We have found two types of important exact solutions, compacton solutions, which are solitary waves with the property that after colliding with their own kind, they re-emerge with the same coherent shape very much as ...We have found two types of important exact solutions, compacton solutions, which are solitary waves with the property that after colliding with their own kind, they re-emerge with the same coherent shape very much as the solitons do during a completely elastic interaction, in the and even models, and dromion solutions (exponentially decaying solutions in all direction) in many and models. In this paper, symmetry reductions in are considered for the break soliton-type equation with fully nonlinear dispersion (called equation) , which is a generalized model of break soliton equation , by using the extended direct reduction method. As a result, six types of symmetry reductions are obtained. Starting from the reduction equations and some simple transformations, we obtain the solitary wave solutions of equations, compacton solutions of equations and the compacton-like solution of the potential form (called ) . In addition, we show that the variable admits dromion solutions rather than the field itself in equation.展开更多
The two coupled governing differential equations for the out-of-plane vibrations of non-uniform beams with variable curvature are derived via the Hamilton’s principle.These equations are expressed in terms of flexura...The two coupled governing differential equations for the out-of-plane vibrations of non-uniform beams with variable curvature are derived via the Hamilton’s principle.These equations are expressed in terms of flexural and torsional displacements simultaneously.In this study,the analytical method is proposed.Firstly,two physical parameters are introduced to simplify the analysis.One derives the explicit relations between the flexural and the torsional displacements which can also be used to reduce the difficulty in experimental measurements.Based on the relation,the two governing characteristic differential equations with variable coefficients can be uncoupled into a sixth-order ordinary differential equation in terms of the flexural displacement only.When the material and geometric properties of the beam are in arbitrary polynomial forms,the exact solutions with regard to the outof-plane vibrations of non-uniform beams with variable curvature can be obtained by the recurrence formula.In addition,the mode transition mechanism is revealed and the influence of several parameters on the vibration of the non-uniform beam with variable curvature is explored.展开更多
Three (2 + 1)-dimensional equations—Burgers equation, cylindrical Burgers equation and spherical Burgers equation, have been reduced to the classical Burgers equation by different transformation of variables respecti...Three (2 + 1)-dimensional equations—Burgers equation, cylindrical Burgers equation and spherical Burgers equation, have been reduced to the classical Burgers equation by different transformation of variables respectively. The decay mode solutions of the Burgers equation have been obtained by using the extended -expansion method, substituting the solutions obtained into the corresponding transformation of variables, the decay mode solutions of the three (2 + 1)-dimensional equations have been obtained successfully.展开更多
The dynamic density functional theory is applied to study the diffusion of nanoparticles in polymer solutions, in which different diffusion modes have been identified by exploiting the density and free energy evolutio...The dynamic density functional theory is applied to study the diffusion of nanoparticles in polymer solutions, in which different diffusion modes have been identified by exploiting the density and free energy evolutions. Under the condition of low polymer concentration, diffusion is controlled by particle free motion with a normal Gaussian type. As the concentration increases, the non- Gaussian behavior can be observed when the particle size is comparable to the correlation length of polymer chain. Particles need to penetrate through a cage and overcome an entropic barrier, where the hopping and the model-coupling diffusion coexist. Further increase of polymer concentration can result in complete restriction of the particle by surrounding polymer segments. In this case, the non-Gaussian process fades away, and particle diffusion is controlled by Rouse dynamics of polymer chains with the generalized Gaussian characteristics.展开更多
The Earth's rotational normal modes depend on Earth model used, including the layer structures,principal inertia moments of different layers and the compliances. This study focuses on providing numerical solution ...The Earth's rotational normal modes depend on Earth model used, including the layer structures,principal inertia moments of different layers and the compliances. This study focuses on providing numerical solution of the rotational normal modes of a triaxial two-layered anelastic Earth model without external forces but with considering the complex forms of compliances and the electromagnetic coupling between the core and mantle. Based on the present knowledge of the Chandler wobble(CW) and Free Core Nutation(FCN), we provide a set of complete compliances which could be used for reference in further investigations. There are eight rotational normal mode solutions, four of which might exist in nature. However, in reality only two of these four solutions correspond to the present motion status of the prograde CW and the retrograde FCN. On one hand, our numerical calculations show that the periods and quality factors(Qs) of CW and FCN are respectively 434.90 and 429.86 mean solar days(d) and 76.56 and 23988.47 under frequency-dependent assumption, and the triaxiality prolongs CW about 0.01 d and has hardly effect on FCN. On the other hand, we analyze the sensibility of compliances and electromagnetic coupling parameter on the periods and Qs of CW and FCN and find the sensitive parameters with respect to them.展开更多
The decay mode solutions for the Kadomtsev-Petviashvili (KP) equation are derived by Hirota method (direct method).The decay mode solution is a new set of analytical solutions with Airy function.
