The propagation of stress waves in a large-diameter pipe pile for low strain dynamic testing cannot be explained properly by traditional 1D wave theories. A new computational model is established to obtain a wave equa...The propagation of stress waves in a large-diameter pipe pile for low strain dynamic testing cannot be explained properly by traditional 1D wave theories. A new computational model is established to obtain a wave equation that can describe the dynamic response of a large-diameter thin-walled pipe pile to a transient point load during a low strain integrity test. An analytical solution in the time domain is deduced using the separation of variables and variation of constant methods. The validity of this new solution is verifi ed by an existing analytical solution under free boundary conditions. The results of this time domain solution are also compared with the results of a frequency domain solution and fi eld test data. The comparisons indicate that the new solution agrees well with the results of previous solutions. Parametric studies using the new solution with reference to a case study are also carried out. The results show that the mode number affects the accuracy of the dynamic response. A mode number greater than 10 is required to enable the calculated dynamic responses to be independent of the mode number. The dynamic response is also greatly affected by soil properties. The larger the side resistance, the smaller the displacement response and the smaller the refl ected velocity wave crest. The displacement increases as the stress waves propagate along the pile when the pile shaft is free. The incident waves of displacement and velocity responses of the pile are not the same among different points in the circumferential direction on the pile top. However, the arrival time and peak value of the pile tip refl ected waves are almost the same among different points on the pile top.展开更多
Traditionally,numerical trajectory integration for shooting equation calculation and iterations for shooting with randomly guessed initial solutions deteriorate the real-time performance of indirect methods for on-boa...Traditionally,numerical trajectory integration for shooting equation calculation and iterations for shooting with randomly guessed initial solutions deteriorate the real-time performance of indirect methods for on-board applications.In this study,the indirect method is improved to achieve real-time trajectory optimization of fuel-optimal powered planetary landings with the help of analytical shooting equation derivations and a practical homotopy technique.Specifically,the contributions of this paper are threefold.First,the analytical expressions for shooting equation calculation are derived to replace the traditional time-consuming trajectory integration.Consequently,the computational efficiency is significantly improved.Second,the original three-dimensional landing problem is connected with a simplified one-dimensional problem that only involves the vertical dynamics,and its analytical solution is obtained based on Pontryagin’s minimum principle.Third,starting with the analytical solution,the accurate solution of the original landing problem can be obtained through an adaptive homotopy process.Simulation results of Earth landing scenarios are given to substantiate the effectiveness of the proposed techniques and illustrate that the developed method can obtain a fuel-optimal landing trajectory in 5 ms with 100%success rate.展开更多
Surface defects,including dents,spalls,and cracks,for rolling element bearings are the most common faults in rotating machinery.The accurate model for the time-varying excitation is the basis for the vibration mechani...Surface defects,including dents,spalls,and cracks,for rolling element bearings are the most common faults in rotating machinery.The accurate model for the time-varying excitation is the basis for the vibration mechanism analysis and fault feature extraction.However,in conventional investigations,this issue is not well and fully addressed from the perspective of theoretical analysis and physical derivation.In this study,an improved analytical model for time-varying displacement excitations(TVDEs)caused by surface defects is theoretically formulated.First and foremost,the physical mechanism for the effect of defect sizes on the physical process of rolling element-defect interaction is revealed.According to the physical interaction mechanism between the rolling element and different types of defects,the relationship between time-varying displacement pulse and defect sizes is further analytically derived.With the obtained time-varying displacement pulse,the dynamic model for the deep groove bearings considering the internal excitation caused by the surface defect is established.The nonlinear vibration responses and fault features induced by surface defects are analyzed using the proposed TVDE model.The results suggest that the presence of surface defects may result in the occurrence of the dual-impulse phenomenon,which can serve as indexes for surface-defect fault diagnosis.展开更多
The long-term stability of the roof is particularly important in designing underground rock structures.To estimate the durability of roof strata in underground excavation,a computation scheme of subcritical crack grow...The long-term stability of the roof is particularly important in designing underground rock structures.To estimate the durability of roof strata in underground excavation,a computation scheme of subcritical crack growth is proposed in this study.By adopting the proposed method,the potential collapse location of strata is derivable in accordance with a static model,the durability of roof strata can be estimated,a dynamic time step control strategy is achieved to balance the accuracy and speed of computing,and the initial crack size of rock can be estimated.In addition to the above,a mechanical model of underground excavation with non-uniformly distributed loads and partially yielded foundation is presented as the prototypical case.A set of case studies is carried out that showcase a power correlation between applied stress and roof durability.The allowable applied tensile stress for a 100-year life cycle is about 76%of the tensile strength.By using the proposed subcritical crack growth computation scheme,the roof stability in an underground excavation can be identified not only from the spatial view but also from the temporal perspective.展开更多
