Subgrade settlement is a common issue in soil ground within earthquake-prone regions,posing a threat to the safe operation of train-slab track coupled system(TSCS)in high-speed railways(HSRs).This study aims to analyz...Subgrade settlement is a common issue in soil ground within earthquake-prone regions,posing a threat to the safe operation of train-slab track coupled system(TSCS)in high-speed railways(HSRs).This study aims to analyze the mechanical behavior evolution of TSCS under subgrade settlement and earthquake excitation.The refined numerical model of slab track under subgrade differential settlement is established.The short settlement wavelength of 10 m causes the separation between the base and subgrade.The dynamic model of TSCS under subgrade settlement and earthquake excitation is developed.The dynamic response of TSCS exhibits more pronounced fluctuations under the combined effects of subgrade settlement and earthquake excitation than under the effects of settlement or earthquake alone.The evaluation indexes for the running safety of train on slab track under different settlement wavelengths exhibit varying degrees of increase with settlement amplitude and are particularly sensitive to the short settlement wavelength of 10 m.The wheel unloading rate and derailment coefficient of TSCS increase with earthquake intensity.Under the settlement wavelength of 10 m and amplitude of 20 mm,the wheel unloading rate of TSCS exceeds the allowable limit when the earthquake intensity exceeds 0.17g,and the derailment coefficient exceeds the allowable limit when the earthquake intensity surpasses 0.29g.展开更多
In this paper,we investigate the(2+1)-dimensional three-component long-wave-short-wave resonance interaction system,which describes complex systems and nonlinear wave phenomena in physics.By employing the Hirota bilin...In this paper,we investigate the(2+1)-dimensional three-component long-wave-short-wave resonance interaction system,which describes complex systems and nonlinear wave phenomena in physics.By employing the Hirota bilinear method,we derive the general nondegenerate N-soliton solution of the system,where each short-wave component contains N arbitrary functions of the independent variable y.The presence of these arbitrary functions in the analytical solution enables the construction of a wide range of nondegenerate soliton types.Finally,we illustrate the structural features of several novel nondegenerate solitons,including M-shaped,multiple double-hump,and sawtooth double-striped solitons,as well as interactions between nondegenerate solitons,such as dromion-like solitons and solitoffs,with the aid of figures.展开更多
The collective dynamic of a fractional-order globally coupled system with time delays and fluctuating frequency is investigated.The power-law memory of the system is characterized using the Caputo fractional derivativ...The collective dynamic of a fractional-order globally coupled system with time delays and fluctuating frequency is investigated.The power-law memory of the system is characterized using the Caputo fractional derivative operator.Additionally,time delays in the potential field force and coupling force transmission are both considered.Firstly,based on the delay decoupling formula,combined with statistical mean method and the fractional-order Shapiro–Loginov formula,the“statistic synchronization”among particles is obtained,revealing the statistical equivalence between the mean field behavior of the system and the behavior of individual particles.Due to the existence of the coupling delay,the impact of the coupling force on synchronization exhibits non-monotonic,which is different from the previous monotonic effects.Then,two kinds of theoretical expression of output amplitude gains G and G are derived by time-delay decoupling formula and small delay approximation theorem,respectively.Compared to G,G is an exact theoretical solution,which means that G is not only more accurate in the region of small delay,but also applies to the region of large delay.Finally,the study of the output amplitude gain G and its resonance behavior are explored.Due to the presence of the potential field delay,a new resonance phenomenon termed“periodic resonance”is discovered,which arises from the periodic matching between the potential field delay and the driving frequency.This resonance phenomenon is analyzed qualitatively and quantitatively,uncovering undiscovered characteristics in previous studies.展开更多
This paper is concerned with the existence of global solutions to the Cauchy problem of a hyperbolic-parabolic coupled system with large initial data. To this end, we first construct its local solutions by the standar...This paper is concerned with the existence of global solutions to the Cauchy problem of a hyperbolic-parabolic coupled system with large initial data. To this end, we first construct its local solutions by the standard iteration technique, then we deduce the basic energy estimate by constructing a convex entropy-entropy flux pair to this system. Moreover, the L∞-estimates and H^2-estimates of solutions are obtained through some delicate estimates. In our results, we do not ask the far fields of the initial data to be equal and the initial data can be arbitrarily large which generalize the result obtained in [7].展开更多
