For a class of mixed initial-boundary value problem for general quasilinear hyperbolic systems, this paper establishes the local exact boundary controllability with boundary controls only acting on one end. As an appl...For a class of mixed initial-boundary value problem for general quasilinear hyperbolic systems, this paper establishes the local exact boundary controllability with boundary controls only acting on one end. As an application, the authors show the local exact boundary controllability for a kind of nonlinear vibrating string problem.展开更多
The paper proposes an analytical approach to investigate the synchronization of the two coupled exciters in a vibrating system of spatial motion. Introducing the distur- bance parameters for average angular velocity o...The paper proposes an analytical approach to investigate the synchronization of the two coupled exciters in a vibrating system of spatial motion. Introducing the distur- bance parameters for average angular velocity of two excit- ers, we deduce the non-dimensional coupling equations of angular velocities of two exciters, in which the inertia cou- pling matrix is symmetric and the stiffness coupling matrix is antisymmetric in a non-resonant vibrating system. The analysis of the coupling dynamic characteristic shows that the coupled cosine effect of the phase angles will cause the torque acting on two motors to limit the increase of phase difference between two exciters as well as sustain its sym- metry of two exciters during the running process. It physi- cally explains the peculiarity of self-synchronization of two exciters. The cosine effect of phase angles of the vibrations excited by each exciter will decrease its moment of inertia. The residual moment of inertia of each exciter represents its relative moment of inertia. The stability condition of synchro- nization of two exciters is that the relative non-dimensional moments of inertia of two exciters are all greater than zero and four times their product is greater than the square of their coefficient of coupled cosine effect of phase angles, which is equivalent to that the inertia coupling matrix is positive definite and all its elements are positive. The numeric results show that the structure of the vibrating system can ensure the stability condition of synchronous operation.展开更多
The motion of a particle on a screen is directly affected by the motion of the screen if airflow and inter- granular friction are ignored. To study this effect, a mathematical model was established to analyze the moti...The motion of a particle on a screen is directly affected by the motion of the screen if airflow and inter- granular friction are ignored. To study this effect, a mathematical model was established to analyze the motion of a planar reciprocating vibrating screen, and a matrix method was employed to derive its equa- tion of motion. The motion of the screen was simulated numerically and analyzed using MATLAB. The results show that the screen undergoes non-simple harmonic motion and the law of motion of each point in the screen is different. The tilt angle of the screen during screening is not constant but varies according to a specific periodic function. The results of numerical simulations were verified through experiments. A high-speed camera was used to track the motion of three points in the longitudinal direction of the screen. The balance equation for forces acting on a single particle on the screen was derived based on the non-simple harmonic motion of the screen, These forces were simulated using MATLAB. Different types of particle motion like slipping forward, moving backward, and being tossed to different parts of the screen were analyzed. A vibro-impact motion model for a particle on the non-simple harmonic vibrating screen was established based on the nonlinear law of motion of the particle. The stability of fixed points of the map is discussed. Regimes of different particle behaviors such as stable periodic motion, period-doubling bifurcation motion, Hopf bifurcation motion, and chaotic motion were obtained. With the actual law of motion of the screen and the behavior of a particle on the screen, a theoretical basis for design optimization of the screen is provided.展开更多
A numerical study of the motion particulates follow along a circularly vibrating screen deck was done using the three dimensional Discrete Element Method (DEM). The motion of the particles was analyzed. The effects of...A numerical study of the motion particulates follow along a circularly vibrating screen deck was done using the three dimensional Discrete Element Method (DEM). The motion of the particles was analyzed. The effects of vibration amplitude, throwing index, and screen deck inclination angle on the screening process are discussed. The results show that the average velocity of the particles increases along the lon- gitudinal direction of the deck. The screening efficiency is highest when the vibration amplitude, throw- ing index, and screen deck inclination angle are 3-3.5 mm, 2.7 and 15°, respectively. This work is helpful for developing a deep understanding of particle motion and for optimizing screen separator designs.展开更多
