Subgrade frost heave in seasonally frozen ground can greatly influence the safety and smooth running of high-speed trains and the service performance of track structures.In this study,we used a static model to:(1)inve...Subgrade frost heave in seasonally frozen ground can greatly influence the safety and smooth running of high-speed trains and the service performance of track structures.In this study,we used a static model to:(1)investigate track-subgrade frost heave and develop a dynamic model of vehicle-track-subgrade frost heave;(2)explore the transfer relation between subgrade frost heave and track structure deformation;(3)examine the characteristics of interlayer debonding;(4)study the influence of subgrade frost heave on the dynamic response of vehicles in high-speed railways in seasonally frozen regions.A Fourier series was used to fit the frost heave waveform and simulate the behavior of subgrade uneven frost heave using data collected on-site.The results show:(i)The position of frost heave significantly affects the transfer of deformation to a slab track.The largest deformation of the track slab,with the amplitude transfer ratio reaching 20%,was recorded when the frost heave occurred near the joint of the base plate.(ii)At the same frost heave amplitude,long-wave frost heave causes smaller deformation and debonding of the track structure than short-wave frost heave.In the wavelength range of 10-30 m,the main frequency of the acceleration spectral density was concentrated between 3.5 and 3.7 Hz,with larger frost heave wavelengths producing smaller superposition on the vertical acceleration of the vehicle.(ii)The maximum wheel-rail force occurs when the front bogie passes the frost heave peak,with greater frost heave amplitudes producing greater wheel-rail force.From these results,we conclude there is a clear need to control the frost heave deformation of the track to reduce the dynamic response of the vehicle and in turn improve train operatSubgrade frost heave in seasonally frozen ground can greatly influence the safety and smooth running of high-speed trains and the service performance of track structures.In this study,we used a static model to:(1)investigate track`-subgrade frost heave and develop a dynamic model of vehicle`-track`-subgrade frost heave;(2)explore the transfer relation between subgrade frost heave and track structure deformation;(3)examine the characteristics of interlayer debonding;(4)study the influence of subgrade frost heave on the dynamic response of vehicles in high-speed railways in seasonally frozen regions.A Fourier series was used to fit the frost heave waveform and simulate the behavior of subgrade uneven frost heave using data collected on-site.The results show:(i)The position of frost heave significantly affects the transfer of deformation to a slab track.The largest deformation of the track slab,with the amplitude transfer ratio reaching 20%,was recorded when the frost heave occurred near the joint of the base plate.(ii)At the same frost heave amplitude,long-wave frost heave causes smaller deformation and debonding of the track structure than short-wave frost heave.In the wavelength range of 10-30 m,the main frequency of the acceleration spectral density was concentrated between 3.5 and 3.7 Hz,with larger frost heave wavelengths producing smaller superposition on the vertical acceleration of the vehicle.(iii)The maximum wheel`-rail force occurs when the front bogie passes the frost heave peak,with greater frost heave amplitudes producing greater wheel`-rail force.From these results,we conclude there is a clear need to control the frost heave deformation of the track to reduce the dynamic response of the vehicle and in turn improve train operations.ions.展开更多
The equations of motion governing the quasi-static and dynamical behavior of a viscoelastic Timoshenko beam are derived. The viscoelastic material is assumed to obey a three-dimensional fractional derivative constitut...The equations of motion governing the quasi-static and dynamical behavior of a viscoelastic Timoshenko beam are derived. The viscoelastic material is assumed to obey a three-dimensional fractional derivative constitutive relation. ne quasi-static behavior of the viscoelastic Timoshenko beam under step loading is analyzed and the analytical solution is obtained. The influence of material parameters on the deflection is investigated. The dynamical response of the viscoelastic Timoshenko beam subjected to a periodic excitation is studied by means of mode shape functions. And the effect of both transverse shear and rotational inertia on the vibration of the beam is discussed.展开更多
An online dynamic method based on electrical conductivity probe, tensiometer and datataker was presented to measure saturation-capillary pressure （S-p） relation in water-light nonaqueous phase liquid （LNAPL） two-p...An online dynamic method based on electrical conductivity probe, tensiometer and datataker was presented to measure saturation-capillary pressure （S-p） relation in water-light nonaqueous phase liquid （LNAPL） two-phase sandy medium under water level fluctuation. Three-electrode electrical conductivity probe （ECP） was used to measure water saturation. Hydrophobic tensiometer was obtained by spraying waterproof material to the ceramic cup of commercially available hydrophilic tensiometer. A couple of hydrophilic tensiometer and hydrophobic tensiometer were used to measure pore water pressure and pore LNAPL pressure of the sandy medium, respectively. All the signals from ECP and tensiometer were collected by a data taker connected with a computer. The results show that this method can finish the measurement of S-R relation of a complete drainage or imbibition process in less than 60 min. It is much more timesaving compared with 10-40 d of traditional methods. Two cycles of water level fluctuation were produced, and four saturation-capillary pressure relations including two stable residual LNAPL saturations of the sandy medium were obtained during in 350 h. The results show that this method has a good durable performance and feasibility in the porous medium with complicated multiphase flow. Although further studies are needed on the signal stability and accuracy drift of the ECP, this online dynamic method can be used successfully in the rapid characterization of a LNAPL migration in porous media.展开更多