To systematically study the vehicle-bridge coupled dynamic response and its change rule with different parameters, a vehicle model with seven degrees of freedom was built and the total potential energy of vehicle spac...To systematically study the vehicle-bridge coupled dynamic response and its change rule with different parameters, a vehicle model with seven degrees of freedom was built and the total potential energy of vehicle space vibration system was deduced. Considering the stimulation of road roughness, the dynamic response equation of vehicle-bridge coupled system was established in accordance with the elastic system principle of total potential energy with stationary value and the ＂set-in-right-position＂ rule. On the basis of the self-compiled Fortran program and bridge engineering, the dynamic response of long- span continuous girder bridge under vehicle load was studied. This study also included the calculation of vehicle impact coefficient, evaluation of vibration comfort, and analysis of dynamic response parameters. Results show the impact coefficient changes with lane number and is larger than the value calculated by the ＂general code for design of highway bridges and culverts （China）＂. The Dieckmann index of bridge vibration is also related to lane number, and the vibration comfort evaluation is good in normal conditions. The relevant conclusions from parametric analyses have practical significance to dynamic design and daily operation of long-span continuous girder bridges in expressways. Safety and comfort are expected to improve significantly with further control of the vibration of vehicle-bridge system.展开更多
Mathematical simulation of nonlinear physical and abstract systems is a very vital process for predicting the solution behavior of fractional partial differential equations(FPDEs)corresponding to different application...Mathematical simulation of nonlinear physical and abstract systems is a very vital process for predicting the solution behavior of fractional partial differential equations(FPDEs)corresponding to different applications in science and engineering. In this paper, an attractive reliable analytical technique, the conformable residual power series, is implemented for constructing approximate series solutions for a class of nonlinear coupled FPDEs arising in fluid mechanics and fluid flow, which are often designed to demonstrate the behavior of weakly nonlinear and long waves and describe the interaction of shallow water waves. In the proposed technique the n-truncated representation is substituted into the original system and it is assumed the(n-1) conformable derivative of the residuum is zero. This allows us to estimate coefficients of truncation and successively add the subordinate terms in the multiple fractional power series with a rapidly convergent form. The influence, capacity, and feasibility of the presented approach are verified by testing some real-world applications. Finally, highlights and some closing comments are attached.展开更多
The effect of hydrostatic pressure on the vibration dispersion characteristics of fluid-shell coupled structures was studied.Both fluid-loaded cylindrical shells and fluid-filled cylindrical shells were considered.Num...The effect of hydrostatic pressure on the vibration dispersion characteristics of fluid-shell coupled structures was studied.Both fluid-loaded cylindrical shells and fluid-filled cylindrical shells were considered.Numerical analysis was applied to solve the dispersion equations for shells filled with or loaded with fluid at various hydrostatic pressures.The results for external pressure showed that non-dimensional axial wave numbers are nearly independent when the pressure is below the critical level.The influence of internal pressure on wave numbers was found significant for the real branch s=1 and the complex branches of dispersion curves.The presence of internal pressure increased the cut on frequencies for the branch s=1 for high order wave modes.展开更多
In this article, authors study the Cauch problem for a model of hyperbolic-elliptic coupled system derived from the one-dimensional system of the rudiating gas. By considering the initial data as a small disturbances ...In this article, authors study the Cauch problem for a model of hyperbolic-elliptic coupled system derived from the one-dimensional system of the rudiating gas. By considering the initial data as a small disturbances of rarefaction wave of inviscid Burgers equation, the global existence of the solution to the corresponding Cauchy problem and asymptotic stability of rarefaction wave is proved. The analysis is based on a priori estimates and L^2-energy method.展开更多
A novel combined model of the vibration control for the coupled flexiblesystem and its general mathematic description are developed. In presented model, active and passivecontrols as well as force and moment controls ...A novel combined model of the vibration control for the coupled flexiblesystem and its general mathematic description are developed. In presented model, active and passivecontrols as well as force and moment controls are combined into a single unit to achieve theefficient vibration control of the flexible structures by multi-approaches. Considering thecomplexity of the energy transmission in the vibrating system, the transmission channels of thepower flow transmitted into the foundation are discussed, and the general forces and thecorresponding velocities are combined into a single function, respectively. Under the controlstrategy of the minimum power flow, the transmission characteristics of the power flow areinvestigated. From the presented numerical examples, it is obvious that the analytical model iseffective, and both force and moment controls are able to depress vibration energy substantially.展开更多
