A modified slow-fast analysis method is presented for the periodically excited non-autonomous dynamical system with an order gap between the exciting frequency and the natural frequency.By regarding the exciting term ...A modified slow-fast analysis method is presented for the periodically excited non-autonomous dynamical system with an order gap between the exciting frequency and the natural frequency.By regarding the exciting term as a slow-varying parameter,a generalized autonomous fast subsystem can be defined,the equilibrium branches as well as the bifurcations of which can be employed to account for the mechanism of the bursting oscillations by combining the transformed phase portrait introduced.As an example,a typical periodically excited Hartley model is used to demonstrate the validness of the method,in which the exciting frequency is far less than the natural frequency.The equilibrium branches and their bifurcations of the fast subsystem with the variation of the slow-varying parameter are presented.Bursting oscillations for two typical cases are considered,which reveals that,fold bifurcation may cause the the trajectory to jump between different equilibrium branches,while Hopf bifurcation may cause the trajectory to oscillate around the stable limit cycle.展开更多
Through a higher-order boundary element method based on NURBS （Non-uniform Rational B-splines）, the calculation of second-order low-frequency forces and slow drift motions is conducted for floating bodies. In the fl...Through a higher-order boundary element method based on NURBS （Non-uniform Rational B-splines）, the calculation of second-order low-frequency forces and slow drift motions is conducted for floating bodies. In the floating body＇s inner domain, an auxiliary equation is obtained by applying a Green function which satisfies the solid surface condition. Then, the auxiliary equation and the velocity potential equation are combined in the fluid domain to remove the solid angle coefficient and the singularity of the double layer potentials in the integral equation. Thus, a new velocity potential integral equation is obtained. The new equation is extended to the inner domain to reheve the irregular frequency effects; on the basis of the order analysis, the comparison is made about the contribution of all integral terms with the result in the second-order tow-frequency problem; the higher-order boundary element method based on NURBS is apphed to calculate the geometric position and velocity potentials; the slow drift motions are calculated by the spectrum analysis method. Removing the solid angle coefficient can apply NURBS technology to the hydrodynamic calculation of floating bodies with complex surfaces, and the extended boundary integral method can reduce the irregular frequency effects. Order analysis shows that free surface integral can be neglected, and the numerical results can also prove the correctness of order analysis. The results of second-order low-frequency forces and slow drift motions and the comparison with the results from references show that the application of the NURBS technology to the second-order low-frequency problem is of high efficiency and credible results.展开更多
In this paper, equations of atmospheric and oceanic dynamics are reduced to a kind of evolutionary equation in operator form, based on which a conclusion that the separability of motion stages is relative is made and ...In this paper, equations of atmospheric and oceanic dynamics are reduced to a kind of evolutionary equation in operator form, based on which a conclusion that the separability of motion stages is relative is made and an issue that the tractional splitting methods established on the physical separability of the fast stage and the slow stage neglect the interaction between the two stages to some extent is shown. Also, three splitting patterns are summed up from the splitting methods in common use so that a comparison between them is carried out. The comparison shows that only the improved splitting pattern (ISP) can be in second order and keep the interaction well. Finally, the applications of some splitting methods on numerical simulations of typhoon tracks made clear that ISP owns the best effect and can save more than 80% CPU time.展开更多
The influence of temperature on the hydrogen diffusion behavior in X80 pipeline steel during stacking for slow cooling was studied using electrochemical penetration method, the temperature field and the hydrogen diffu...The influence of temperature on the hydrogen diffusion behavior in X80 pipeline steel during stacking for slow cooling was studied using electrochemical penetration method, the temperature field and the hydrogen diffusion in this pipeline steel during stacking for slow cooling were simulated by ABAQUS finite element method （FEM） software. The results show that in this process there is a reciprocal relationship between the natural logarithm of hydrogen diffusion coefficient and temperature. The cooling rate decreases gradually with the increase of steel plate thickness. The hydrogen content is higher at high temperature （500-400 ℃） than that in low temperature region （300-100 ℃）. The FEM simulation results are consistent with the experimental ones, and the model can be used to predict the hydrogen diffusion behavior in industrial production of X80 pipeline steel.展开更多