[Objectives]To investigate the effect of healthcare failure mode and effect analysis(HFMEA)on reducing error risk of neonatal parenteral nutrition solution dispensing.[Methods]A research team was established to identi...[Objectives]To investigate the effect of healthcare failure mode and effect analysis(HFMEA)on reducing error risk of neonatal parenteral nutrition solution dispensing.[Methods]A research team was established to identify the failure mode(FM)in each link of the formulation process of neonatal parenteral nutrition solution by HFMEA,quantify the severity(S),occurrence(O)and detection(D)of FM,and evaluate FM by risk priority number(RPN).For FM with the values of RPN>16,failure cause analysis was conducted,and corresponding improvement measures were formulated.The weight coefficient and random consistency ratio(CR)of deployment process were calculated in Matlab R2018a by compiling the Analytic Hierarchy Process(AHP)program.Six months after the implementation of improvement measures,the implementation effect was evaluated by comparing the changes of the values of RPN which was evaluated comprehensively and the rate of dispensing errors before and after the implementation of HFMEA.[Results]In the preparation process of neonatal parenteral nutrition solution,a total of 13 FMs with medium and above risk were found,the weight coefficient of medical order review,dosing and mixing was 0.2703,the weight coefficient of drug dispensing check and review was 0.1432,the weight coefficient of print label was 0.1015,the weight coefficient of distribution was 0.0716,and CR=0.0491<0.1.After six months of intervention,the total RPN value decreased by 64.81%from 127.8 to 45.0.The deployment error rates were significantly lower after the implementation,and the difference was statistically significant(P<0.05).[Conclusions]HFMEA can effectively reduce the error risk in preparation of neonatal parenteral nutrition solution,improve the quality of dispensing and promote the safety of neonatal medication.展开更多
Molecular dynamics(MD)is a powerful method widely used in materials science and solid-state physics.The accuracy of MD simulations depends on the quality of the interatomic potentials.In this work,a special class of e...Molecular dynamics(MD)is a powerful method widely used in materials science and solid-state physics.The accuracy of MD simulations depends on the quality of the interatomic potentials.In this work,a special class of exact solutions to the equations of motion of atoms in a body-centered cubic(bcc)lattice is analyzed.These solutions take the form of delocalized nonlinear vibrational modes(DNVMs)and can serve as an excellent test of the accuracy of the interatomic potentials used in MD modeling for bcc crystals.The accuracy of the potentials can be checked by comparing the frequency response of DNVMs calculated using this or that interatomic potential with that calculated using the more accurate ab initio approach.DNVMs can also be used to train new,more accurate machine learning potentials for bcc metals.To address the above issues,it is important to analyze the properties of DNVMs,which is the main goal of this work.Considering only the point symmetry groups of the bcc lattice,34 DNVMs are found.Since interatomic potentials are not used in finding DNVMs,they are exact solutions for any type of potential.Here,the simplest interatomic potentials with cubic anharmonicity are used to simplify the analysis and to obtain some analytical results.For example,the dispersion relations for small-amplitude phonon modes are derived,taking into account interactions between up to the fourth nearest neighbor.The frequency response of the DNVMs is calculated numerically,and for some DNVMs examples of analytical analysis are given.The energy stored by the interatomic bonds of different lengths is calculated,which is important for testing interatomic potentials.The pros and cons of using DNVMs to test and improve interatomic potentials for metals are discussed.Since DNVMs are the natural vibrational modes of bcc crystals,any reliable interatomic potential must reproduce their properties with reasonable accuracy.展开更多
All possible exact solutions are successfully obtained in terms of 10 sets of distinct eigensolutions for the free in-plane vibration of isotropic rectangular plates. The plates have simply supported condition at two ...All possible exact solutions are successfully obtained in terms of 10 sets of distinct eigensolutions for the free in-plane vibration of isotropic rectangular plates. The plates have simply supported condition at two opposite edges and any combination of classical boundary conditions at the other two edges. The exact solutions are validated through both mathematical proof and comparisons with the solutions of differential quadrature method. Some unusual phenomena are revealed in free in-plane vibrations of rectangular plates due to one of the eigenvalues being zero. This work constitutes an improved version of very recent corresponding work by the same authors lint. J. Mech. Sci., 2009, 51： 246-255]. Both the solution forms and solving procedures in the previous work are substantially simplified. Some new results are also given, which are useful for validation purpose in future.展开更多