A new mechanism is proposed to implement the synchronization of the four unbalanced rotors in a vibrating system, which consists of a main rigid frame (MRF) and two accessorial rigid frames (ARF). An analytical approa...A new mechanism is proposed to implement the synchronization of the four unbalanced rotors in a vibrating system, which consists of a main rigid frame (MRF) and two accessorial rigid frames (ARF). An analytical approach is developed to study the coupling dynamic characteristics of the four unbalanced rotors, which converts the problem of synchronization of the four unbalanced rotors into the existence and the stability of zero solutions for the non-dimensional differential equations of the angular velocity disturbance parameters (NDDEDP). The stability of zero solutions of the NDDEDP is decomposed into that of its generalized system and a system of the three first order differential equations for the disturbance parameters of the phase differences. The coupling dynamic characteristic of the four unbalanced rotors includes the inertia coupling, the stiffness coupling of angular velocity and the load torque coupling. The non-dimensional inertia coupling matrix is symmetric, the non dimensional matrix of the stiffness coupling of angular velocity is antisymmetric and its diagonal elements are all negative. Hence, the general system of the NDDEDP automatically satisfies the generalized Lyapunov equations when the non-dimensional inertia coupling matrix is positive definite and its elements are all positive. Using Routh-Hurwitz criterion the condition of stability of differential equations for the disturbance parameters of the phase differences is obtained. The load torque coupling makes the vibrating system have the dynamic characteristic of selecting motions and self-synchronization of the four unbalanced rotors arises from the dynamic characteristic of selecting motion of the vibrating system. When the two coefficients of coupling cosine effect of phase angles are all greater than 0 and the three indexes of synchronization are all far greater than 1, the vibrating system can implement an elliptical motion of the main rigid frame required in engineering. Numeric results show that the structural parameters of the pro展开更多
A virtual sieving experimental simulation system was built using physical simulation principles.The effects of vibration frequency and amplitude,the inclination angle of the screen-deck and the vibration direction ang...A virtual sieving experimental simulation system was built using physical simulation principles.The effects of vibration frequency and amplitude,the inclination angle of the screen-deck and the vibration direction angle of screen on single particle kinematics were predicted.Properties such as the average velocity and the average throw height were studied.The results show that the amplitude and the angle of vibration have a great effect on particle average velocity and average height.The vibration frequency and the screen-deck inclination angle appear to have little influence on these responses.For materials that are difficult to screen the vibration frequency and amplitude,the screen-deck inclination angle and the vibration angle should be set to 14 Hz,6.6 mm,6° and 40°,respectively,to obtain optimal particle kinematics.A screening process can be simulated reliably by means of a virtual experiment and these results provide references for both screening theory research and sieving practice.展开更多
Galvanic corrosion of tri-metallic couples is more complicated than that of bi-metallic couples. In this study, the effect of the pH of corrosive media on the galvanic corrosion of 2024 A1 alloy/Q235 mild steel/304 st...Galvanic corrosion of tri-metallic couples is more complicated than that of bi-metallic couples. In this study, the effect of the pH of corrosive media on the galvanic corrosion of 2024 A1 alloy/Q235 mild steel/304 stainless steel tri-metallic couples was investigated using potentiodynamic polarization, scanning electron microscopy, scanning vibrating electrode technique and a multi-channel galvanic corrosion meter. The results show that 2024 always acts as the only anode in 3.5 wt% NaCl at pH 5.56,9.72 and 12.0, while both Q235 and 2024 act as anodes at pH 2.39 in the initial stage and then the role of Q235 changes at longer coupling time, which can be attributed to the effect of pH on the surface film of 2024. It is also found that the galvanic current density of a tri-metallic couple is the superposition of two bi-metallic couples when cathodic reactions are controlled by the diffusion of oxygen, otherwise it is smaller than that of the sum of two bi-metallic couples. The localized corrosion instead of uniform corrosion of anodic metal is accelerated by galvanic corrosion.展开更多
This paper concerns the impact of an operating metro train on the structure of a shield tunnel lining and its soft foundation. An elastoplastic 3D dynamic finite difference model was established by using the FLAC3D nu...This paper concerns the impact of an operating metro train on the structure of a shield tunnel lining and its soft foundation. An elastoplastic 3D dynamic finite difference model was established by using the FLAC3D numerical soft- ware. By fully considering the joints, the A-B-K segments and the soft stratum, the dynamic response of the shield tunnel buried in thick, soft soil under the vibrating load induced by a metro train was numerically simulated. The simulation result, for which the joint was considered, was compared with the result when the joint was not considered. The results show that an operating metro train induces a significant dynamic response in the structure of the lining of the shield tunnel and its soft foundation. The severe dynamic response zones of the lining structure are largely distributed in the range of the lower half of the segment-ring and the nearer to the bottom of the segment-ring, the more severe the response. Of two horizontally symmetric, corresponding places on the segment lining, the one near the joint is more severe in its dynamic response than that of the one far from the joint; the nearer the zone of the foundation soil to the lower half of the seg- ment-ring, the more severe the dynamic response. The maximum shear strain of the foundation soil takes place near the joint between two normal segments at the bottom. The dynamic response influenced by joints is more severe than the response not influenced by joints, showing that the non-joint assumption is somewhat impractical.展开更多
基金Project supported by the Special Funds forMajor State Basic Research Projects ofChina.