In conventional slowness-time coherence(STC)method,slowness and time need to be searched at the same time,which limits the precision and lowers the efficiency.The dichotomy method combined with slowness-time coherence...In conventional slowness-time coherence(STC)method,slowness and time need to be searched at the same time,which limits the precision and lowers the efficiency.The dichotomy method combined with slowness-time coherence algorithm aims to enhance the efficiency of data processing and to improve the precision.The algorithm changes the searching pattern of conventional slowness-time coherence method to acquire the slowness of component waves in array acoustic logging data.Based on energy ratio of short time window versus long time window and slowness-time coherence method,the algorithm first acquires the arrivals of the component waves using energy ratio of short time window versus long time window method.It then uses the calculated results as the arrivals in conventional slowness-time coherence method,so the slowness-time two-dimensional searching process is simplified to slowness searching process.Based on dichotomy method,the searching pattern is further optimized in replace of the ergodic searching pattern in conventional slowness-time coherence method,which means that as the iteration proceeds,the current searching interval is reduced to half of the former,so the number of searching times is decreased.The dichotomy method combined with slowness-time coherence algorithm is applied to well L in the data processing.Compared with conventional slowness-time coherence method,for compressional wave,the searching efficiency of the algorithm is 4.53 times better,while for Stoneley wave,the searching efficiency is 1.85 times better.Compared with conventional logging data,the average absolute error of the results of the dichotomy method combined with slowness-time coherence algorithm is 1.14μs/ft smaller than that of the conventional method,while the average relative error is 1.2 percent lower.The dichotomy method combined with slowness-time coherence algorithm shows good results in its application,which can enhance the processing efficiency remarkably while getting reliable results at the same time.展开更多
The variational method is applied to calculate the dispersion characteristics of disc-loaded waveguide slow-wave structures. The parameters describing the waveguide discontinuities in disc-loaded waveguide are calcula...The variational method is applied to calculate the dispersion characteristics of disc-loaded waveguide slow-wave structures. The parameters describing the waveguide discontinuities in disc-loaded waveguide are calculated by the variational method. Then the dispersion characteristics of slow-wave structures are obtained using lossless microwave quadrupole theory. Good agreement was observed between results of the Variational method and those of field matching method and high frequency structure simulator. In the case of broad band, results of the variational method are better than those of field matching method.展开更多
This paper studies chaotic motions in quasi-integrable Hamiltonian systems with slow-varying parameters under both harmonic and noise excitations. Based on the dynamic theory and some assumptions of excited noises, an...This paper studies chaotic motions in quasi-integrable Hamiltonian systems with slow-varying parameters under both harmonic and noise excitations. Based on the dynamic theory and some assumptions of excited noises, an extended form of the stochastic Melnikov method is presented. Using this extended method, the homoclinic bifurcations and chaotic behavior of a nonlinear Hamiltonian system with weak feed-back control under both harmonic and Gaussian white noise excitations are analyzed in detail. It is shown that the addition of stochastic excitations can make the parameter threshold value for the occurrence of chaotic motions vary in a wider region. Therefore, chaotic motions may arise easily in the system. By the Monte-Carlo method, the numerical results for the time-history and the maximum Lyapunov exponents of an example system are finally given to illustrate that the presented method is effective.展开更多
With the rapid development of large-scale regional interconnected power grids,the risk of cascading failures under extreme condi-tions,such as natural disasters and military strikes,has increased significantly.To enha...With the rapid development of large-scale regional interconnected power grids,the risk of cascading failures under extreme condi-tions,such as natural disasters and military strikes,has increased significantly.To enhance the response capability of power systems to extreme events,this study focuses on a method for generator coherency detection.To overcome the shortcomings of the traditional slow coherency method,this paper introduces a novel coherent group identification algorithm based on the theory of nonlinear dynam-ical systems.By analyzing the changing trend of the Euclidean norm of the state variable derivatives in the reduced system,the algorithm can accurately identify the magnitude of the disturbances.Based on the slow coherency methods,the algorithm can correctly recognize coherent generator groups by analyzing system characteristics under varying disturbance magnitudes.This improvement enhances the applicability and accuracy of the coherency detection algorithm under extreme conditions,providing support for emergency control and protection in the power system.Simulations and comparison analyses on IEEE 39-bus system are conducted to validate the accuracy and superiority of the proposed coherent generator group identification method under extreme conditions.展开更多