An exact analysis of the modes Ⅱ and Ⅲ problems of a penny- shaped crack in a transversely isotropic piezoelectric medium is performed in this paper.The potential theory method is employed based on the general solut...An exact analysis of the modes Ⅱ and Ⅲ problems of a penny- shaped crack in a transversely isotropic piezoelectric medium is performed in this paper.The potential theory method is employed based on the general solution of three-dimensional piezoelasticity and the four harmonics involved are represented by one complex potential.Previous results in potential theory are then utilized to obtain the exact solution that is expressed in terms of elementary functions.Comparison is made between the current results with those published and good agreement is obtained.展开更多
Rock bolting has advanced rapidly during the past 4 decades due to a better understanding of load transfer mechanisms and advances made in the bolt system technology. Bolts are used as permanent and temporary support ...Rock bolting has advanced rapidly during the past 4 decades due to a better understanding of load transfer mechanisms and advances made in the bolt system technology. Bolts are used as permanent and temporary support systems in tunnelling and mining operations. A review of has indicated that three systems of reinforcement devices have evolved as part of rock bolt and ground anchor while the rock is not generally thought of as being a component of the reinforcement system. A classification of rock bolting reinforcement systems is presented, followed by the fundamental theory of the load transfer mechanism. The failure mode of two phases of rock bolting system is formularised. The failure modes of cable bolting are discussed using a bond strength model as well as an iterative method. Finally, the interfacial shear stress model for ribbed bar is introduced and a closed form solution is obtained using a tri-line stress strain relationship.展开更多
This paper proposes a time-varying sliding mode control method to address nonlinear missile body kinematics based on the suboptimal control theory.The analytical solution of suboptimal time-varying sliding surface and...This paper proposes a time-varying sliding mode control method to address nonlinear missile body kinematics based on the suboptimal control theory.The analytical solution of suboptimal time-varying sliding surface and the corresponding suboptimal control law are obtained by solving the state-dependent Riccati equation analytically.Then,the Lyapunov method is used to analyze the motion trend in sliding surface and the asymptotic stability of the closed-loop system is validated.The suboptimal control law is transformed to the form of pseudo-angle-of-attack feedback.The simulation results indicate that the satisfactory performance can be obtained and the control law can overcome the influence of parameter errors.展开更多
We present an approach to solve Bethe-Salpeter (BS) equations exactly withoutany approximation if the kernel of the BS equations exactly is instantaneous, and take positroniumas an example to illustrate the general fe...We present an approach to solve Bethe-Salpeter (BS) equations exactly withoutany approximation if the kernel of the BS equations exactly is instantaneous, and take positroniumas an example to illustrate the general features of the exact solutions. The key step for theapproach is from the BS equations to derive a set of coupled and well-determined integrationequations in linear eigenvalue for the components of the BS wave functions equivalently, which maybe solvable numerically under a controlled accuracy, even though there is no analytic solution. Forpositronium, the exact solutions precisely present corrections to those of the correspondingSchrodinger equation in order υ~1 (υ is the relative velocity) for eigenfunctions, in order υ~2for eigenvalues, and the mixing between S and D components in J~(PC) = 1~(--) states etc.,quantitatively. Moreover, we also point out that there is a questionable step in some existentderivations for the instantaneous BS equations if one is pursuing the exact solutions. Finally, weemphasize that one should take the O(υ) corrections emerging in the exact solutions into accountaccordingly if one is interested in the relativistic corrections for relevant problems to the boundstates.展开更多
