The singularities, oscillatory performances and the contributing factors to the 3-＇D translating-pulsating source Green function of deep-water Havelock form which consists of a local disturbance part and a far-field ...The singularities, oscillatory performances and the contributing factors to the 3-＇D translating-pulsating source Green function of deep-water Havelock form which consists of a local disturbance part and a far-field wave-like part, are analyzed systematically. Relative numerical integral methods about the two parts are presented in this paper. An improved method based on LOBATTO rule is used to eliminate singularities caused respectively by infinite discontinuity and jump discontinuous node from the local disturbance part function, which makes the improvement of calculation efficiency and accuracy possible. And variable substitution is applied to remove the singularity existing at the end of the integral interval of the far-field wave-like part function. Two auxiliary techniques such as valid interval calculation and local refinement of integral steps technique in narrow zones near false singularities are applied so as to avoid unnecessary integration of invalid interval and improve integral accordance. Numerical test results have proved the efficiency and accuracy in these integral methods that thus can be applied to calculate hydrodynamic performance of floating structures moving in waves.展开更多
As children mature, bike products for children in the market develop at the same time, and the conditions are frequently updated. Certain problems occur when using a bike, such as cycle overlapping, repeating function...As children mature, bike products for children in the market develop at the same time, and the conditions are frequently updated. Certain problems occur when using a bike, such as cycle overlapping, repeating function, and short life cycle, which go against the principles of energy conservation and the environmental protection intensive design concept. In this paper, a rational multi-function method of design through functional superposition, transformation, and technical implementation is proposed. An organic combination of frog-style scooter and children’s tricycle is developed using the multi-function method. From the ergonomic perspective, the paper elaborates on the body size of children aged 5 to 12 and effectively extracts data for a multi-function children’s bike, which can be used for gliding and riding. By inverting the body, parts can be interchanged between the handles and the pedals of the bike. Finally, the paper provides a detailed analysis of the components and structural design, body material, and processing technology of the bike. The study of Industrial Product Innovation Design provides an effective design method to solve the bicycle problems, extends the function problems, improves the product market situation, and enhances the energy saving feature while implementing intensive product development effectively at the same time.展开更多
The singularities and oscillatory performance of translating-pulsating source Green＇s function in Bessho form were analyzed. Relative numerical integration methods such as Gaussian quadrature rule, variable substitut...The singularities and oscillatory performance of translating-pulsating source Green＇s function in Bessho form were analyzed. Relative numerical integration methods such as Gaussian quadrature rule, variable substitution method （VSM）, and steepest descent integration method （SDIM） were used to evaluate this type of Green＇s function. For SDIM, the complex domain was restricted only on the 0-plane. Meanwhile, the integral along the real axis was computed by use of the VSM to avoid the complication of a numerical search of the steepest descent line. Furthermore, the steepest descent line was represented by the B-spline function. Based on this representation, a new self-compatible integration method corresponding to parametric t was established. The numerical method was validated through comparison with other existing results, and was shown to be efficient and reliable in the calculation of the velocity potentials for the 3D seakeeping and hydrodynamic performance of floating struc- tures moving in waves.展开更多