Temperature profiles down to 1500m(CTD) collected by Academia Sinica from 1986 to 1990 are used and discussed in relation to the dynamic heights at130 E across the North Equatorial Current (NEC). An extremely high cor...Temperature profiles down to 1500m(CTD) collected by Academia Sinica from 1986 to 1990 are used and discussed in relation to the dynamic heights at130 E across the North Equatorial Current (NEC). An extremely high correlation between subsurface (say at 400 m depth) temperature and dynamic height relative to 1500 db is found, and the corresponding regression relationships suggest a method to estimate gpostrophic circulation from subsurface temperature alone. These suggest that the conclusions from extensive studies on this topic in Australian waters also apply to the NEC region, at least at130 E , thus making the subsurface thermal structure an excellent indicator of the variation of the NEC.展开更多
The dynamic stability of simple supported viscoelastic column, subjected to a periodic axial force, is investigated. The viscoelastic material was assumed to obey the fractional derivative constitutive relation. The g...The dynamic stability of simple supported viscoelastic column, subjected to a periodic axial force, is investigated. The viscoelastic material was assumed to obey the fractional derivative constitutive relation. The governing equation of motion was derived as a weakly singular Volterra integro-partial-differential equation, and it was simplified into weakly singular Volterra integro-ordinary-differential equation by the Galerkin method. In terms of the averaging method, the dynamical stability was analyzed. A new numerical method is proposed to avoid storing all history data. Numerical examples are presented and the numerical results agree with the analytical ones.展开更多
- Starting from satellite remote sensing data, the dynamical processes of shear waves occurring at the boundary between the western boundary current and the shelf slope water are studied and dynamically analyzed in th...- Starting from satellite remote sensing data, the dynamical processes of shear waves occurring at the boundary between the western boundary current and the shelf slope water are studied and dynamically analyzed in this study. The average wavelength is 75 km, and the average amplitude (from crest to trough )17 km. the average phase speed 100 cms-1 for the shear waves along the north wall of the Gulf Stream to the east of Cape Hatteras measured from NOAA satellite IR (infrared ) images. The average wavelength of shear waves along the north wall of the Kuroshio Current is 57 km, and the average amplitude 17 km. For the shear waves occurring along the west wall of the Gulf Stream to the south of Cape Hatteras, the average wavelength is 131 km, and the average amplitude 33 km measured from Seasat SAR (synthetic aperture radar )images. The time for one cycle of shear wave event is about one week.In order to explore the dynamical mechanisms of shear waves, we solved the vorticity equation for a stratified fluid, and obtained an analytical expression of dispersion relation of shear waves. The results indicated that there was a parabolic relation between the phase speed and the wavelength of shear waves, and the mean flow field was an important factor in the dispersion relation. The latter point means that the horizontal tangent variation of velocity is a basic condition for shear wave occurrence. Theoretical analyses are confirmed by satellite remote sensing data.展开更多
The dynamic compressive behavior and constitutive relations of Lanthanum（La） metal was determined by using the first compression in split Hopkinson pressure bar（SHPB） tests at different strain rates and temperatur...The dynamic compressive behavior and constitutive relations of Lanthanum（La） metal was determined by using the first compression in split Hopkinson pressure bar（SHPB） tests at different strain rates and temperatures.The constitutive relation of La metal determined in a certain range of strains was employed and adjusted in numerically simulating large deformations of La metal specimens generated by multi-compression in SHPB tests and recorded by a high-speed camera.The dynamic compressive behavior and constitutive relations of La metal under multiple SHPB tests loading was also revealed.The results of scanning electron microscope（SEM） investigation of the recovered La metal specimens for typical tests showed that there was a variety of deformation microstructures depending on strain rate,temperature and stress state.展开更多
Aim To study the Lie symmetries and conserved quantities of the dynamical equationsof relative motion for holonomic mechanical systems. Methods Lie's method of the invariance of ordinary differential equations u...Aim To study the Lie symmetries and conserved quantities of the dynamical equationsof relative motion for holonomic mechanical systems. Methods Lie's method of the invariance of ordinary differential equations under infinitesimal transformations was used. Results and Conclusion The determining equaiton of the Lie symmetries for the dynamical equationS of relative motion is established.The structure quation and the form conserved quantities are obtained. An example iD illustrate the application of the result is given.展开更多