Li transient concentration distribution in spherical active material particles can affect the maximum power density and the safe operating regime of the electric vehicles(EVs). On one hand, the quasiexact/exact soluti...Li transient concentration distribution in spherical active material particles can affect the maximum power density and the safe operating regime of the electric vehicles(EVs). On one hand, the quasiexact/exact solution obtained in the time/frequency domain is time-consuming and just as a reference value for approximate solutions;on the other hand, calculation errors and application range of approximate solutions not only rely on approximate algorithms but also on discharge modes. For the purpose to track the transient dynamics for Li solid-phase diffusion in spherical active particles with a tolerable error range and for a wide applicable range, it is necessary to choose optimal approximate algorithms in terms of discharge modes and the nature of active material particles. In this study, approximation methods,such as diffusion length method, polynomial profile approximation method, Padé approximation method,pseudo steady state method, eigenfunction-based Galerkin collocation method, and separation of variables method for solving Li solid-phase diffusion in spherical active particles are compared from calculation fundamentals to algorithm implementation. Furthermore, these approximate solutions are quantitatively compared to the quasi-exact/exact solution in the time/frequency domain under typical discharge modes, i.e., start-up, slow-down, and speed-up. The results obtained from the viewpoint of time-frequency analysis offer a theoretical foundation on how to track Li transient concentration profile in spherical active particles with a high precision and for a wide application range. In turn, optimal solutions of Li solid diffusion equations for spherical active particles can improve the reliability in predicting safe operating regime and estimating maximum power for automotive batteries.展开更多
Excitation and propagation of Lamb waves by using rectangular and circular piezoelectric transducers surface- bonded to an isotropic plate are investigated in this work. Analytical stain wave solutions are derived for...Excitation and propagation of Lamb waves by using rectangular and circular piezoelectric transducers surface- bonded to an isotropic plate are investigated in this work. Analytical stain wave solutions are derived for the two transducer shapes, giving the responses of these transducers in Lamb wave fields. The analytical study is supported by a numericM simulation using the finite element method. Symmetric and antisymmetric components in the wave propagation responses are inspected in detail with respect to test parameters such as the transducer geometry, the length and the excitation frequency. By placing only one piezoelectric transducer on the top or the bottom surface of the plate and weakening the strength of one mode while enhancing the strength of the other modes to find the centre frequency, with which the peak wave amplitude ratio between the SO and A0 modes is maximum, a single mode excitation from the multiple modes of the Lamb waves can be achieved approximately. Experimental data are presented to show the validity of the analyses. The results are used to optimize the Lamb wave detection system.展开更多
A GPS baseline solution model is presented,based on the Empirical Mode Decomposition(EMD),which has the advan- tage of eliminating the error effects outside the model.The EMD technique is a new signal processing metho...A GPS baseline solution model is presented,based on the Empirical Mode Decomposition(EMD),which has the advan- tage of eliminating the error effects outside the model.The EMD technique is a new signal processing method for non-linear time series,which decomposes a time series into a finite and often small number of Intrinsic Mode Functions(IMFs).The decomposition procedure is adaptive and data-driven which is suitable for non-linear data series analysis.A multi-scale decomposition and recon- struction architecture is defined on the basis of the EMD theory and the error mitigation model is demonstrated as well.A standard of the scale selection for the elimination of errors,outside the model,was given in terms of the mean of the accumulated standard- ized modes.Thereafter,the scheme of the GPS baseline solution based on the EMD is suggested.The float solution residuals of the Double-Difference(DD)observation equation are used to extract the errors outside the model applied to modify the GPS DD measurements.Then the float solution was given again and the fixed solution was obtained by a Lambda algorithm.Three schemes are designed to test the proposed model and the experimental results show that the proposed model dramatically improves the reli- ability of ambiguity resolution after the elimination of errors outside the model.展开更多
文摘We have found two types of important exact solutions, compacton solutions, which are solitary waves with the property that after colliding with their own kind, they re-emerge with the same coherent shape very much as the solitons do during a completely elastic interaction, in the and even models, and dromion solutions (exponentially decaying solutions in all direction) in many and models. In this paper, symmetry reductions in are considered for the break soliton-type equation with fully nonlinear dispersion (called equation) , which is a generalized model of break soliton equation , by using the extended direct reduction method. As a result, six types of symmetry reductions are obtained. Starting from the reduction equations and some simple transformations, we obtain the solitary wave solutions of equations, compacton solutions of equations and the compacton-like solution of the potential form (called ) . In addition, we show that the variable admits dromion solutions rather than the field itself in equation.