A system of m (≥2) linear convection-diffusion two-point boundary value problems is examined,where the diffusion term in each equation is multiplied by a small parameterεand the equations are coupled through their c...A system of m (≥2) linear convection-diffusion two-point boundary value problems is examined,where the diffusion term in each equation is multiplied by a small parameterεand the equations are coupled through their convective and reactive terms via matrices B and A respectively.This system is in general singularly perturbed. Unlike the case of a single equation,it does not satisfy a conventional maximum princi- ple.Certain hypotheses are placed on the coupling matrices B and A that ensure exis- tence and uniqueness of a solution to the system and also permit boundary layers in the components of this solution at only one endpoint of the domain;these hypotheses can be regarded as a strong form of diagonal dominance of B.This solution is decomposed into a sum of regular and layer components.Bounds are established on these compo- nents and their derivatives to show explicitly their dependence on the small parameterε.Finally,numerical methods consisting of upwinding on piecewise-uniform Shishkin meshes are proved to yield numerical solutions that are essentially first-order conver- gent,uniformly inε,to the true solution in the discrete maximum norm.Numerical results on Shishkin meshes are presented to support these theoretical bounds.展开更多
A coupled system of three nonlinear oscillators with symmetric couplings is studied.It turns out that there exists a reduced variational equation to the in phase periodic solution of such a coupled system.By the symme...A coupled system of three nonlinear oscillators with symmetric couplings is studied.It turns out that there exists a reduced variational equation to the in phase periodic solution of such a coupled system.By the symmetry one establishes a structural property for the monodromy matrix of the reduced variational equation,which simplifies the computation of multipliers to a great extent.As an application of the above results,a coupled system of three Poincare oscillators is discussed as well.展开更多
The dynamic characteristics of a beam-cable coupled system are investigated using an improved Chebyshev spectral element method in order to observe the effects of adding cables on the beam. The system is modeled as a ...The dynamic characteristics of a beam-cable coupled system are investigated using an improved Chebyshev spectral element method in order to observe the effects of adding cables on the beam. The system is modeled as a double Timoshenko beam system interconnected by discrete springs. Utilizing Chebyshev series expansion and meshing the system according to the locations of its connections, numerical results of the natural frequencies and mode shapes are obtained using only a few elements, and the results are validated by comparing them with the results of a finite-element method. Then the effects of the cable parameters and layout of connections on the natural frequencies and mode shapes of a fixed-pinned beam are studied. The results show that the modes of a beam-cable coupled system can be classified into two types, beam mode and cable mode, according to the dominant deformation. To avoid undesirable vibrations of the cable, its parameters should be controlled in a reasonable range, or the layout of the connections should be optimized.展开更多
The steel turnout is one of the key components in the medium–low-speed maglev line system.However,the vehicle under active control is prone to vehicle–turnout coupled vibration,and thus,it is necessary to identify t...The steel turnout is one of the key components in the medium–low-speed maglev line system.However,the vehicle under active control is prone to vehicle–turnout coupled vibration,and thus,it is necessary to identify the vibration characteristics of this coupled system through field tests.To this end,dynamic performance tests were conducted on a vehicle–turnout coupled system in a medium–low-speed maglev test line.Firstly,the dynamic response data of the coupled system under various operating conditions were obtained.Then,the natural vibration characteristics of the turnout were analysed using the free attenuation method and the finite element method,indicating a good agreement between the simulation results and the measured results;the acceleration response characteristics of the coupled system were analysed in detail,and the ride quality of the vehicle was assessed by Sperling index.Finally,the frequency distribution characteristics of the coupled system were discussed.All these test results could provide references for model validation and optimized design of medium–low-speed maglev transport systems.展开更多
The anaerobic digestion（AD）and microbial electrolysis cell（MEC）coupled system has been proved to be a promising process for biomethane production.In this paper,it was found that by co-cultivating Geobacter with Me...The anaerobic digestion（AD）and microbial electrolysis cell（MEC）coupled system has been proved to be a promising process for biomethane production.In this paper,it was found that by co-cultivating Geobacter with Methanosarcina in an AD–MEC coupled system,methane yield was further increased by 24.1%,achieving to 360.2 m L/g-COD,which was comparable to the theoretical methane yield of an anaerobic digester.With the presence of Geobacter,the maximum chemical oxygen demand（COD）removal rate（216.8 mg COD/（L·hr））and current density（304.3 A/m3）were both increased by 1.3 and 1.8 fold compared to the previous study without Geobacter,resulting in overall energy efficiency reaching up to 74.6%.Community analysis demonstrated that Geobacter and Methanosarcina could coexist together in the biofilm,and the electrochemical activities of both were confirmed by cyclic voltammetry.Our study observed that the carbon dioxide content in total gas generated from the AD reactor with Geobacter was only half of that generated from the same reactor without Geobacter,suggesting that Methanosarcina may obtain the electron transferred from Geobacter for the reduction of carbon dioxide to methane.Taken together,Geobacter not only can improve the performance of the MEC system,but also can enhance methane production.展开更多