The possible exotic nuclear properties in the neutron-rich Ca,Ni,Zr,and Sn isotopes are examined with the continuum Skyrme Hartree-Fock-Bogoliubov theory in the framework of the Green’s function method.The pairing co...The possible exotic nuclear properties in the neutron-rich Ca,Ni,Zr,and Sn isotopes are examined with the continuum Skyrme Hartree-Fock-Bogoliubov theory in the framework of the Green’s function method.The pairing correlation,the couplings with the continuum,and the blocking effects for the unpaired nucleon in odd-A nuclei are properly treated.The Skyrme interaction SLy4 is adopted for the ph channel and the density-dependentinteraction is adopted for the pp chan-nel,which well reproduce the experimental two-neutron separation energies S_(2n)and one-neutron separation energies Sn.It is found that the criterion S_(n)>0 predicts a neutron drip line with neutron numbers much smaller than those for S_(2n)>0.Owing to the unpaired odd neutron,the neutron pairing energies−E_(pair)in odd-A nuclei are much lower than those in the neighbor-ing even-even nuclei.By investigating the single-particle structures,the possible halo structures in the neutron-rich Ca,Ni,and Sn isotopes are predicted,where sharp increases in the root-mean-square(rms)radii with significant deviations from the traditional rA^(1∕3)rule and diffuse spatial density distributions are observed.Analyzing the contributions of various partial waves to the total neutron densityρlj(r)∕ρ(r)reveals that the orbitals located around the Fermi surface-particularly those with small angular momenta-significantly affect the extended nuclear density and large rms radii.The number of neutrons Nλ(N_(0))occupying above the Fermi surfacen(continuum threshold)is discussed,whose evolution as a function of the mass number A in each isotope is consistent with that of the pairing energy,supporting the key role of the pairing correlation in halo phenomena.展开更多
Understanding the effects of point liquid loading on transversely isotropic poroelastic media is crucial for advancing geomechanics and biomechanics, where precise modeling of fluid-structure interactions is essential...Understanding the effects of point liquid loading on transversely isotropic poroelastic media is crucial for advancing geomechanics and biomechanics, where precise modeling of fluid-structure interactions is essential. This paper presents a comprehensive analysis of infinite transversely isotropic poroelasticity under a fluid source, based on Biot's theory, aiming to uncover new and previously unexplored insights in the literature. We begin our study by deriving a general solution for fluid-saturated, transversely isotropic poroelastic materials in terms of harmonic functions that satisfy sixth-order homogeneous partial differential equations, using potential theory and Almansi's theorem. Based on these general solutions and potential functions, we construct a Green's function for a point fluid source, introducing three new harmonic functions with undetermined constants. These constants are determined by enforcing continuity and equilibrium conditions. Substituting these into the general solution yields fundamental solutions for poroelasticity that provide crucial support for a wide range of project problems. Numerical results and comparisons with existing literature are provided to illustrate physical mechanisms through contour plots. Our observations reveal that all components tend to zero in the far field and become singular at the concentrated source. Additionally, the contours exhibit rapid changes near the point fluid source but display gradual variations at a distance from it. These findings highlight the intricate behavior of the system under point liquid loading, offering valuable insights for further research and practical applications.展开更多
The numerical simulation of the fluid flow and the flexible rod(s)interaction is more complicated and has lower efficiency due to the high computational cost.In this paper,a semi-resolved model coupling the computatio...The numerical simulation of the fluid flow and the flexible rod(s)interaction is more complicated and has lower efficiency due to the high computational cost.In this paper,a semi-resolved model coupling the computational fluid dynamics and the flexible rod dynamics is proposed using a two-way domain expansion method.The gov-erning equations of the flexible rod dynamics are discretized and solved by the finite element method,and the fluid flow is simulated by the finite volume method.The interaction between fluids and solid rods is modeled by introducing body force terms into the momentum equations.Referred to the traditional semi-resolved numerical model,an anisotropic Gaussian kernel function method is proposed to specify the interactive forces between flu-ids and solid bodies for non-circle rod cross-sections.A benchmark of the flow passing around a single flexible plate with a rectangular cross-section is used to validate the algorithm.Focused on the engineering applications,a test case of a finite patch of cylinders is implemented to validate the accuracy and efficiency of the coupled model.展开更多