Practical resolution of consolidation problems that we often face requires an extensive and solid knowledge of the different parameters highlighted by the Terzaghi one-dimensional consolidation theory. This theory, wi...Practical resolution of consolidation problems that we often face requires an extensive and solid knowledge of the different parameters highlighted by the Terzaghi one-dimensional consolidation theory. This theory, with its assumptions, leads to a partial differential equation of second order in space and first order in time of pore water pressure. Analytical and numerical resolutions of this equation allow determining the water pressure variation before and after the application of a charge. Numerical modeling has enabled the simulation of the whole results obtained by the two methods of resolution (pressure, degree of consolidation, time factor, among others) to have a physical analysis and a lawful observation that lead to a suitable understanding of the phenomenon of Terzaghi one-dimensional consolidation.展开更多
Previous studies suggest that there are three different jam phases in the cellular automata automaton model with a slow-to-start rule under open boundaries.In the present paper,the dynamics of each free-flow-jam phase...Previous studies suggest that there are three different jam phases in the cellular automata automaton model with a slow-to-start rule under open boundaries.In the present paper,the dynamics of each free-flow-jam phase transition is studied.By analysing the microscopic behaviour of the traffic flow,we obtain analytical results on the phase transition dynamics.Our results can describe the detailed time evolution of the system during phase transition,while they provide good approximation for the numerical simulation data.These findings can perfectly explain the microscopic mechanism and details of the boundary-triggered phase transition dynamics.展开更多
The description of modern differential geometry for time-dependent Chetaev nonholonomic mechanical systems with unilateral constraints is studied. By using the structure of exact contact manifold, the geometric framew...The description of modern differential geometry for time-dependent Chetaev nonholonomic mechanical systems with unilateral constraints is studied. By using the structure of exact contact manifold, the geometric framework of time- dependent nonholonomic mechanical systems subject to unilateral nonholonomic constraints and unilateral holonomic constraints respectively is presented.展开更多
For a general nonlinear fractional-order differential equation, the numerical solution is a good way to approximate the trajectory of such systems. In this paper, a novel algorithm for numerical solution of fractional...For a general nonlinear fractional-order differential equation, the numerical solution is a good way to approximate the trajectory of such systems. In this paper, a novel algorithm for numerical solution of fractional-order differential equations based on the definition of Grunwald-Letnikov is presented. The results of numerical solution by using the novel method and the frequency-domain method are compared, and the limitations of frequency-domain method are discussed.展开更多
Vacuum combined surcharge preloading is an effective method which has been used in ground treatment. This study presents the analytical solution of vertical drains with vacuum combined surcharge preloading. The surcha...Vacuum combined surcharge preloading is an effective method which has been used in ground treatment. This study presents the analytical solution of vertical drains with vacuum combined surcharge preloading. The surcharge was considered to be time-dependent preloading due to its reflection of the real situation.Moreover,the free strain,instead of equal strain hypothesis of the surface,was adopted for the mathematical rigor. Both vertical and horizontal drainages,along with the well resistance were considered.Besides,the time-dependent surcharge preloading was resolved with the impulse theorem which has been presented in the study,and the solutions for pore water pressure and degree of consolidation were derived by applying the approach of separation of variables.Furthermore,the solution is compared with previous solutions and numerical solutions,and the results verify the correctness of the proposed model.展开更多
The free surface problem bound by two cylinders is analysed based on the velocity potential theory. An analytical solution in the take domain is obtained up to the second order in the perturbation expansion. The resul...The free surface problem bound by two cylinders is analysed based on the velocity potential theory. An analytical solution in the take domain is obtained up to the second order in the perturbation expansion. The results are compared with those obtainal from the fully nonlinear theory based on a finite element formulation.It is found that the second order solutiongives a fsr better agreement with the fully nonlinear solution.展开更多
Employing multiple pulsars and using an appropriate algorithm to establish ensemble pulsar timescale can reduce the influences of various noises on the long-term stability of pulsar timescale,compared to a single puls...Employing multiple pulsars and using an appropriate algorithm to establish ensemble pulsar timescale can reduce the influences of various noises on the long-term stability of pulsar timescale,compared to a single pulsar.However,due to the low timing precision and significant red noises of some pulsars,their participation in the construction of ensemble pulsar timescale is often limited.Inspired by the principle of solving non-stationary sequence modeling using co-integration theory,we put forward an algorithm based on co-integration theory to establish an ensemble pulsar timescale.It is found that this algorithm can effectively suppress some noise sources if a co-integration relationship between different pulsar data exists.Different from the classical weighted average algorithm,the co-integration method provides the chance for a pulsar with significant red noises to be included in the establishment of an ensemble pulsar timescale.Based on data from the North American Nanohertz Observatory for Gravitational Waves(NANOGrav),we found that the co-integration algorithm can successfully reduce several timing noises and improve the long-term stability of the ensemble pulsar timescale.展开更多