This paper presents an energy principle, zero different principle of coupledsystems in photoelasticity, from which the potential energy, the complementary energy,generalized potential energy and generalized complemen...This paper presents an energy principle, zero different principle of coupledsystems in photoelasticity, from which the potential energy, the complementary energy,generalized potential energy and generalized complementary energy variationalprinciples of the coupled systems in photoelasticity are derived What is called the coupled systems means that two deformational bodies, forwhich figures, sizes,loads and boundary conditions are the same and they are all inactual states but they are made of different materials.Prototype body and model body in photoelasticity are essentially the coupledsystems, therefore the above principles become the theoretical basis of defining theinflunce of Poissons ratio v on accuracy of the frozen-stress method.展开更多
This paper employs the integral-averaged method of thickness to approximate the periodical flows in a piezoelectric micropump, with a shallow water equation including nonlinearity and viscous damp presented to charact...This paper employs the integral-averaged method of thickness to approximate the periodical flows in a piezoelectric micropump, with a shallow water equation including nonlinearity and viscous damp presented to characterize the flows in micropump. The finite element method is used to obtain a matrix equation of fluid pressure. The fluid pressure equation is combined with the vibration equation of a silicon diaphragm to construct a liquid-solid coupled equation for reflecting the interaction between solid diaphragm and fluid motion in a micropump. Numerical results of a mode analysis of the coupled system indicate that the natural frequencies of the coupled system are much lower than those of the non-coupled system. The influence of additional mass and viscous damp of fluid on the natural frequencies of the coupled system is more significant as the pump thickness is small. It is found that the vibration shape functions of silicon diaphragm of the coupled system are almost the same as those of the non-coupled system. This paper also gives the first-order amplitude-frequency relationship of the silicon diaphragm, which is necessary for the flow-rate-frequency analysis of a micropump.展开更多
We establish the existence of positive periodic solutions of the second-order singular coupled systems{x′′＋ p_1（t）x′＋ q_1（t）x = f_1（t, y（t）） ＋ c_1（t）,y′′＋ p_2（t）y′＋ q_2（t）y = f_2（t, x（t）） ...We establish the existence of positive periodic solutions of the second-order singular coupled systems{x′′＋ p_1（t）x′＋ q_1（t）x = f_1（t, y（t）） ＋ c_1（t）,y′′＋ p_2（t）y′＋ q_2（t）y = f_2（t, x（t）） ＋ c_2（t）,where pi, qi, ci ∈ C（R/T Z; R）, i = 1, 2; f_1, f_2 ∈ C（R/T Z ×（0, ∞）, R） and may be singular near the zero. The proof relies on Schauder＇s fixed point theorem and anti-maximum principle.Our main results generalize and improve those available in the literature.展开更多
Coupled system of multilayer dynamics of fluids in porous media is to describe the history of oil-gas transport and accumulation in basin evolution.It is of great value in rational evaluation of prospecting and exploi...Coupled system of multilayer dynamics of fluids in porous media is to describe the history of oil-gas transport and accumulation in basin evolution.It is of great value in rational evaluation of prospecting and exploiting oil-gas resources.The mathematical model can be described as a coupled system of nonlinear partial differential equations with moving boundary values.The upwind finite difference schemes applicable to parallel arithmetic are put forward and two-dimensional and three-dimensional schemes are used to form a complete set.Some techniques,such as change of variables,calculus of variations, multiplicative commutation rule of difference operators,decomposition of high order difference operators and prior estimates,are adopted.The estimates in l~2 norm are derived to determine the error in the approximate solution.This method was already applied to the numerical simulation of migration-accumulation of oil resources.展开更多
Nonlinear coupling dynamics between a spring-mass system and a finite amplitude sloshing system with liquid in a cylindrical tank is investigated. Based on a group of nonlinear coupling equations of six degrees of fre...Nonlinear coupling dynamics between a spring-mass system and a finite amplitude sloshing system with liquid in a cylindrical tank is investigated. Based on a group of nonlinear coupling equations of six degrees of freedoms, analytical formulae of forces and moments of the liquid large amplitude sloshing were obtained. Nonlinearity of the forces and moments of the sloshing was induced by integrating on final configuration of liquid sloshing and the nonlinear terms in the liquid pressure formula. The symmetry between the formula of Ox and Oy direction proves that the derivation is correct. According to the coupled mechanism, the formulae are available in other liquid-solid coupled systems. Simulations and corresponding experimental results arecompared. It is shown that the forces and moments formulae by integrating on the final sloshing configuration are more reasonable. The omitted high-dimensional modal bases and high-order nonlinear terms and the complexity of sloshing damping are main sources of errors.展开更多