文摘For a class of mixed initial-boundary value problem for general quasilinear hyperbolic systems, this paper establishes the local exact boundary controllability with boundary controls only acting on one end. As an application, the authors show the local exact boundary controllability for a kind of nonlinear vibrating string problem.
基金supported by Liaoning Province College Science and Research(2008S095)the Key Project of the National Natural Science Foundation of China(50535010,50805020)High-tech Research and Development Program of China(2007AA04Z442)
文摘The paper proposes an analytical approach to investigate the synchronization of the two coupled exciters in a vibrating system of spatial motion. Introducing the distur- bance parameters for average angular velocity of two excit- ers, we deduce the non-dimensional coupling equations of angular velocities of two exciters, in which the inertia cou- pling matrix is symmetric and the stiffness coupling matrix is antisymmetric in a non-resonant vibrating system. The analysis of the coupling dynamic characteristic shows that the coupled cosine effect of the phase angles will cause the torque acting on two motors to limit the increase of phase difference between two exciters as well as sustain its sym- metry of two exciters during the running process. It physi- cally explains the peculiarity of self-synchronization of two exciters. The cosine effect of phase angles of the vibrations excited by each exciter will decrease its moment of inertia. The residual moment of inertia of each exciter represents its relative moment of inertia. The stability condition of synchro- nization of two exciters is that the relative non-dimensional moments of inertia of two exciters are all greater than zero and four times their product is greater than the square of their coefficient of coupled cosine effect of phase angles, which is equivalent to that the inertia coupling matrix is positive definite and all its elements are positive. The numeric results show that the structure of the vibrating system can ensure the stability condition of synchronous operation.
基金This work was financially supported by the Chinese Natural Science Foundation （Grant No. 51475090）, New Century Excel- lent Talents of General Universities of Heilongjiang Province, China （Grant No. 1254-NCET-003） and Youth Science and Technology Innovation Fund of Harbin City, China （Grant No. 2014RFQXJ142）, and Science Backbone Project of the Northeast Agricultural University.
文摘The motion of a particle on a screen is directly affected by the motion of the screen if airflow and inter- granular friction are ignored. To study this effect, a mathematical model was established to analyze the motion of a planar reciprocating vibrating screen, and a matrix method was employed to derive its equa- tion of motion. The motion of the screen was simulated numerically and analyzed using MATLAB. The results show that the screen undergoes non-simple harmonic motion and the law of motion of each point in the screen is different. The tilt angle of the screen during screening is not constant but varies according to a specific periodic function. The results of numerical simulations were verified through experiments. A high-speed camera was used to track the motion of three points in the longitudinal direction of the screen. The balance equation for forces acting on a single particle on the screen was derived based on the non-simple harmonic motion of the screen, These forces were simulated using MATLAB. Different types of particle motion like slipping forward, moving backward, and being tossed to different parts of the screen were analyzed. A vibro-impact motion model for a particle on the non-simple harmonic vibrating screen was established based on the nonlinear law of motion of the particle. The stability of fixed points of the map is discussed. Regimes of different particle behaviors such as stable periodic motion, period-doubling bifurcation motion, Hopf bifurcation motion, and chaotic motion were obtained. With the actual law of motion of the screen and the behavior of a particle on the screen, a theoretical basis for design optimization of the screen is provided.
基金support from the Innovative Research Groups of the National Natural Science Foundation of China (No. 50921002)the Natural Science Foundation of Jiangsu Province of China (No. BK2010002)+1 种基金the Fundamental Research Funds for the Central Universities (Nos. 2011QNA10,2010QNB17)the China Postdoctoral Science Foundation (No.20110491485)
文摘A numerical study of the motion particulates follow along a circularly vibrating screen deck was done using the three dimensional Discrete Element Method (DEM). The motion of the particles was analyzed. The effects of vibration amplitude, throwing index, and screen deck inclination angle on the screening process are discussed. The results show that the average velocity of the particles increases along the lon- gitudinal direction of the deck. The screening efficiency is highest when the vibration amplitude, throw- ing index, and screen deck inclination angle are 3-3.5 mm, 2.7 and 15°, respectively. This work is helpful for developing a deep understanding of particle motion and for optimizing screen separator designs.