基金supported by the National Natural Science Foundation of China(Grants11632008 and 11872189)
文摘A modified slow-fast analysis method is presented for the periodically excited non-autonomous dynamical system with an order gap between the exciting frequency and the natural frequency.By regarding the exciting term as a slow-varying parameter,a generalized autonomous fast subsystem can be defined,the equilibrium branches as well as the bifurcations of which can be employed to account for the mechanism of the bursting oscillations by combining the transformed phase portrait introduced.As an example,a typical periodically excited Hartley model is used to demonstrate the validness of the method,in which the exciting frequency is far less than the natural frequency.The equilibrium branches and their bifurcations of the fast subsystem with the variation of the slow-varying parameter are presented.Bursting oscillations for two typical cases are considered,which reveals that,fold bifurcation may cause the the trajectory to jump between different equilibrium branches,while Hopf bifurcation may cause the trajectory to oscillate around the stable limit cycle.
文摘Through a higher-order boundary element method based on NURBS （Non-uniform Rational B-splines）, the calculation of second-order low-frequency forces and slow drift motions is conducted for floating bodies. In the floating body＇s inner domain, an auxiliary equation is obtained by applying a Green function which satisfies the solid surface condition. Then, the auxiliary equation and the velocity potential equation are combined in the fluid domain to remove the solid angle coefficient and the singularity of the double layer potentials in the integral equation. Thus, a new velocity potential integral equation is obtained. The new equation is extended to the inner domain to reheve the irregular frequency effects; on the basis of the order analysis, the comparison is made about the contribution of all integral terms with the result in the second-order tow-frequency problem; the higher-order boundary element method based on NURBS is apphed to calculate the geometric position and velocity potentials; the slow drift motions are calculated by the spectrum analysis method. Removing the solid angle coefficient can apply NURBS technology to the hydrodynamic calculation of floating bodies with complex surfaces, and the extended boundary integral method can reduce the irregular frequency effects. Order analysis shows that free surface integral can be neglected, and the numerical results can also prove the correctness of order analysis. The results of second-order low-frequency forces and slow drift motions and the comparison with the results from references show that the application of the NURBS technology to the second-order low-frequency problem is of high efficiency and credible results.
基金Partly supported by the State Major Key Project for Researches and Project 85-906-04.
文摘In this paper, equations of atmospheric and oceanic dynamics are reduced to a kind of evolutionary equation in operator form, based on which a conclusion that the separability of motion stages is relative is made and an issue that the tractional splitting methods established on the physical separability of the fast stage and the slow stage neglect the interaction between the two stages to some extent is shown. Also, three splitting patterns are summed up from the splitting methods in common use so that a comparison between them is carried out. The comparison shows that only the improved splitting pattern (ISP) can be in second order and keep the interaction well. Finally, the applications of some splitting methods on numerical simulations of typhoon tracks made clear that ISP owns the best effect and can save more than 80% CPU time.
文摘The influence of temperature on the hydrogen diffusion behavior in X80 pipeline steel during stacking for slow cooling was studied using electrochemical penetration method, the temperature field and the hydrogen diffusion in this pipeline steel during stacking for slow cooling were simulated by ABAQUS finite element method （FEM） software. The results show that in this process there is a reciprocal relationship between the natural logarithm of hydrogen diffusion coefficient and temperature. The cooling rate decreases gradually with the increase of steel plate thickness. The hydrogen content is higher at high temperature （500-400 ℃） than that in low temperature region （300-100 ℃）. The FEM simulation results are consistent with the experimental ones, and the model can be used to predict the hydrogen diffusion behavior in industrial production of X80 pipeline steel.