In this paper, the Adomian decomposition method with Green’s function (Standard Adomian and Modified Technique) is applied to solve linear and nonlinear tenth-order boundary value problems with boundary conditions de...In this paper, the Adomian decomposition method with Green’s function (Standard Adomian and Modified Technique) is applied to solve linear and nonlinear tenth-order boundary value problems with boundary conditions defined at any order derivatives. The numerical results obtained with a small amount of computation are compared with the exact solutions to show the efficiency of the method. The results show that the decomposition method is of high accuracy, more convenient and efficient for solving high-order boundary value problems.展开更多
We study the nonlinear parabolic equations for travelling wave solutions of Burger’s equations. The purpose of the present work is to study various types of Burger’s equations describing waves and those are based on...We study the nonlinear parabolic equations for travelling wave solutions of Burger’s equations. The purpose of the present work is to study various types of Burger’s equations describing waves and those are based on nonlinear equations. We focus on to describe the analytic solution in the special pattern of travelling wave solutions using tan-cot function method. We discuss about inviscid and viscous version of Burger’s equation for fluid flow and investigate the effects of internal friction of a fluid via Reynolds number. By changing the velocity amplitude, the nature of flows with shock wave and disturbance are observed. For numerical solutions, the Crank-Nicolson scheme is introduced to establish the wave solutions.展开更多
This study evaluates the effectiveness of a new technique that transforms doma in integrals into boundary integrals that is applicable to the boundary element method.Si mulations were conducted in which two-dimensiona...This study evaluates the effectiveness of a new technique that transforms doma in integrals into boundary integrals that is applicable to the boundary element method.Si mulations were conducted in which two-dimensional surfaces were approximated by inter polation using radial basis functions with full and compact supports.Examples involving Poisson’s equation are presented using the boundary element method and the proposed te chnique with compact radial basis functions.The advantages and the disadvantages are e xamined through simulations.The effects of internal poles,the boundary mesh refinemen t and the value for the support of the radial basis functions on performance are assessed.展开更多
The dynamic stiffness method combined with the Fourier transform is utilized to derive the in-plane Green’s functions for inclined and uniformly distributed loads in a multi-layered transversely isotropic（TI）half-s...The dynamic stiffness method combined with the Fourier transform is utilized to derive the in-plane Green’s functions for inclined and uniformly distributed loads in a multi-layered transversely isotropic（TI）half-space.The loaded layer is fixed to obtain solutions restricted in it and the corresponding reactions forces,which are then applied to the total system with the opposite sign.By adding solutions restricted in the loaded layer to solutions from the reaction forces,the global solutions in the wavenumber domain are obtained,and the dynamic Green’s functions in the space domain are recovered by the inverse Fourier transform.The presented formulations can be reduced to the isotropic case developed by Wolf（1985）,and are further verified by comparisons with existing solutions in a uniform isotropic as well as a layered TI halfspace subjected to horizontally distributed loads which are special cases of the more general problem addressed.The deduced Green’s functions,in conjunction with boundary element methods,will lead to significant advances in the investigation of a variety of wave scattering,wave radiation and soil-structure interaction problems in a layered TI site.Selected numerical results are given to investigate the influence of material anisotropy,frequency of excitation,inclination angle and layered on the responses of displacement and stress,and some conclusions are drawn.展开更多
The accurate analyses for a plate fin heat sink with the ability to control the temperature of the avionics devices within a pre-set controllable temperature range are required both in the process of circuit design an...The accurate analyses for a plate fin heat sink with the ability to control the temperature of the avionics devices within a pre-set controllable temperature range are required both in the process of circuit design and for the real-time temperature monitoring purposes. In order to provide an insight into the behavior of the temperature of a plate fin heat sink subjected non-uniform heat density on the surfaces, it is necessary to obtain accurate analytical solutions yielding explicit formulas relating the dissipated power to the temperature rise at any point of avionics devices. This paper presents a method for thermal simulation of a plate fin heat sink using an analytical solution of the three-dimensional heat equation resulting from an appropriate plate fin heat sink transient thermal model. The entire solution methodology is illustrated in detail on the particular examples of the plate fin heat sink subjected non-uniform heat density on the surfaces. The transient temperature profiles are obtained for different positions at the surface of the plate fin heat sink. The analytical results are compared with measurements made on the surface of the cold plate and it is found that they are in good agreement with an error of less than 3 K.展开更多