基金The 111 Project under Grant No.B13024the National Natural Science Foundation of China under Grant No.51378177+1 种基金the Program for New Century Excellent Talents in University under Grant No.NCET-12-0843the Fundamental Research Funds for the Central Universities under Grant No.106112014CDJZR200007
文摘The propagation of stress waves in a large-diameter pipe pile for low strain dynamic testing cannot be explained properly by traditional 1D wave theories. A new computational model is established to obtain a wave equation that can describe the dynamic response of a large-diameter thin-walled pipe pile to a transient point load during a low strain integrity test. An analytical solution in the time domain is deduced using the separation of variables and variation of constant methods. The validity of this new solution is verifi ed by an existing analytical solution under free boundary conditions. The results of this time domain solution are also compared with the results of a frequency domain solution and fi eld test data. The comparisons indicate that the new solution agrees well with the results of previous solutions. Parametric studies using the new solution with reference to a case study are also carried out. The results show that the mode number affects the accuracy of the dynamic response. A mode number greater than 10 is required to enable the calculated dynamic responses to be independent of the mode number. The dynamic response is also greatly affected by soil properties. The larger the side resistance, the smaller the displacement response and the smaller the refl ected velocity wave crest. The displacement increases as the stress waves propagate along the pile when the pile shaft is free. The incident waves of displacement and velocity responses of the pile are not the same among different points in the circumferential direction on the pile top. However, the arrival time and peak value of the pile tip refl ected waves are almost the same among different points on the pile top.
基金supported by the National Natural Science Foundation of China(Nos.11872223,11902174,11772167)。
文摘Traditionally,numerical trajectory integration for shooting equation calculation and iterations for shooting with randomly guessed initial solutions deteriorate the real-time performance of indirect methods for on-board applications.In this study,the indirect method is improved to achieve real-time trajectory optimization of fuel-optimal powered planetary landings with the help of analytical shooting equation derivations and a practical homotopy technique.Specifically,the contributions of this paper are threefold.First,the analytical expressions for shooting equation calculation are derived to replace the traditional time-consuming trajectory integration.Consequently,the computational efficiency is significantly improved.Second,the original three-dimensional landing problem is connected with a simplified one-dimensional problem that only involves the vertical dynamics,and its analytical solution is obtained based on Pontryagin’s minimum principle.Third,starting with the analytical solution,the accurate solution of the original landing problem can be obtained through an adaptive homotopy process.Simulation results of Earth landing scenarios are given to substantiate the effectiveness of the proposed techniques and illustrate that the developed method can obtain a fuel-optimal landing trajectory in 5 ms with 100%success rate.
基金This work is sponsored by the National Natural Science Foundation of China(Nos.52105117&52105118).
文摘Surface defects,including dents,spalls,and cracks,for rolling element bearings are the most common faults in rotating machinery.The accurate model for the time-varying excitation is the basis for the vibration mechanism analysis and fault feature extraction.However,in conventional investigations,this issue is not well and fully addressed from the perspective of theoretical analysis and physical derivation.In this study,an improved analytical model for time-varying displacement excitations(TVDEs)caused by surface defects is theoretically formulated.First and foremost,the physical mechanism for the effect of defect sizes on the physical process of rolling element-defect interaction is revealed.According to the physical interaction mechanism between the rolling element and different types of defects,the relationship between time-varying displacement pulse and defect sizes is further analytically derived.With the obtained time-varying displacement pulse,the dynamic model for the deep groove bearings considering the internal excitation caused by the surface defect is established.The nonlinear vibration responses and fault features induced by surface defects are analyzed using the proposed TVDE model.The results suggest that the presence of surface defects may result in the occurrence of the dual-impulse phenomenon,which can serve as indexes for surface-defect fault diagnosis.
基金China Scholarship Council(CSC)The University of Queensland for a Ph D fellowship。
文摘The long-term stability of the roof is particularly important in designing underground rock structures.To estimate the durability of roof strata in underground excavation,a computation scheme of subcritical crack growth is proposed in this study.By adopting the proposed method,the potential collapse location of strata is derivable in accordance with a static model,the durability of roof strata can be estimated,a dynamic time step control strategy is achieved to balance the accuracy and speed of computing,and the initial crack size of rock can be estimated.In addition to the above,a mechanical model of underground excavation with non-uniformly distributed loads and partially yielded foundation is presented as the prototypical case.A set of case studies is carried out that showcase a power correlation between applied stress and roof durability.The allowable applied tensile stress for a 100-year life cycle is about 76%of the tensile strength.By using the proposed subcritical crack growth computation scheme,the roof stability in an underground excavation can be identified not only from the spatial view but also from the temporal perspective.