基金supported by the National Natural Science Foundation of China (Grant No. 50535010)Project of Liaoning Province College Science and Research (Grant No. 2008S095)Program for Changjiang Scholars and Innovative Research Team in University
文摘A new mechanism is proposed to implement the synchronization of the four unbalanced rotors in a vibrating system, which consists of a main rigid frame (MRF) and two accessorial rigid frames (ARF). An analytical approach is developed to study the coupling dynamic characteristics of the four unbalanced rotors, which converts the problem of synchronization of the four unbalanced rotors into the existence and the stability of zero solutions for the non-dimensional differential equations of the angular velocity disturbance parameters (NDDEDP). The stability of zero solutions of the NDDEDP is decomposed into that of its generalized system and a system of the three first order differential equations for the disturbance parameters of the phase differences. The coupling dynamic characteristic of the four unbalanced rotors includes the inertia coupling, the stiffness coupling of angular velocity and the load torque coupling. The non-dimensional inertia coupling matrix is symmetric, the non dimensional matrix of the stiffness coupling of angular velocity is antisymmetric and its diagonal elements are all negative. Hence, the general system of the NDDEDP automatically satisfies the generalized Lyapunov equations when the non-dimensional inertia coupling matrix is positive definite and its elements are all positive. Using Routh-Hurwitz criterion the condition of stability of differential equations for the disturbance parameters of the phase differences is obtained. The load torque coupling makes the vibrating system have the dynamic characteristic of selecting motions and self-synchronization of the four unbalanced rotors arises from the dynamic characteristic of selecting motion of the vibrating system. When the two coefficients of coupling cosine effect of phase angles are all greater than 0 and the three indexes of synchronization are all far greater than 1, the vibrating system can implement an elliptical motion of the main rigid frame required in engineering. Numeric results show that the structural parameters of the pro
基金support from the Innovative Research Groups of the National Natural Science Foundation of China (No.50921002)the National Natural Science Foundation of China (Nos.50574091 and 50774084)+1 种基金the "333 Project" Foundation of Jiangsu Provincethe Key Laboratory of Coal Processing & Efficient Utilization,Ministry of Education Foundation (No.CPEUKF 08-02) for this work
文摘A virtual sieving experimental simulation system was built using physical simulation principles.The effects of vibration frequency and amplitude,the inclination angle of the screen-deck and the vibration direction angle of screen on single particle kinematics were predicted.Properties such as the average velocity and the average throw height were studied.The results show that the amplitude and the angle of vibration have a great effect on particle average velocity and average height.The vibration frequency and the screen-deck inclination angle appear to have little influence on these responses.For materials that are difficult to screen the vibration frequency and amplitude,the screen-deck inclination angle and the vibration angle should be set to 14 Hz,6.6 mm,6° and 40°,respectively,to obtain optimal particle kinematics.A screening process can be simulated reliably by means of a virtual experiment and these results provide references for both screening theory research and sieving practice.
基金supported financially by the National Key Research and Development Program of China (No. 2017YFB0702100)the Natural Science Foundation of Liaoning Province (No. 20170540666)
文摘Galvanic corrosion of tri-metallic couples is more complicated than that of bi-metallic couples. In this study, the effect of the pH of corrosive media on the galvanic corrosion of 2024 A1 alloy/Q235 mild steel/304 stainless steel tri-metallic couples was investigated using potentiodynamic polarization, scanning electron microscopy, scanning vibrating electrode technique and a multi-channel galvanic corrosion meter. The results show that 2024 always acts as the only anode in 3.5 wt% NaCl at pH 5.56,9.72 and 12.0, while both Q235 and 2024 act as anodes at pH 2.39 in the initial stage and then the role of Q235 changes at longer coupling time, which can be attributed to the effect of pH on the surface film of 2024. It is also found that the galvanic current density of a tri-metallic couple is the superposition of two bi-metallic couples when cathodic reactions are controlled by the diffusion of oxygen, otherwise it is smaller than that of the sum of two bi-metallic couples. The localized corrosion instead of uniform corrosion of anodic metal is accelerated by galvanic corrosion.
文摘This paper concerns the impact of an operating metro train on the structure of a shield tunnel lining and its soft foundation. An elastoplastic 3D dynamic finite difference model was established by using the FLAC3D numerical soft- ware. By fully considering the joints, the A-B-K segments and the soft stratum, the dynamic response of the shield tunnel buried in thick, soft soil under the vibrating load induced by a metro train was numerically simulated. The simulation result, for which the joint was considered, was compared with the result when the joint was not considered. The results show that an operating metro train induces a significant dynamic response in the structure of the lining of the shield tunnel and its soft foundation. The severe dynamic response zones of the lining structure are largely distributed in the range of the lower half of the segment-ring and the nearer to the bottom of the segment-ring, the more severe the response. Of two horizontally symmetric, corresponding places on the segment lining, the one near the joint is more severe in its dynamic response than that of the one far from the joint; the nearer the zone of the foundation soil to the lower half of the seg- ment-ring, the more severe the dynamic response. The maximum shear strain of the foundation soil takes place near the joint between two normal segments at the bottom. The dynamic response influenced by joints is more severe than the response not influenced by joints, showing that the non-joint assumption is somewhat impractical.