A new algorithm is presented for solving Troesch’s problem. The numerical scheme based on the sinc-collocation technique is deduced. The equation is reduced to systems of nonlinear algebraic equations. Some numerical...A new algorithm is presented for solving Troesch’s problem. The numerical scheme based on the sinc-collocation technique is deduced. The equation is reduced to systems of nonlinear algebraic equations. Some numerical experiments are made. Compared with the modified homotopy perturbation technique (MHP), the variational iteration method and the Adomian decomposition method. It is shown that the sinc-collocation method yields better results.展开更多
In heating, ventilating and air-conditioning （HVAC） systems, there exist severe nonlinearity, time-varying nature, disturbances and uncertainties. A new predictive functional control based on Takagi-Sugeno （T-S） f...In heating, ventilating and air-conditioning （HVAC） systems, there exist severe nonlinearity, time-varying nature, disturbances and uncertainties. A new predictive functional control based on Takagi-Sugeno （T-S） fuzzy model was proposed to control HVAC systems. The T-S fuzzy model of stabilized controlled process was obtained using the least squares method, then on the basis of global linear predictive model from T-S fuzzy model, the process was controlled by the predictive functional controller. Especially the feedback regulation part was developed to compensate uncertainties of fuzzy predictive model. Finally simulation test results in HVAC systems control applications showed that the proposed fuzzy model predictive functional control improves tracking effect and robustness. Compared with the conventional PID controller, this control strategy has the advantages of less overshoot and shorter setting time, etc.展开更多
To reduce computational costs, an improved form of the frequency domain boundary element method（BEM） is proposed for two-dimensional radiation and propagation acoustic problems in a subsonic uniform flow with arbitr...To reduce computational costs, an improved form of the frequency domain boundary element method（BEM） is proposed for two-dimensional radiation and propagation acoustic problems in a subsonic uniform flow with arbitrary orientation. The boundary integral equation（BIE） representation solves the two-dimensional convected Helmholtz equation（CHE） and its fundamental solution, which must satisfy a new Sommerfeld radiation condition（SRC） in the physical space. In order to facilitate conventional formulations, the variables of the advanced form are expressed only in terms of the acoustic pressure as well as its normal and tangential derivatives, and their multiplication operators are based on the convected Green＇s kernel and its modified derivative. The proposed approach significantly reduces the CPU times of classical computational codes for modeling acoustic domains with arbitrary mean flow. It is validated by a comparison with the analytical solutions for the sound radiation problems of monopole,dipole and quadrupole sources in the presence of a subsonic uniform flow with arbitrary orientation.展开更多
Geometrically nonlinear oscillations are investigated on sigmoid functionally graded material （S-FGM） plates with a longitudinal speed. The material properties of the plates obey a sigmoid distribution rule along th...Geometrically nonlinear oscillations are investigated on sigmoid functionally graded material （S-FGM） plates with a longitudinal speed. The material properties of the plates obey a sigmoid distribution rule along the thickness direction. Based on the D＇Alembert＇s principle, a nonlinear equation of motion is derived for the moving S-FGM plates, where the von K^rm^n nonlinear plate theory is adopted. Utilizing the Galerkin method, the equation of motion is discretized and solved via the method of harmonic bal- ance. The approximate analytical solutions are validated through the adaptive step-size fourth-order Runge-Kutta method. Besides, the stability of the steady-state solutions is examined. The results reveal that the mode interaction behavior can happen between the first two modes of the moving S-FGM plates, leading to a complex nonlinear frequency response. It is further found that the power-law index, the longitudinal speed, the exci- tation amplitude, and the in-plane pretension force can significantly affect the nonlinear frequency-response characteristics of longitudinally traveling S-FGM plates.展开更多