文摘Practical resolution of consolidation problems that we often face requires an extensive and solid knowledge of the different parameters highlighted by the Terzaghi one-dimensional consolidation theory. This theory, with its assumptions, leads to a partial differential equation of second order in space and first order in time of pore water pressure. Analytical and numerical resolutions of this equation allow determining the water pressure variation before and after the application of a charge. Numerical modeling has enabled the simulation of the whole results obtained by the two methods of resolution (pressure, degree of consolidation, time factor, among others) to have a physical analysis and a lawful observation that lead to a suitable understanding of the phenomenon of Terzaghi one-dimensional consolidation.
基金Project supported by the National Natural Science Foundation of China (Grant Nos. 70971094 and 50908155)the Program for Changjiang Scholars and Innovative Research Team in University (PCSIRT)
文摘Previous studies suggest that there are three different jam phases in the cellular automata automaton model with a slow-to-start rule under open boundaries.In the present paper,the dynamics of each free-flow-jam phase transition is studied.By analysing the microscopic behaviour of the traffic flow,we obtain analytical results on the phase transition dynamics.Our results can describe the detailed time evolution of the system during phase transition,while they provide good approximation for the numerical simulation data.These findings can perfectly explain the microscopic mechanism and details of the boundary-triggered phase transition dynamics.
基金Project supported by the National Natural Science Foundation of China （Grant No 10272021）, the Natural Science Foundation of High Education of Jiangsu Province, China （Grant No 04KJA130135） and the ＂Qing Lan＂ Project Foundation of Jiangsu Province, China.
文摘The description of modern differential geometry for time-dependent Chetaev nonholonomic mechanical systems with unilateral constraints is studied. By using the structure of exact contact manifold, the geometric framework of time- dependent nonholonomic mechanical systems subject to unilateral nonholonomic constraints and unilateral holonomic constraints respectively is presented.
基金the Natural Science Foundation of CQ CSTC under Grant No. 2007BB2161.
文摘For a general nonlinear fractional-order differential equation, the numerical solution is a good way to approximate the trajectory of such systems. In this paper, a novel algorithm for numerical solution of fractional-order differential equations based on the definition of Grunwald-Letnikov is presented. The results of numerical solution by using the novel method and the frequency-domain method are compared, and the limitations of frequency-domain method are discussed.
基金National Natural Science Foundation of China(No.51578214)
文摘Vacuum combined surcharge preloading is an effective method which has been used in ground treatment. This study presents the analytical solution of vertical drains with vacuum combined surcharge preloading. The surcharge was considered to be time-dependent preloading due to its reflection of the real situation.Moreover,the free strain,instead of equal strain hypothesis of the surface,was adopted for the mathematical rigor. Both vertical and horizontal drainages,along with the well resistance were considered.Besides,the time-dependent surcharge preloading was resolved with the impulse theorem which has been presented in the study,and the solutions for pore water pressure and degree of consolidation were derived by applying the approach of separation of variables.Furthermore,the solution is compared with previous solutions and numerical solutions,and the results verify the correctness of the proposed model.
文摘The free surface problem bound by two cylinders is analysed based on the velocity potential theory. An analytical solution in the take domain is obtained up to the second order in the perturbation expansion. The results are compared with those obtainal from the fully nonlinear theory based on a finite element formulation.It is found that the second order solutiongives a fsr better agreement with the fully nonlinear solution.
基金funded by the National Natural Science Foundation of China (Grant Nos.11373028,U1531112,91736207,11873050, 11873049 and U1831130)the A Project of the Young Scholar of the “West Light” of the Chinese Academy of Sciences (XAB2015A06)the Cultivation Fund of Xi’an University of Science and Technology (No. 201707)
文摘Employing multiple pulsars and using an appropriate algorithm to establish ensemble pulsar timescale can reduce the influences of various noises on the long-term stability of pulsar timescale,compared to a single pulsar.However,due to the low timing precision and significant red noises of some pulsars,their participation in the construction of ensemble pulsar timescale is often limited.Inspired by the principle of solving non-stationary sequence modeling using co-integration theory,we put forward an algorithm based on co-integration theory to establish an ensemble pulsar timescale.It is found that this algorithm can effectively suppress some noise sources if a co-integration relationship between different pulsar data exists.Different from the classical weighted average algorithm,the co-integration method provides the chance for a pulsar with significant red noises to be included in the establishment of an ensemble pulsar timescale.Based on data from the North American Nanohertz Observatory for Gravitational Waves(NANOGrav),we found that the co-integration algorithm can successfully reduce several timing noises and improve the long-term stability of the ensemble pulsar timescale.