This paper discusses in detail the conformal invariance by infinitesimal transformations of a dynamical system of relative motion. The necessary and sufficient conditions of conformal invariance and Lie symmetry are g...This paper discusses in detail the conformal invariance by infinitesimal transformations of a dynamical system of relative motion. The necessary and sufficient conditions of conformal invariance and Lie symmetry are given simultaneously by the action of infinitesimal transformations. Then it obtains the conserved quantities of conformal invariance by the infinitesimal transformations. Finally an example is given to illustrate the application of the results.展开更多
This paper focuses on studying the Poisson theory and the integration method of dynamics of relative motion. Equations of a dynamical system of relative motion in phase space are given. Poisson theory of the system is...This paper focuses on studying the Poisson theory and the integration method of dynamics of relative motion. Equations of a dynamical system of relative motion in phase space are given. Poisson theory of the system is established. The Jacobi last multiplier of the system is defined, and the relation between the Jacobi last multiplier and the first integrals of the system is studied. Our research shows that for a dynamical system of relative motion, whose configuration is determined by n generalized coordinates, the solution of the system can be found by using the Jacobi last multiplier if （2n-1） first integrals of the system are known. At the end of the paper, an example is given to illustrate the application of the results.展开更多
Special Lie symmetry and the Hojman conserved quantity for Appell equations in a dynamical system of relative motion are investigated. The definition and the criterion of the special Lie symmetry of Appell equations i...Special Lie symmetry and the Hojman conserved quantity for Appell equations in a dynamical system of relative motion are investigated. The definition and the criterion of the special Lie symmetry of Appell equations in a dynamical system of relative motion under infinitesimal group transformation are presented. The expression of the equation for the special Lie symmetry of Appell equations and the Hojman conserved quantity, deduced directly from the special Lie symmetry in a dynamical system of relative motion, are obtained. An example is given to illustrate the application of the results.展开更多
Lie symmetry and conserved quantity deduced from Lie symmetry of Appell equations in a dynamical system of relative motion with Chetaev-type nonholonomic constraints are studied.The differential equations of motion of...Lie symmetry and conserved quantity deduced from Lie symmetry of Appell equations in a dynamical system of relative motion with Chetaev-type nonholonomic constraints are studied.The differential equations of motion of the Appell equation for the system,the definition and criterion of Lie symmetry,the condition and the expression of generalized Hojman conserved quantity deduced from Lie symmetry for the system are obtained.The condition and the expression of Hojman conserved quantity deduced from special Lie symmetry for the system under invariable time are further obtained.An example is given to illustrate the application of the results.展开更多
This paper focuses on Gauss principle of least compulsion for relative motion dynamics and derives differential equations of motion from it. Firstly, starting from the dynamic equation of the relative motion of partic...This paper focuses on Gauss principle of least compulsion for relative motion dynamics and derives differential equations of motion from it. Firstly, starting from the dynamic equation of the relative motion of particles, we give the Gauss principle of relative motion dynamics. By constructing a compulsion function of relative motion, we prove that at any instant, its real motion minimizes the compulsion function under Gaussian variation, compared with the possible motions with the same configuration and velocity but different accelerations. Secondly, the formula of acceleration energy and the formula of compulsion function for relative motion are derived because the carried body is rigid and moving in a plane. Thirdly, the Gauss principle we obtained is expressed as Appell, Lagrange, and Nielsen forms in generalized coordinates. Utilizing Gauss principle, the dynamical equations of relative motion are established. Finally, two relative motion examples also verify the results' correctness.展开更多
This paper studies the chaotic behaviours of a relative rotation nonlinear dynamical system under parametric excitation and its control. The dynamical equation of relative rotation nonlinear dynamical system under par...This paper studies the chaotic behaviours of a relative rotation nonlinear dynamical system under parametric excitation and its control. The dynamical equation of relative rotation nonlinear dynamical system under parametric excitation is deduced by using the dissipation Lagrange equation. The. criterion of existence of chaos under parametric excitation is given by using the Melnikov theory. The chaotic behaviours are detected by numerical simulations including bifurcation diagrams, Poincare map and maximal Lyapunov exponent. Furthermore, it implements chaotic control using nomfeedback method. It obtains the parameter condition of chaotic control by the Melnikov theory. Numerical simulation results show the consistence with the theoretical analysis. The chaotic motions can be controlled to periodmotions by adding an excitation term.展开更多