文摘The two coupled governing differential equations for the out-of-plane vibrations of non-uniform beams with variable curvature are derived via the Hamilton’s principle.These equations are expressed in terms of flexural and torsional displacements simultaneously.In this study,the analytical method is proposed.Firstly,two physical parameters are introduced to simplify the analysis.One derives the explicit relations between the flexural and the torsional displacements which can also be used to reduce the difficulty in experimental measurements.Based on the relation,the two governing characteristic differential equations with variable coefficients can be uncoupled into a sixth-order ordinary differential equation in terms of the flexural displacement only.When the material and geometric properties of the beam are in arbitrary polynomial forms,the exact solutions with regard to the outof-plane vibrations of non-uniform beams with variable curvature can be obtained by the recurrence formula.In addition,the mode transition mechanism is revealed and the influence of several parameters on the vibration of the non-uniform beam with variable curvature is explored.
文摘Three (2 + 1)-dimensional equations—Burgers equation, cylindrical Burgers equation and spherical Burgers equation, have been reduced to the classical Burgers equation by different transformation of variables respectively. The decay mode solutions of the Burgers equation have been obtained by using the extended -expansion method, substituting the solutions obtained into the corresponding transformation of variables, the decay mode solutions of the three (2 + 1)-dimensional equations have been obtained successfully.
基金financially supported by the National Natural Science Foundation of China (Nos. 51790502 and 51525301)the National Supercomputer Centre in GuangzhouChemcloudcomputing of Beijing University of Chemical Technology
文摘The dynamic density functional theory is applied to study the diffusion of nanoparticles in polymer solutions, in which different diffusion modes have been identified by exploiting the density and free energy evolutions. Under the condition of low polymer concentration, diffusion is controlled by particle free motion with a normal Gaussian type. As the concentration increases, the non- Gaussian behavior can be observed when the particle size is comparable to the correlation length of polymer chain. Particles need to penetrate through a cage and overcome an entropic barrier, where the hopping and the model-coupling diffusion coexist. Further increase of polymer concentration can result in complete restriction of the particle by surrounding polymer segments. In this case, the non-Gaussian process fades away, and particle diffusion is controlled by Rouse dynamics of polymer chains with the generalized Gaussian characteristics.
基金supported by the NSFC (grant Nos. 41631072, 41721003, 41874023, 41574007, and 41429401)the Discipline Innovative Engineering Plan of Modern Geodesy and Geodynamics (grant No. B17033)the DAAD Thematic Network Project (grant No. 57173947)
文摘The Earth's rotational normal modes depend on Earth model used, including the layer structures,principal inertia moments of different layers and the compliances. This study focuses on providing numerical solution of the rotational normal modes of a triaxial two-layered anelastic Earth model without external forces but with considering the complex forms of compliances and the electromagnetic coupling between the core and mantle. Based on the present knowledge of the Chandler wobble(CW) and Free Core Nutation(FCN), we provide a set of complete compliances which could be used for reference in further investigations. There are eight rotational normal mode solutions, four of which might exist in nature. However, in reality only two of these four solutions correspond to the present motion status of the prograde CW and the retrograde FCN. On one hand, our numerical calculations show that the periods and quality factors(Qs) of CW and FCN are respectively 434.90 and 429.86 mean solar days(d) and 76.56 and 23988.47 under frequency-dependent assumption, and the triaxiality prolongs CW about 0.01 d and has hardly effect on FCN. On the other hand, we analyze the sensibility of compliances and electromagnetic coupling parameter on the periods and Qs of CW and FCN and find the sensitive parameters with respect to them.