The extended F-expansion method or mapping method is used to construct exact solutions for the coupled KleinGordon Schr/Sdinger equations （K-G-S equations） by the aid of the symbolic computation system Mathematica. ...The extended F-expansion method or mapping method is used to construct exact solutions for the coupled KleinGordon Schr/Sdinger equations （K-G-S equations） by the aid of the symbolic computation system Mathematica. More solutions in the Jacobi elliptic function form are obtained, including the single Jacobi elliptic function solutions, combined Jacobi elliptic function solutions, rational solutions, triangular solutions, soliton solutions and combined soliton solutions.展开更多
In this paper we give an almost sharp error estimate of Halley’s iteration for the majorizing sequence. Compared with the corresponding results in [6,14], it is far better. Meanwhile,the convergence theorem is establ...In this paper we give an almost sharp error estimate of Halley’s iteration for the majorizing sequence. Compared with the corresponding results in [6,14], it is far better. Meanwhile,the convergence theorem is established .for Halley’s iteration in Banach spaces.展开更多
Making an exact computation of added resistance in sea waves is of high interest due to the economic effects relating to ship design and operation. In this paper, a B-spline based method is developed for computation o...Making an exact computation of added resistance in sea waves is of high interest due to the economic effects relating to ship design and operation. In this paper, a B-spline based method is developed for computation of added resistance. Based on the potential flow assumption, the velocity potential is computed using Green＇s formula. The Kochin function is applied to compute added resistance using Maruo＇s far-field method, the body surface is described by a B-spline curve and potentials and normal derivation of potentials are also described by B-spline basis functions and B-spline derivations. A collocation approach is applied for numerical computation, and integral equations are then evaluated by applying Gauss–Legendre quadrature. Computations are performed for a spheroid and different hull forms; results are validated by a comparison with experimental results. All results obtained with the present method show good agreement with experimental results.展开更多
Using a linear scaling self-consistent-charge density functional tight binding （SCC-DFTB） and an ab initio Omol method, the bonding characteristics and Young＇s modulus of （10, 0） and （10,10） single-walled carbo...Using a linear scaling self-consistent-charge density functional tight binding （SCC-DFTB） and an ab initio Omol method, the bonding characteristics and Young＇s modulus of （10, 0） and （10,10） single-walled carbon nanotubes are calculated. The structure of a graphene is also calculated. It is found that the C-C and C-H bond length, their distribution characteristics on the tube, and Young^s modulus of the tube by linear scaling SCC-DFTB are identical to those by ab initio, while the computing cost by the linear scaling SCC-DFTB is reduced by more than 30 times as compared with that by the Dmol for the （10,0） and （10,10） tubes. By computing the structure of a graphene it is also found that the linear scaling SCCDFTB is reliable and time-saving.展开更多
基金supported by the National Natural Science Foundation of China (Grant No. 50879090)
文摘The singularities, oscillatory performances and the contributing factors to the 3-＇D translating-pulsating source Green function of deep-water Havelock form which consists of a local disturbance part and a far-field wave-like part, are analyzed systematically. Relative numerical integral methods about the two parts are presented in this paper. An improved method based on LOBATTO rule is used to eliminate singularities caused respectively by infinite discontinuity and jump discontinuous node from the local disturbance part function, which makes the improvement of calculation efficiency and accuracy possible. And variable substitution is applied to remove the singularity existing at the end of the integral interval of the far-field wave-like part function. Two auxiliary techniques such as valid interval calculation and local refinement of integral steps technique in narrow zones near false singularities are applied so as to avoid unnecessary integration of invalid interval and improve integral accordance. Numerical test results have proved the efficiency and accuracy in these integral methods that thus can be applied to calculate hydrodynamic performance of floating structures moving in waves.
