cured in water for 90 days, the brucite forms as hexaflaggy-shaped crystal, which is less than 0.1 μm and tends to aggregates. The effect of curing temperature on the hydration of MgO expansive material is obvious.
2019, 36(4):680-685.
DOI: 10.16356/j.1005-1120.2019.04.015
Abstract:
Perturbation to Noether symmetry and adiabatic invariants for Birkhoffian system, Hamiltonian system and Lagrangian system with delta derivative are investigated, respectively. Firstly, the definition and some related properties of time scale calculus are listed simply as preliminaries. Secondly, the Birkhoffian system with delta derivative is studied. Based on the differential equation of motion as well as Noether symmetry and conserved quantity, perturbation to Noether symmetry and adiabatic invariant are investigated. Thirdly, adiabatic invariants for the Hamiltonian system and the Lagrangian system are presented through some transformations. And finally, an example is given to illustrate the methods and results.
Perturbation to Noether symmetry and adiabatic invariants for Birkhoffian system, Hamiltonian system and Lagrangian system with delta derivative are investigated, respectively. Firstly, the definition and some related properties of time scale calculus are listed simply as preliminaries. Secondly, the Birkhoffian system with delta derivative is studied. Based on the differential equation of motion as well as Noether symmetry and conserved quantity, perturbation to Noether symmetry and adiabatic invariant are investigated. Thirdly, adiabatic invariants for the Hamiltonian system and the Lagrangian system are presented through some transformations. And finally, an example is given to illustrate the methods and results.
2019, 36(4):686-692.
DOI: 10.16356/j.1005-1120.2019.04.016
Abstract:
The main purpose of the paper is to obtain the experimental yield loci of TRIP590 advanced high strength steel, and to compare it with the theoretical loci in order to obtain the best yield criterion for this material. First, the biaxial loading tests under different loading paths in the method of load control are carried out. Then, the experimental yield loci of different deformation stages are obtained. Finally, the experimental yield loci are compared with the theoretical loci of Mises criterion and Hill48 criterion, the parameters of which are calculated based on the r-value and the yield stress method, respectively. The results show that the accuracy of the theoretical yield loci of Hill48 based on the yield stress is higher than that of Mises criterion and Hill 48 criterion based on r-value method.
The main purpose of the paper is to obtain the experimental yield loci of TRIP590 advanced high strength steel, and to compare it with the theoretical loci in order to obtain the best yield criterion for this material. First, the biaxial loading tests under different loading paths in the method of load control are carried out. Then, the experimental yield loci of different deformation stages are obtained. Finally, the experimental yield loci are compared with the theoretical loci of Mises criterion and Hill48 criterion, the parameters of which are calculated based on the r-value and the yield stress method, respectively. The results show that the accuracy of the theoretical yield loci of Hill48 based on the yield stress is higher than that of Mises criterion and Hill 48 criterion based on r-value method.
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