基金Supported by the Fundamental Research Funds for the Central Universities (WM0911003) and (WM0911005)
文摘The decay mode solutions for the Kadomtsev-Petviashvili (KP) equation are derived by Hirota method (direct method).The decay mode solution is a new set of analytical solutions with Airy function.
基金Young Scholar Program of Hebei Pharmaceutical Association Hospital Pharmaceutical Research Project(2020—Hbsyxhqn0029)Science and Technology Research and Development Project of Chengde City,Hebei Province(201706A043).
文摘[Objectives]To investigate the effect of healthcare failure mode and effect analysis(HFMEA)on reducing error risk of neonatal parenteral nutrition solution dispensing.[Methods]A research team was established to identify the failure mode(FM)in each link of the formulation process of neonatal parenteral nutrition solution by HFMEA,quantify the severity(S),occurrence(O)and detection(D)of FM,and evaluate FM by risk priority number(RPN).For FM with the values of RPN>16,failure cause analysis was conducted,and corresponding improvement measures were formulated.The weight coefficient and random consistency ratio(CR)of deployment process were calculated in Matlab R2018a by compiling the Analytic Hierarchy Process(AHP)program.Six months after the implementation of improvement measures,the implementation effect was evaluated by comparing the changes of the values of RPN which was evaluated comprehensively and the rate of dispensing errors before and after the implementation of HFMEA.[Results]In the preparation process of neonatal parenteral nutrition solution,a total of 13 FMs with medium and above risk were found,the weight coefficient of medical order review,dosing and mixing was 0.2703,the weight coefficient of drug dispensing check and review was 0.1432,the weight coefficient of print label was 0.1015,the weight coefficient of distribution was 0.0716,and CR=0.0491<0.1.After six months of intervention,the total RPN value decreased by 64.81%from 127.8 to 45.0.The deployment error rates were significantly lower after the implementation,and the difference was statistically significant(P<0.05).[Conclusions]HFMEA can effectively reduce the error risk in preparation of neonatal parenteral nutrition solution,improve the quality of dispensing and promote the safety of neonatal medication.
基金support of the RSF Grant No.24-11-00139(analytics,numerical results,manuscript writing)Daxing Xiong acknowledges the support of the NNSF Grant No.12275116,the NSF Grant No.2021J02051,and the startup fund Grant No.MJY21035For Aleksey A.Kudreyko,this work was supported by the Bashkir StateMedicalUniversity StrategicAcademic Leadership Program(PRIORITY-2030)(analytics).
文摘Molecular dynamics(MD)is a powerful method widely used in materials science and solid-state physics.The accuracy of MD simulations depends on the quality of the interatomic potentials.In this work,a special class of exact solutions to the equations of motion of atoms in a body-centered cubic(bcc)lattice is analyzed.These solutions take the form of delocalized nonlinear vibrational modes(DNVMs)and can serve as an excellent test of the accuracy of the interatomic potentials used in MD modeling for bcc crystals.The accuracy of the potentials can be checked by comparing the frequency response of DNVMs calculated using this or that interatomic potential with that calculated using the more accurate ab initio approach.DNVMs can also be used to train new,more accurate machine learning potentials for bcc metals.To address the above issues,it is important to analyze the properties of DNVMs,which is the main goal of this work.Considering only the point symmetry groups of the bcc lattice,34 DNVMs are found.Since interatomic potentials are not used in finding DNVMs,they are exact solutions for any type of potential.Here,the simplest interatomic potentials with cubic anharmonicity are used to simplify the analysis and to obtain some analytical results.For example,the dispersion relations for small-amplitude phonon modes are derived,taking into account interactions between up to the fourth nearest neighbor.The frequency response of the DNVMs is calculated numerically,and for some DNVMs examples of analytical analysis are given.The energy stored by the interatomic bonds of different lengths is calculated,which is important for testing interatomic potentials.The pros and cons of using DNVMs to test and improve interatomic potentials for metals are discussed.Since DNVMs are the natural vibrational modes of bcc crystals,any reliable interatomic potential must reproduce their properties with reasonable accuracy.