Based on the theory of symmetries and conserved quantities, the exact invariants and adiabatic invariants of nonholonomic dynamical system of relative motion are studied. The perturbation to symmetries for the nonholo...Based on the theory of symmetries and conserved quantities, the exact invariants and adiabatic invariants of nonholonomic dynamical system of relative motion are studied. The perturbation to symmetries for the nonholonomic dynamical system of relative motion under small excitation is discussed. The concept of high-order adiabatic invariant is presented, and the form of exact invariants and adiabatic invariants as well as the conditions for their existence are given. Then the corresponding inverse problem is studied.展开更多
The tool point frequency response function(FRF) is commonly obtained by impacting test or semi-analytical techniques.Regardless of the approach,it is assumed that the workpiece system is rigid.The assumption is valid ...The tool point frequency response function(FRF) is commonly obtained by impacting test or semi-analytical techniques.Regardless of the approach,it is assumed that the workpiece system is rigid.The assumption is valid in common machining,but it doesn’t work well in the cutting processes of thin-wall products.In order to solve the problem,a multi-degree-of-freedom dynamic model is employed to obtain the relative dynamic stiffness between the cutting tool and the workpiece system.The relative direct and cross FRFs between the cutting tool and workpiece system are achieved by relative excitation experiment,and compared with the tool point FRFs at x and y axial direction.The comparison results indicate that the relative excitation method could be used to obtain the relative dynamic compliance of machine-tool-workpiece system more actually and precisely.Based on the more precise relative FRFs,four evaluation criterions of dynamic stiffness are proposed,and the variation trend curves of these criterions during the last six months are achieved and analyzed.The analysis results show that the lowest natural frequency,the maximum and the average dynamic compliances at x axial direction deteriorate more quickly than that at y axial direction.Therefore,the main cutting direction and the large-size direction of workpieces should be arranged at y axial direction to slow down the deterioration of the dynamic stiffness of machining centers.The compliance of workpiece system is considered,which can help master the deterioration rules of the dynamic stiffness of machining centers,and enhance the reliability of machine centers and the consistency of machining processes.展开更多
Noether symmetry of Nielsen equation and Noether conserved quantity deduced directly from Noether symmetry for dynamical systems of the relative motion are studied. The definition and criteria of Noether symmetry of a...Noether symmetry of Nielsen equation and Noether conserved quantity deduced directly from Noether symmetry for dynamical systems of the relative motion are studied. The definition and criteria of Noether symmetry of a Nielsen equation under the infinitesimal transformations of groups are given. Expression of Noether conserved quantity deduced directly from Noether symmetry of Nielsen equation for the system are obtained. Finally, an example is given to illustrate the application of the results.展开更多
The Mei symmetry and the Mei conserved quantity of Appell equations in a dynamical system of relative motion with non-Chetaev nonholonomic constraints are studied.The differential equations of motion of the Appell equ...The Mei symmetry and the Mei conserved quantity of Appell equations in a dynamical system of relative motion with non-Chetaev nonholonomic constraints are studied.The differential equations of motion of the Appell equation for the system,the definition and the criterion of the Mei symmetry,and the expression of the Mei conserved quantity deduced directly from the Mei symmetry for the system are obtained.An example is given to illustrate the application of the results.展开更多
The relative motion of the electrodes is a typical feature of sliding electrical contact systems.The system fault caused by the arc is the key problem that restricts the service life of the sliding electrical contact ...The relative motion of the electrodes is a typical feature of sliding electrical contact systems.The system fault caused by the arc is the key problem that restricts the service life of the sliding electrical contact system.In this paper,an arcing experimental platform that can accurately control the relative speed and distance of electrodes is built,and the influence of different electrode speeds and electrode distances on arc motion characteristics is explored.It is found that there are three different modes of arc root motion:single arc root motion mode,single and double arc roots alternating motion mode,and multiple arc roots motion mode.The physical process and influence mechanism of different arc root motion modes are further studied,and the corresponding relationship between arc root motion modes and electrode speed is revealed.In addition,to further explore the distribution characteristics of arc temperature and its influencing factors,an arc magnetohydrodynamic model under the relative motion of electrodes is established,and the variation law of arc temperature under the effect of different electrode speeds and electrode distances is summarized.Finally,the influence mechanism of electrode speed and electrode distance on arc temperature,arc root distance,and arc root speed is clarified.The research results enrich the research system of arc dynamic characteristics in the field of sliding electrical contact,and provide theoretical support for restraining arc erosion and improving the service life of the sliding electrical contact system.展开更多
基金This work is supported by the National Key R&D Program of China(No.2021YFF0502100)the National Natural Science Foundation of China(Nos.52022085 and 52278461)+1 种基金the Sichuan Provincial Youth Science and Technology Innovation Team(No.2022JDTD0015)the Research and Development Program of China State Railway Group Co.,Ltd.(No.N2022G033),China.