This paper considers a two-phase free boundary problem for coupled system including one parabolic equation and two elliptic equations. The problem comes from the discussion of a growth model of self-maintaining protoc...This paper considers a two-phase free boundary problem for coupled system including one parabolic equation and two elliptic equations. The problem comes from the discussion of a growth model of self-maintaining protocell in multidimensional case. The local classical solution of the problem with free boundary (?) y = g(x,t) between two domains is being seeked. The local existence and uniqueness of the problem will be proved in multidimensional case.展开更多
基金Project(52078501)supported by the National Natural Science Foundation of ChinaProject(2022-Major-14)supported by the Science and Technology Research and Development Program Project of China Railway Group LimitedProject(2023ZZTS0342)supported by the Fundamental Research Funds for the Central Universities,China。
文摘Subgrade settlement is a common issue in soil ground within earthquake-prone regions,posing a threat to the safe operation of train-slab track coupled system(TSCS)in high-speed railways(HSRs).This study aims to analyze the mechanical behavior evolution of TSCS under subgrade settlement and earthquake excitation.The refined numerical model of slab track under subgrade differential settlement is established.The short settlement wavelength of 10 m causes the separation between the base and subgrade.The dynamic model of TSCS under subgrade settlement and earthquake excitation is developed.The dynamic response of TSCS exhibits more pronounced fluctuations under the combined effects of subgrade settlement and earthquake excitation than under the effects of settlement or earthquake alone.The evaluation indexes for the running safety of train on slab track under different settlement wavelengths exhibit varying degrees of increase with settlement amplitude and are particularly sensitive to the short settlement wavelength of 10 m.The wheel unloading rate and derailment coefficient of TSCS increase with earthquake intensity.Under the settlement wavelength of 10 m and amplitude of 20 mm,the wheel unloading rate of TSCS exceeds the allowable limit when the earthquake intensity exceeds 0.17g,and the derailment coefficient exceeds the allowable limit when the earthquake intensity surpasses 0.29g.
基金supported by the National Natural Science Foundation of China,Grant No.12375006。
文摘In this paper,we investigate the(2+1)-dimensional three-component long-wave-short-wave resonance interaction system,which describes complex systems and nonlinear wave phenomena in physics.By employing the Hirota bilinear method,we derive the general nondegenerate N-soliton solution of the system,where each short-wave component contains N arbitrary functions of the independent variable y.The presence of these arbitrary functions in the analytical solution enables the construction of a wide range of nondegenerate soliton types.Finally,we illustrate the structural features of several novel nondegenerate solitons,including M-shaped,multiple double-hump,and sawtooth double-striped solitons,as well as interactions between nondegenerate solitons,such as dromion-like solitons and solitoffs,with the aid of figures.
基金supported by the Natural Science Foundation of Sichuan Province,China(Youth Science Foundation)(Grant No.2022NSFSC1952).
文摘The collective dynamic of a fractional-order globally coupled system with time delays and fluctuating frequency is investigated.The power-law memory of the system is characterized using the Caputo fractional derivative operator.Additionally,time delays in the potential field force and coupling force transmission are both considered.Firstly,based on the delay decoupling formula,combined with statistical mean method and the fractional-order Shapiro–Loginov formula,the“statistic synchronization”among particles is obtained,revealing the statistical equivalence between the mean field behavior of the system and the behavior of individual particles.Due to the existence of the coupling delay,the impact of the coupling force on synchronization exhibits non-monotonic,which is different from the previous monotonic effects.Then,two kinds of theoretical expression of output amplitude gains G and G are derived by time-delay decoupling formula and small delay approximation theorem,respectively.Compared to G,G is an exact theoretical solution,which means that G is not only more accurate in the region of small delay,but also applies to the region of large delay.Finally,the study of the output amplitude gain G and its resonance behavior are explored.Due to the presence of the potential field delay,a new resonance phenomenon termed“periodic resonance”is discovered,which arises from the periodic matching between the potential field delay and the driving frequency.This resonance phenomenon is analyzed qualitatively and quantitatively,uncovering undiscovered characteristics in previous studies.
基金Huijiang Zhao was supported by the National Natural Science Foundation of China (10871151)Changjiang Zhu was supported by the National Natural Science Foundation of China (10625105 and 10431060)the Program for New Century Excellent Talentsin University (NCET-04-0745)
文摘This paper is concerned with the existence of global solutions to the Cauchy problem of a hyperbolic-parabolic coupled system with large initial data. To this end, we first construct its local solutions by the standard iteration technique, then we deduce the basic energy estimate by constructing a convex entropy-entropy flux pair to this system. Moreover, the L∞-estimates and H^2-estimates of solutions are obtained through some delicate estimates. In our results, we do not ask the far fields of the initial data to be equal and the initial data can be arbitrarily large which generalize the result obtained in [7].