基金supported by the China Postdoctoral Science Foundation (No. 20100470179)
文摘All possible exact solutions are successfully obtained in terms of 10 sets of distinct eigensolutions for the free in-plane vibration of isotropic rectangular plates. The plates have simply supported condition at two opposite edges and any combination of classical boundary conditions at the other two edges. The exact solutions are validated through both mathematical proof and comparisons with the solutions of differential quadrature method. Some unusual phenomena are revealed in free in-plane vibrations of rectangular plates due to one of the eigenvalues being zero. This work constitutes an improved version of very recent corresponding work by the same authors lint. J. Mech. Sci., 2009, 51： 246-255]. Both the solution forms and solving procedures in the previous work are substantially simplified. Some new results are also given, which are useful for validation purpose in future.
基金The project supported by the National Natural Science Foundation of China(No.19872060)
文摘An exact analysis of the modes Ⅱ and Ⅲ problems of a penny- shaped crack in a transversely isotropic piezoelectric medium is performed in this paper.The potential theory method is employed based on the general solution of three-dimensional piezoelasticity and the four harmonics involved are represented by one complex potential.Previous results in potential theory are then utilized to obtain the exact solution that is expressed in terms of elementary functions.Comparison is made between the current results with those published and good agreement is obtained.
文摘Rock bolting has advanced rapidly during the past 4 decades due to a better understanding of load transfer mechanisms and advances made in the bolt system technology. Bolts are used as permanent and temporary support systems in tunnelling and mining operations. A review of has indicated that three systems of reinforcement devices have evolved as part of rock bolt and ground anchor while the rock is not generally thought of as being a component of the reinforcement system. A classification of rock bolting reinforcement systems is presented, followed by the fundamental theory of the load transfer mechanism. The failure mode of two phases of rock bolting system is formularised. The failure modes of cable bolting are discussed using a bond strength model as well as an iterative method. Finally, the interfacial shear stress model for ribbed bar is introduced and a closed form solution is obtained using a tri-line stress strain relationship.
基金supported by the China Postdoctoral Science Foundation(2017M620863).
文摘This paper proposes a time-varying sliding mode control method to address nonlinear missile body kinematics based on the suboptimal control theory.The analytical solution of suboptimal time-varying sliding surface and the corresponding suboptimal control law are obtained by solving the state-dependent Riccati equation analytically.Then,the Lyapunov method is used to analyze the motion trend in sliding surface and the asymptotic stability of the closed-loop system is validated.The suboptimal control law is transformed to the form of pseudo-angle-of-attack feedback.The simulation results indicate that the satisfactory performance can be obtained and the control law can overcome the influence of parameter errors.
文摘We present an approach to solve Bethe-Salpeter (BS) equations exactly withoutany approximation if the kernel of the BS equations exactly is instantaneous, and take positroniumas an example to illustrate the general features of the exact solutions. The key step for theapproach is from the BS equations to derive a set of coupled and well-determined integrationequations in linear eigenvalue for the components of the BS wave functions equivalently, which maybe solvable numerically under a controlled accuracy, even though there is no analytic solution. Forpositronium, the exact solutions precisely present corrections to those of the correspondingSchrodinger equation in order υ~1 (υ is the relative velocity) for eigenfunctions, in order υ~2for eigenvalues, and the mixing between S and D components in J~(PC) = 1~(--) states etc.,quantitatively. Moreover, we also point out that there is a questionable step in some existentderivations for the instantaneous BS equations if one is pursuing the exact solutions. Finally, weemphasize that one should take the O(υ) corrections emerging in the exact solutions into accountaccordingly if one is interested in the relativistic corrections for relevant problems to the boundstates.