文摘Subgrade frost heave in seasonally frozen ground can greatly influence the safety and smooth running of high-speed trains and the service performance of track structures.In this study,we used a static model to:(1)investigate track-subgrade frost heave and develop a dynamic model of vehicle-track-subgrade frost heave;(2)explore the transfer relation between subgrade frost heave and track structure deformation;(3)examine the characteristics of interlayer debonding;(4)study the influence of subgrade frost heave on the dynamic response of vehicles in high-speed railways in seasonally frozen regions.A Fourier series was used to fit the frost heave waveform and simulate the behavior of subgrade uneven frost heave using data collected on-site.The results show:(i)The position of frost heave significantly affects the transfer of deformation to a slab track.The largest deformation of the track slab,with the amplitude transfer ratio reaching 20%,was recorded when the frost heave occurred near the joint of the base plate.(ii)At the same frost heave amplitude,long-wave frost heave causes smaller deformation and debonding of the track structure than short-wave frost heave.In the wavelength range of 10-30 m,the main frequency of the acceleration spectral density was concentrated between 3.5 and 3.7 Hz,with larger frost heave wavelengths producing smaller superposition on the vertical acceleration of the vehicle.(ii)The maximum wheel-rail force occurs when the front bogie passes the frost heave peak,with greater frost heave amplitudes producing greater wheel-rail force.From these results,we conclude there is a clear need to control the frost heave deformation of the track to reduce the dynamic response of the vehicle and in turn improve train operatSubgrade frost heave in seasonally frozen ground can greatly influence the safety and smooth running of high-speed trains and the service performance of track structures.In this study,we used a static model to:(1)investigate track`-subgrade frost heave and develop a dynamic model of vehicle`-track`-subgrade frost heave;(2)explore the transfer relation between subgrade frost heave and track structure deformation;(3)examine the characteristics of interlayer debonding;(4)study the influence of subgrade frost heave on the dynamic response of vehicles in high-speed railways in seasonally frozen regions.A Fourier series was used to fit the frost heave waveform and simulate the behavior of subgrade uneven frost heave using data collected on-site.The results show:(i)The position of frost heave significantly affects the transfer of deformation to a slab track.The largest deformation of the track slab,with the amplitude transfer ratio reaching 20%,was recorded when the frost heave occurred near the joint of the base plate.(ii)At the same frost heave amplitude,long-wave frost heave causes smaller deformation and debonding of the track structure than short-wave frost heave.In the wavelength range of 10-30 m,the main frequency of the acceleration spectral density was concentrated between 3.5 and 3.7 Hz,with larger frost heave wavelengths producing smaller superposition on the vertical acceleration of the vehicle.(iii)The maximum wheel`-rail force occurs when the front bogie passes the frost heave peak,with greater frost heave amplitudes producing greater wheel`-rail force.From these results,we conclude there is a clear need to control the frost heave deformation of the track to reduce the dynamic response of the vehicle and in turn improve train operations.ions.
文摘The equations of motion governing the quasi-static and dynamical behavior of a viscoelastic Timoshenko beam are derived. The viscoelastic material is assumed to obey a three-dimensional fractional derivative constitutive relation. ne quasi-static behavior of the viscoelastic Timoshenko beam under step loading is analyzed and the analytical solution is obtained. The influence of material parameters on the deflection is investigated. The dynamical response of the viscoelastic Timoshenko beam subjected to a periodic excitation is studied by means of mode shape functions. And the effect of both transverse shear and rotational inertia on the vibration of the beam is discussed.