基金provided by the National Natural Science Foundation of China (51378504)Funding Project of Traffic Science and Technology Program of Hunan Province (201022)
文摘To systematically study the vehicle-bridge coupled dynamic response and its change rule with different parameters, a vehicle model with seven degrees of freedom was built and the total potential energy of vehicle space vibration system was deduced. Considering the stimulation of road roughness, the dynamic response equation of vehicle-bridge coupled system was established in accordance with the elastic system principle of total potential energy with stationary value and the ＂set-in-right-position＂ rule. On the basis of the self-compiled Fortran program and bridge engineering, the dynamic response of long- span continuous girder bridge under vehicle load was studied. This study also included the calculation of vehicle impact coefficient, evaluation of vibration comfort, and analysis of dynamic response parameters. Results show the impact coefficient changes with lane number and is larger than the value calculated by the ＂general code for design of highway bridges and culverts （China）＂. The Dieckmann index of bridge vibration is also related to lane number, and the vibration comfort evaluation is good in normal conditions. The relevant conclusions from parametric analyses have practical significance to dynamic design and daily operation of long-span continuous girder bridges in expressways. Safety and comfort are expected to improve significantly with further control of the vibration of vehicle-bridge system.
基金Authors gratefully acknowledge Ajman University for providing facilities for our research under Grant Ref.No.2019-IRG-HBS-11.
文摘Mathematical simulation of nonlinear physical and abstract systems is a very vital process for predicting the solution behavior of fractional partial differential equations(FPDEs)corresponding to different applications in science and engineering. In this paper, an attractive reliable analytical technique, the conformable residual power series, is implemented for constructing approximate series solutions for a class of nonlinear coupled FPDEs arising in fluid mechanics and fluid flow, which are often designed to demonstrate the behavior of weakly nonlinear and long waves and describe the interaction of shallow water waves. In the proposed technique the n-truncated representation is substituted into the original system and it is assumed the(n-1) conformable derivative of the residuum is zero. This allows us to estimate coefficients of truncation and successively add the subordinate terms in the multiple fractional power series with a rapidly convergent form. The influence, capacity, and feasibility of the presented approach are verified by testing some real-world applications. Finally, highlights and some closing comments are attached.
文摘The effect of hydrostatic pressure on the vibration dispersion characteristics of fluid-shell coupled structures was studied.Both fluid-loaded cylindrical shells and fluid-filled cylindrical shells were considered.Numerical analysis was applied to solve the dispersion equations for shells filled with or loaded with fluid at various hydrostatic pressures.The results for external pressure showed that non-dimensional axial wave numbers are nearly independent when the pressure is below the critical level.The influence of internal pressure on wave numbers was found significant for the real branch s=1 and the complex branches of dispersion curves.The presence of internal pressure increased the cut on frequencies for the branch s=1 for high order wave modes.
基金The research was supported by three grants from the Key Project of the Natural Science Foundation of China (10431060)the Key Project of Chinese Ministry of Education (104128)the South-Central University For Nationalities Natural Science Foundation of China (YZY05008)
文摘In this article, authors study the Cauch problem for a model of hyperbolic-elliptic coupled system derived from the one-dimensional system of the rudiating gas. By considering the initial data as a small disturbances of rarefaction wave of inviscid Burgers equation, the global existence of the solution to the corresponding Cauchy problem and asymptotic stability of rarefaction wave is proved. The analysis is based on a priori estimates and L^2-energy method.
文摘A novel combined model of the vibration control for the coupled flexiblesystem and its general mathematic description are developed. In presented model, active and passivecontrols as well as force and moment controls are combined into a single unit to achieve theefficient vibration control of the flexible structures by multi-approaches. Considering thecomplexity of the energy transmission in the vibrating system, the transmission channels of thepower flow transmitted into the foundation are discussed, and the general forces and thecorresponding velocities are combined into a single function, respectively. Under the controlstrategy of the minimum power flow, the transmission characteristics of the power flow areinvestigated. From the presented numerical examples, it is obvious that the analytical model iseffective, and both force and moment controls are able to depress vibration energy substantially.