基金Supported by the National High Technology Research and Development of China(863 Programme)(No.2013AA092501)
文摘In conventional slowness-time coherence(STC)method,slowness and time need to be searched at the same time,which limits the precision and lowers the efficiency.The dichotomy method combined with slowness-time coherence algorithm aims to enhance the efficiency of data processing and to improve the precision.The algorithm changes the searching pattern of conventional slowness-time coherence method to acquire the slowness of component waves in array acoustic logging data.Based on energy ratio of short time window versus long time window and slowness-time coherence method,the algorithm first acquires the arrivals of the component waves using energy ratio of short time window versus long time window method.It then uses the calculated results as the arrivals in conventional slowness-time coherence method,so the slowness-time two-dimensional searching process is simplified to slowness searching process.Based on dichotomy method,the searching pattern is further optimized in replace of the ergodic searching pattern in conventional slowness-time coherence method,which means that as the iteration proceeds,the current searching interval is reduced to half of the former,so the number of searching times is decreased.The dichotomy method combined with slowness-time coherence algorithm is applied to well L in the data processing.Compared with conventional slowness-time coherence method,for compressional wave,the searching efficiency of the algorithm is 4.53 times better,while for Stoneley wave,the searching efficiency is 1.85 times better.Compared with conventional logging data,the average absolute error of the results of the dichotomy method combined with slowness-time coherence algorithm is 1.14μs/ft smaller than that of the conventional method,while the average relative error is 1.2 percent lower.The dichotomy method combined with slowness-time coherence algorithm shows good results in its application,which can enhance the processing efficiency remarkably while getting reliable results at the same time.
文摘The variational method is applied to calculate the dispersion characteristics of disc-loaded waveguide slow-wave structures. The parameters describing the waveguide discontinuities in disc-loaded waveguide are calculated by the variational method. Then the dispersion characteristics of slow-wave structures are obtained using lossless microwave quadrupole theory. Good agreement was observed between results of the Variational method and those of field matching method and high frequency structure simulator. In the case of broad band, results of the variational method are better than those of field matching method.
文摘This paper studies chaotic motions in quasi-integrable Hamiltonian systems with slow-varying parameters under both harmonic and noise excitations. Based on the dynamic theory and some assumptions of excited noises, an extended form of the stochastic Melnikov method is presented. Using this extended method, the homoclinic bifurcations and chaotic behavior of a nonlinear Hamiltonian system with weak feed-back control under both harmonic and Gaussian white noise excitations are analyzed in detail. It is shown that the addition of stochastic excitations can make the parameter threshold value for the occurrence of chaotic motions vary in a wider region. Therefore, chaotic motions may arise easily in the system. By the Monte-Carlo method, the numerical results for the time-history and the maximum Lyapunov exponents of an example system are finally given to illustrate that the presented method is effective.
基金supported by National Natural Science Foundation of China(Grant No:52477133)Science and Technology Project of China Southern Power Grid(Grant No.GDKJXM20231178(036100KC23110012)+1 种基金GDKJXM20240389(030000KC24040053))Sanya Yazhou Bay Science and Technology City(Grant No:SKJC-JYRC-2024-66).
文摘With the rapid development of large-scale regional interconnected power grids,the risk of cascading failures under extreme condi-tions,such as natural disasters and military strikes,has increased significantly.To enhance the response capability of power systems to extreme events,this study focuses on a method for generator coherency detection.To overcome the shortcomings of the traditional slow coherency method,this paper introduces a novel coherent group identification algorithm based on the theory of nonlinear dynam-ical systems.By analyzing the changing trend of the Euclidean norm of the state variable derivatives in the reduced system,the algorithm can accurately identify the magnitude of the disturbances.Based on the slow coherency methods,the algorithm can correctly recognize coherent generator groups by analyzing system characteristics under varying disturbance magnitudes.This improvement enhances the applicability and accuracy of the coherency detection algorithm under extreme conditions,providing support for emergency control and protection in the power system.Simulations and comparison analyses on IEEE 39-bus system are conducted to validate the accuracy and superiority of the proposed coherent generator group identification method under extreme conditions.