基金Project(8151027501000008) supported by Guangdong Natural Science Foundation, ChinaProject(2007490511) supported by the Open Foundation of State Key Laboratory of Hydrology-Water Resources and Hydraulic Engineering, Hohai University, ChinaProject (2006K0006) supported by the Open Foundation of Guangdong Provincial Key Laboratory of Environmental Pollution Control and Remediation Technology, China
文摘An online dynamic method based on electrical conductivity probe, tensiometer and datataker was presented to measure saturation-capillary pressure （S-p） relation in water-light nonaqueous phase liquid （LNAPL） two-phase sandy medium under water level fluctuation. Three-electrode electrical conductivity probe （ECP） was used to measure water saturation. Hydrophobic tensiometer was obtained by spraying waterproof material to the ceramic cup of commercially available hydrophilic tensiometer. A couple of hydrophilic tensiometer and hydrophobic tensiometer were used to measure pore water pressure and pore LNAPL pressure of the sandy medium, respectively. All the signals from ECP and tensiometer were collected by a data taker connected with a computer. The results show that this method can finish the measurement of S-R relation of a complete drainage or imbibition process in less than 60 min. It is much more timesaving compared with 10-40 d of traditional methods. Two cycles of water level fluctuation were produced, and four saturation-capillary pressure relations including two stable residual LNAPL saturations of the sandy medium were obtained during in 350 h. The results show that this method has a good durable performance and feasibility in the porous medium with complicated multiphase flow. Although further studies are needed on the signal stability and accuracy drift of the ECP, this online dynamic method can be used successfully in the rapid characterization of a LNAPL migration in porous media.
文摘Temperature profiles down to 1500m(CTD) collected by Academia Sinica from 1986 to 1990 are used and discussed in relation to the dynamic heights at130 E across the North Equatorial Current (NEC). An extremely high correlation between subsurface (say at 400 m depth) temperature and dynamic height relative to 1500 db is found, and the corresponding regression relationships suggest a method to estimate gpostrophic circulation from subsurface temperature alone. These suggest that the conclusions from extensive studies on this topic in Australian waters also apply to the NEC region, at least at130 E , thus making the subsurface thermal structure an excellent indicator of the variation of the NEC.
文摘The dynamic stability of simple supported viscoelastic column, subjected to a periodic axial force, is investigated. The viscoelastic material was assumed to obey the fractional derivative constitutive relation. The governing equation of motion was derived as a weakly singular Volterra integro-partial-differential equation, and it was simplified into weakly singular Volterra integro-ordinary-differential equation by the Galerkin method. In terms of the averaging method, the dynamical stability was analyzed. A new numerical method is proposed to avoid storing all history data. Numerical examples are presented and the numerical results agree with the analytical ones.
文摘- Starting from satellite remote sensing data, the dynamical processes of shear waves occurring at the boundary between the western boundary current and the shelf slope water are studied and dynamically analyzed in this study. The average wavelength is 75 km, and the average amplitude (from crest to trough )17 km. the average phase speed 100 cms-1 for the shear waves along the north wall of the Gulf Stream to the east of Cape Hatteras measured from NOAA satellite IR (infrared ) images. The average wavelength of shear waves along the north wall of the Kuroshio Current is 57 km, and the average amplitude 17 km. For the shear waves occurring along the west wall of the Gulf Stream to the south of Cape Hatteras, the average wavelength is 131 km, and the average amplitude 33 km measured from Seasat SAR (synthetic aperture radar )images. The time for one cycle of shear wave event is about one week.In order to explore the dynamical mechanisms of shear waves, we solved the vorticity equation for a stratified fluid, and obtained an analytical expression of dispersion relation of shear waves. The results indicated that there was a parabolic relation between the phase speed and the wavelength of shear waves, and the mean flow field was an important factor in the dispersion relation. The latter point means that the horizontal tangent variation of velocity is a basic condition for shear wave occurrence. Theoretical analyses are confirmed by satellite remote sensing data.
基金supported by National Natural Science Foundation of China (10872100,11072118)Natural Science Foundation of Zhejiang(Y12A020008)
文摘The dynamic compressive behavior and constitutive relations of Lanthanum（La） metal was determined by using the first compression in split Hopkinson pressure bar（SHPB） tests at different strain rates and temperatures.The constitutive relation of La metal determined in a certain range of strains was employed and adjusted in numerically simulating large deformations of La metal specimens generated by multi-compression in SHPB tests and recorded by a high-speed camera.The dynamic compressive behavior and constitutive relations of La metal under multiple SHPB tests loading was also revealed.The results of scanning electron microscope（SEM） investigation of the recovered La metal specimens for typical tests showed that there was a variety of deformation microstructures depending on strain rate,temperature and stress state.