文摘A system of m (≥2) linear convection-diffusion two-point boundary value problems is examined,where the diffusion term in each equation is multiplied by a small parameterεand the equations are coupled through their convective and reactive terms via matrices B and A respectively.This system is in general singularly perturbed. Unlike the case of a single equation,it does not satisfy a conventional maximum princi- ple.Certain hypotheses are placed on the coupling matrices B and A that ensure exis- tence and uniqueness of a solution to the system and also permit boundary layers in the components of this solution at only one endpoint of the domain;these hypotheses can be regarded as a strong form of diagonal dominance of B.This solution is decomposed into a sum of regular and layer components.Bounds are established on these compo- nents and their derivatives to show explicitly their dependence on the small parameterε.Finally,numerical methods consisting of upwinding on piecewise-uniform Shishkin meshes are proved to yield numerical solutions that are essentially first-order conver- gent,uniformly inε,to the true solution in the discrete maximum norm.Numerical results on Shishkin meshes are presented to support these theoretical bounds.
文摘A coupled system of three nonlinear oscillators with symmetric couplings is studied.It turns out that there exists a reduced variational equation to the in phase periodic solution of such a coupled system.By the symmetry one establishes a structural property for the monodromy matrix of the reduced variational equation,which simplifies the computation of multipliers to a great extent.As an application of the above results,a coupled system of three Poincare oscillators is discussed as well.
基金supported by the National Basic Research Program of China (Grant 2013CB733004)
文摘The dynamic characteristics of a beam-cable coupled system are investigated using an improved Chebyshev spectral element method in order to observe the effects of adding cables on the beam. The system is modeled as a double Timoshenko beam system interconnected by discrete springs. Utilizing Chebyshev series expansion and meshing the system according to the locations of its connections, numerical results of the natural frequencies and mode shapes are obtained using only a few elements, and the results are validated by comparing them with the results of a finite-element method. Then the effects of the cable parameters and layout of connections on the natural frequencies and mode shapes of a fixed-pinned beam are studied. The results show that the modes of a beam-cable coupled system can be classified into two types, beam mode and cable mode, according to the dominant deformation. To avoid undesirable vibrations of the cable, its parameters should be controlled in a reasonable range, or the layout of the connections should be optimized.
基金This work was supported by the National Natural Science Foundation of China(Grant No.51875483)the Independently Funded Research Project of State Key Laboratory of Traction Power(Grant Nos.2020TPL-T01 and 2020TPL-T04).
文摘The steel turnout is one of the key components in the medium–low-speed maglev line system.However,the vehicle under active control is prone to vehicle–turnout coupled vibration,and thus,it is necessary to identify the vibration characteristics of this coupled system through field tests.To this end,dynamic performance tests were conducted on a vehicle–turnout coupled system in a medium–low-speed maglev test line.Firstly,the dynamic response data of the coupled system under various operating conditions were obtained.Then,the natural vibration characteristics of the turnout were analysed using the free attenuation method and the finite element method,indicating a good agreement between the simulation results and the measured results;the acceleration response characteristics of the coupled system were analysed in detail,and the ride quality of the vehicle was assessed by Sperling index.Finally,the frequency distribution characteristics of the coupled system were discussed.All these test results could provide references for model validation and optimized design of medium–low-speed maglev transport systems.
基金supported by the National Natural Science Foundation of China(Nos.31270166,31300116 and 51408580)the Chinese Academy of Sciences foundation(Nos.Y4C5011100 and KLCAS-2013-03)
文摘The anaerobic digestion（AD）and microbial electrolysis cell（MEC）coupled system has been proved to be a promising process for biomethane production.In this paper,it was found that by co-cultivating Geobacter with Methanosarcina in an AD–MEC coupled system,methane yield was further increased by 24.1%,achieving to 360.2 m L/g-COD,which was comparable to the theoretical methane yield of an anaerobic digester.With the presence of Geobacter,the maximum chemical oxygen demand（COD）removal rate（216.8 mg COD/（L·hr））and current density（304.3 A/m3）were both increased by 1.3 and 1.8 fold compared to the previous study without Geobacter,resulting in overall energy efficiency reaching up to 74.6%.Community analysis demonstrated that Geobacter and Methanosarcina could coexist together in the biofilm,and the electrochemical activities of both were confirmed by cyclic voltammetry.Our study observed that the carbon dioxide content in total gas generated from the AD reactor with Geobacter was only half of that generated from the same reactor without Geobacter,suggesting that Methanosarcina may obtain the electron transferred from Geobacter for the reduction of carbon dioxide to methane.Taken together,Geobacter not only can improve the performance of the MEC system,but also can enhance methane production.