基金the financial support from the National Science Foundation of China(22078190 and 12002196)the National Key Research and Development Program of China(2020YFB1505802)。
文摘Li transient concentration distribution in spherical active material particles can affect the maximum power density and the safe operating regime of the electric vehicles(EVs). On one hand, the quasiexact/exact solution obtained in the time/frequency domain is time-consuming and just as a reference value for approximate solutions;on the other hand, calculation errors and application range of approximate solutions not only rely on approximate algorithms but also on discharge modes. For the purpose to track the transient dynamics for Li solid-phase diffusion in spherical active particles with a tolerable error range and for a wide applicable range, it is necessary to choose optimal approximate algorithms in terms of discharge modes and the nature of active material particles. In this study, approximation methods,such as diffusion length method, polynomial profile approximation method, Padé approximation method,pseudo steady state method, eigenfunction-based Galerkin collocation method, and separation of variables method for solving Li solid-phase diffusion in spherical active particles are compared from calculation fundamentals to algorithm implementation. Furthermore, these approximate solutions are quantitatively compared to the quasi-exact/exact solution in the time/frequency domain under typical discharge modes, i.e., start-up, slow-down, and speed-up. The results obtained from the viewpoint of time-frequency analysis offer a theoretical foundation on how to track Li transient concentration profile in spherical active particles with a high precision and for a wide application range. In turn, optimal solutions of Li solid diffusion equations for spherical active particles can improve the reliability in predicting safe operating regime and estimating maximum power for automotive batteries.
基金Project supported by the National Natural Science Foundation of China (Grant Nos.11074164 and 10874110)the Shanghai Leading Academic Discipline Project,China (Grant No.S30108)+1 种基金the Science and Technology Commission of Shanghai Municipality,China (Grant No.08DZ2231100)the Innovation Foundation of Shanghai Municipal Commission of Education,China (Grant No.11YZ17)
文摘Excitation and propagation of Lamb waves by using rectangular and circular piezoelectric transducers surface- bonded to an isotropic plate are investigated in this work. Analytical stain wave solutions are derived for the two transducer shapes, giving the responses of these transducers in Lamb wave fields. The analytical study is supported by a numericM simulation using the finite element method. Symmetric and antisymmetric components in the wave propagation responses are inspected in detail with respect to test parameters such as the transducer geometry, the length and the excitation frequency. By placing only one piezoelectric transducer on the top or the bottom surface of the plate and weakening the strength of one mode while enhancing the strength of the other modes to find the centre frequency, with which the peak wave amplitude ratio between the SO and A0 modes is maximum, a single mode excitation from the multiple modes of the Lamb waves can be achieved approximately. Experimental data are presented to show the validity of the analyses. The results are used to optimize the Lamb wave detection system.
基金Projects 40774010 supported by the National Natural Science Foundation of China20040290503 by the Research Fund for the Doctoral Program of Higher Education2006A029 by the Youth Scientific Research Foundation of China University of Mining and Technology
文摘A GPS baseline solution model is presented,based on the Empirical Mode Decomposition(EMD),which has the advan- tage of eliminating the error effects outside the model.The EMD technique is a new signal processing method for non-linear time series,which decomposes a time series into a finite and often small number of Intrinsic Mode Functions(IMFs).The decomposition procedure is adaptive and data-driven which is suitable for non-linear data series analysis.A multi-scale decomposition and recon- struction architecture is defined on the basis of the EMD theory and the error mitigation model is demonstrated as well.A standard of the scale selection for the elimination of errors,outside the model,was given in terms of the mean of the accumulated standard- ized modes.Thereafter,the scheme of the GPS baseline solution based on the EMD is suggested.The float solution residuals of the Double-Difference(DD)observation equation are used to extract the errors outside the model applied to modify the GPS DD measurements.Then the float solution was given again and the fixed solution was obtained by a Lambda algorithm.Three schemes are designed to test the proposed model and the experimental results show that the proposed model dramatically improves the reli- ability of ambiguity resolution after the elimination of errors outside the model.