文摘Aim To study the Lie symmetries and conserved quantities of the dynamical equationsof relative motion for holonomic mechanical systems. Methods Lie's method of the invariance of ordinary differential equations under infinitesimal transformations was used. Results and Conclusion The determining equaiton of the Lie symmetries for the dynamical equationS of relative motion is established.The structure quation and the form conserved quantities are obtained. An example iD illustrate the application of the result is given.
基金supported by the National Natural Science Foundation of China (Grant No 10372053)the Natural Science Foundation of Henan Province,China (Grant Nos 082300410330 and 082300410370)
文摘This paper discusses in detail the conformal invariance by infinitesimal transformations of a dynamical system of relative motion. The necessary and sufficient conditions of conformal invariance and Lie symmetry are given simultaneously by the action of infinitesimal transformations. Then it obtains the conserved quantities of conformal invariance by the infinitesimal transformations. Finally an example is given to illustrate the application of the results.
基金supported by the National Natural Science Foundation of China (Grant No. 10972151)
文摘This paper focuses on studying the Poisson theory and the integration method of dynamics of relative motion. Equations of a dynamical system of relative motion in phase space are given. Poisson theory of the system is established. The Jacobi last multiplier of the system is defined, and the relation between the Jacobi last multiplier and the first integrals of the system is studied. Our research shows that for a dynamical system of relative motion, whose configuration is determined by n generalized coordinates, the solution of the system can be found by using the Jacobi last multiplier if （2n-1） first integrals of the system are known. At the end of the paper, an example is given to illustrate the application of the results.
文摘Special Lie symmetry and the Hojman conserved quantity for Appell equations in a dynamical system of relative motion are investigated. The definition and the criterion of the special Lie symmetry of Appell equations in a dynamical system of relative motion under infinitesimal group transformation are presented. The expression of the equation for the special Lie symmetry of Appell equations and the Hojman conserved quantity, deduced directly from the special Lie symmetry in a dynamical system of relative motion, are obtained. An example is given to illustrate the application of the results.
基金Project supported by the National Natural Science Foundation of China (Grant No. 11142014)the Scientific Research and Innovation Plan for College Graduates of Jiangsu Province,China (Grant No. CXLX12_0720)
文摘Lie symmetry and conserved quantity deduced from Lie symmetry of Appell equations in a dynamical system of relative motion with Chetaev-type nonholonomic constraints are studied.The differential equations of motion of the Appell equation for the system,the definition and criterion of Lie symmetry,the condition and the expression of generalized Hojman conserved quantity deduced from Lie symmetry for the system are obtained.The condition and the expression of Hojman conserved quantity deduced from special Lie symmetry for the system under invariable time are further obtained.An example is given to illustrate the application of the results.
基金Supported by the National Natural Science Foundation of China (12272248, 11972241)。
文摘This paper focuses on Gauss principle of least compulsion for relative motion dynamics and derives differential equations of motion from it. Firstly, starting from the dynamic equation of the relative motion of particles, we give the Gauss principle of relative motion dynamics. By constructing a compulsion function of relative motion, we prove that at any instant, its real motion minimizes the compulsion function under Gaussian variation, compared with the possible motions with the same configuration and velocity but different accelerations. Secondly, the formula of acceleration energy and the formula of compulsion function for relative motion are derived because the carried body is rigid and moving in a plane. Thirdly, the Gauss principle we obtained is expressed as Appell, Lagrange, and Nielsen forms in generalized coordinates. Utilizing Gauss principle, the dynamical equations of relative motion are established. Finally, two relative motion examples also verify the results' correctness.
基金supported by the National Natural Science Foundation of China (Grant No.60704037)the Natural Science Foundation of Hebei Province,China (Grant No.F2010001317)the Doctor Foundation of Yanshan University of China (Grant No.B451)
文摘This paper studies the chaotic behaviours of a relative rotation nonlinear dynamical system under parametric excitation and its control. The dynamical equation of relative rotation nonlinear dynamical system under parametric excitation is deduced by using the dissipation Lagrange equation. The. criterion of existence of chaos under parametric excitation is given by using the Melnikov theory. The chaotic behaviours are detected by numerical simulations including bifurcation diagrams, Poincare map and maximal Lyapunov exponent. Furthermore, it implements chaotic control using nomfeedback method. It obtains the parameter condition of chaotic control by the Melnikov theory. Numerical simulation results show the consistence with the theoretical analysis. The chaotic motions can be controlled to periodmotions by adding an excitation term.