文摘This paper presents an energy principle, zero different principle of coupledsystems in photoelasticity, from which the potential energy, the complementary energy,generalized potential energy and generalized complementary energy variationalprinciples of the coupled systems in photoelasticity are derived What is called the coupled systems means that two deformational bodies, forwhich figures, sizes,loads and boundary conditions are the same and they are all inactual states but they are made of different materials.Prototype body and model body in photoelasticity are essentially the coupledsystems, therefore the above principles become the theoretical basis of defining theinflunce of Poissons ratio v on accuracy of the frozen-stress method.
基金Project supported by the National Natural Science Foundation of China (No. 10472036).
文摘This paper employs the integral-averaged method of thickness to approximate the periodical flows in a piezoelectric micropump, with a shallow water equation including nonlinearity and viscous damp presented to characterize the flows in micropump. The finite element method is used to obtain a matrix equation of fluid pressure. The fluid pressure equation is combined with the vibration equation of a silicon diaphragm to construct a liquid-solid coupled equation for reflecting the interaction between solid diaphragm and fluid motion in a micropump. Numerical results of a mode analysis of the coupled system indicate that the natural frequencies of the coupled system are much lower than those of the non-coupled system. The influence of additional mass and viscous damp of fluid on the natural frequencies of the coupled system is more significant as the pump thickness is small. It is found that the vibration shape functions of silicon diaphragm of the coupled system are almost the same as those of the non-coupled system. This paper also gives the first-order amplitude-frequency relationship of the silicon diaphragm, which is necessary for the flow-rate-frequency analysis of a micropump.
基金Supported by the Scientific Research Funds for the Ningxia Universities(Grant No.NGY2015141)
文摘We establish the existence of positive periodic solutions of the second-order singular coupled systems{x′′＋ p_1（t）x′＋ q_1（t）x = f_1（t, y（t）） ＋ c_1（t）,y′′＋ p_2（t）y′＋ q_2（t）y = f_2（t, x（t）） ＋ c_2（t）,where pi, qi, ci ∈ C（R/T Z; R）, i = 1, 2; f_1, f_2 ∈ C（R/T Z ×（0, ∞）, R） and may be singular near the zero. The proof relies on Schauder＇s fixed point theorem and anti-maximum principle.Our main results generalize and improve those available in the literature.
基金supported by the Major State BasicResearch Program of China(19990328)the National Tackling Key Problem Programs(20050200069)+4 种基金the National Natural Science Foundation of China(1077112410372052)the Doctorate Foundation of the Ministryof Education of China(20030422047)Shandong Provance Natural Science Foundation(2R2009AQ12)the Independent Innovation Foundation of Shandong University(2010TS031)
文摘Coupled system of multilayer dynamics of fluids in porous media is to describe the history of oil-gas transport and accumulation in basin evolution.It is of great value in rational evaluation of prospecting and exploiting oil-gas resources.The mathematical model can be described as a coupled system of nonlinear partial differential equations with moving boundary values.The upwind finite difference schemes applicable to parallel arithmetic are put forward and two-dimensional and three-dimensional schemes are used to form a complete set.Some techniques,such as change of variables,calculus of variations, multiplicative commutation rule of difference operators,decomposition of high order difference operators and prior estimates,are adopted.The estimates in l~2 norm are derived to determine the error in the approximate solution.This method was already applied to the numerical simulation of migration-accumulation of oil resources.
文摘Nonlinear coupling dynamics between a spring-mass system and a finite amplitude sloshing system with liquid in a cylindrical tank is investigated. Based on a group of nonlinear coupling equations of six degrees of freedoms, analytical formulae of forces and moments of the liquid large amplitude sloshing were obtained. Nonlinearity of the forces and moments of the sloshing was induced by integrating on final configuration of liquid sloshing and the nonlinear terms in the liquid pressure formula. The symmetry between the formula of Ox and Oy direction proves that the derivation is correct. According to the coupled mechanism, the formulae are available in other liquid-solid coupled systems. Simulations and corresponding experimental results arecompared. It is shown that the forces and moments formulae by integrating on the final sloshing configuration are more reasonable. The omitted high-dimensional modal bases and high-order nonlinear terms and the complexity of sloshing damping are main sources of errors.
基金The project is supported by National Natural Science Foundation of China(10371045)Guangdong Provincial Natural Science Foundation of China(000671)National Natural Science Foundation of China(10426015).
文摘This paper considers a two-phase free boundary problem for coupled system including one parabolic equation and two elliptic equations. The problem comes from the discussion of a growth model of self-maintaining protocell in multidimensional case. The local classical solution of the problem with free boundary (?) y = g(x,t) between two domains is being seeked. The local existence and uniqueness of the problem will be proved in multidimensional case.