文摘Based on the theory of symmetries and conserved quantities, the exact invariants and adiabatic invariants of nonholonomic dynamical system of relative motion are studied. The perturbation to symmetries for the nonholonomic dynamical system of relative motion under small excitation is discussed. The concept of high-order adiabatic invariant is presented, and the form of exact invariants and adiabatic invariants as well as the conditions for their existence are given. Then the corresponding inverse problem is studied.
基金supported by National Natural Science Foundation of China(Grant No.51175208)National Key Basic Research Program of China(973 ProgramGrant No.2011CB706803)
文摘The tool point frequency response function(FRF) is commonly obtained by impacting test or semi-analytical techniques.Regardless of the approach,it is assumed that the workpiece system is rigid.The assumption is valid in common machining,but it doesn’t work well in the cutting processes of thin-wall products.In order to solve the problem,a multi-degree-of-freedom dynamic model is employed to obtain the relative dynamic stiffness between the cutting tool and the workpiece system.The relative direct and cross FRFs between the cutting tool and workpiece system are achieved by relative excitation experiment,and compared with the tool point FRFs at x and y axial direction.The comparison results indicate that the relative excitation method could be used to obtain the relative dynamic compliance of machine-tool-workpiece system more actually and precisely.Based on the more precise relative FRFs,four evaluation criterions of dynamic stiffness are proposed,and the variation trend curves of these criterions during the last six months are achieved and analyzed.The analysis results show that the lowest natural frequency,the maximum and the average dynamic compliances at x axial direction deteriorate more quickly than that at y axial direction.Therefore,the main cutting direction and the large-size direction of workpieces should be arranged at y axial direction to slow down the deterioration of the dynamic stiffness of machining centers.The compliance of workpiece system is considered,which can help master the deterioration rules of the dynamic stiffness of machining centers,and enhance the reliability of machine centers and the consistency of machining processes.
基金Supported by the National Natural Science Foundation of China under Grant No.10572021the Preparatory Research Foundation of Jiangnan University under Grant No.2008LYY011
文摘Noether symmetry of Nielsen equation and Noether conserved quantity deduced directly from Noether symmetry for dynamical systems of the relative motion are studied. The definition and criteria of Noether symmetry of a Nielsen equation under the infinitesimal transformations of groups are given. Expression of Noether conserved quantity deduced directly from Noether symmetry of Nielsen equation for the system are obtained. Finally, an example is given to illustrate the application of the results.
基金Project supported by the National Natural Science Foundation of China (Grant No. 11142014 and 61178032)
文摘The Mei symmetry and the Mei conserved quantity of Appell equations in a dynamical system of relative motion with non-Chetaev nonholonomic constraints are studied.The differential equations of motion of the Appell equation for the system,the definition and the criterion of the Mei symmetry,and the expression of the Mei conserved quantity deduced directly from the Mei symmetry for the system are obtained.An example is given to illustrate the application of the results.
基金supported by National Natural Science Foundation of China(Nos.U19A20105 and 52077182)。
文摘The relative motion of the electrodes is a typical feature of sliding electrical contact systems.The system fault caused by the arc is the key problem that restricts the service life of the sliding electrical contact system.In this paper,an arcing experimental platform that can accurately control the relative speed and distance of electrodes is built,and the influence of different electrode speeds and electrode distances on arc motion characteristics is explored.It is found that there are three different modes of arc root motion:single arc root motion mode,single and double arc roots alternating motion mode,and multiple arc roots motion mode.The physical process and influence mechanism of different arc root motion modes are further studied,and the corresponding relationship between arc root motion modes and electrode speed is revealed.In addition,to further explore the distribution characteristics of arc temperature and its influencing factors,an arc magnetohydrodynamic model under the relative motion of electrodes is established,and the variation law of arc temperature under the effect of different electrode speeds and electrode distances is summarized.Finally,the influence mechanism of electrode speed and electrode distance on arc temperature,arc root distance,and arc root speed is clarified.The research results enrich the research system of arc dynamic characteristics in the field of sliding electrical contact,and provide theoretical support for restraining arc erosion and improving the service life of the sliding electrical contact system.