基金supported by Social Science Fund for Young Scholar of Ministry of Education of China(Grant No. 12YJC760092)Changzhou Key Digital Manufacturing Technology Laboratory Foundation of China(Grant No. CM2007301)
文摘As children mature, bike products for children in the market develop at the same time, and the conditions are frequently updated. Certain problems occur when using a bike, such as cycle overlapping, repeating function, and short life cycle, which go against the principles of energy conservation and the environmental protection intensive design concept. In this paper, a rational multi-function method of design through functional superposition, transformation, and technical implementation is proposed. An organic combination of frog-style scooter and children’s tricycle is developed using the multi-function method. From the ergonomic perspective, the paper elaborates on the body size of children aged 5 to 12 and effectively extracts data for a multi-function children’s bike, which can be used for gliding and riding. By inverting the body, parts can be interchanged between the handles and the pedals of the bike. Finally, the paper provides a detailed analysis of the components and structural design, body material, and processing technology of the bike. The study of Industrial Product Innovation Design provides an effective design method to solve the bicycle problems, extends the function problems, improves the product market situation, and enhances the energy saving feature while implementing intensive product development effectively at the same time.
基金Project supported by the National Natural Science Foundation of China （No. 50879090）, and the Key Research Program of Hydrody- namics of China （No. 9140A 14030712JB 11044）
文摘The singularities and oscillatory performance of translating-pulsating source Green＇s function in Bessho form were analyzed. Relative numerical integration methods such as Gaussian quadrature rule, variable substitution method （VSM）, and steepest descent integration method （SDIM） were used to evaluate this type of Green＇s function. For SDIM, the complex domain was restricted only on the 0-plane. Meanwhile, the integral along the real axis was computed by use of the VSM to avoid the complication of a numerical search of the steepest descent line. Furthermore, the steepest descent line was represented by the B-spline function. Based on this representation, a new self-compatible integration method corresponding to parametric t was established. The numerical method was validated through comparison with other existing results, and was shown to be efficient and reliable in the calculation of the velocity potentials for the 3D seakeeping and hydrodynamic performance of floating struc- tures moving in waves.
基金the National Natural Science Foundation of China(No.U2032141)the Open Project of Guangxi Key Laboratory of Nuclear Physics and Nuclear Technology(No.NLK2022-02)+4 种基金the Central Government Guidance Funds for Local Scientific and Technological Development,China(Guike ZY22096024)the Natural Science Foundation of Henan Province(No.202300410479)the Guizhou Provincial Science and Technology Projects(No.ZK[2022]203)the Foundation of Fundamental Research for Young Teachers of Zhengzhou University(No.JC202041041)the Physics Research and Development Program of Zhengzhou University(No.32410217).
文摘The possible exotic nuclear properties in the neutron-rich Ca,Ni,Zr,and Sn isotopes are examined with the continuum Skyrme Hartree-Fock-Bogoliubov theory in the framework of the Green’s function method.The pairing correlation,the couplings with the continuum,and the blocking effects for the unpaired nucleon in odd-A nuclei are properly treated.The Skyrme interaction SLy4 is adopted for the ph channel and the density-dependentinteraction is adopted for the pp chan-nel,which well reproduce the experimental two-neutron separation energies S_(2n)and one-neutron separation energies Sn.It is found that the criterion S_(n)>0 predicts a neutron drip line with neutron numbers much smaller than those for S_(2n)>0.Owing to the unpaired odd neutron,the neutron pairing energies−E_(pair)in odd-A nuclei are much lower than those in the neighbor-ing even-even nuclei.By investigating the single-particle structures,the possible halo structures in the neutron-rich Ca,Ni,and Sn isotopes are predicted,where sharp increases in the root-mean-square(rms)radii with significant deviations from the traditional rA^(1∕3)rule and diffuse spatial density distributions are observed.Analyzing the contributions of various partial waves to the total neutron densityρlj(r)∕ρ(r)reveals that the orbitals located around the Fermi surface-particularly those with small angular momenta-significantly affect the extended nuclear density and large rms radii.The number of neutrons Nλ(N_(0))occupying above the Fermi surfacen(continuum threshold)is discussed,whose evolution as a function of the mass number A in each isotope is consistent with that of the pairing energy,supporting the key role of the pairing correlation in halo phenomena.
基金supported by the National Natural Science Foundation of China (Grant Nos. 12272269, 11972257,11832014 and 11472193)the Shanghai Pilot Program for Basic Researchthe Shanghai Gaofeng Project for University Academic Program Development。
文摘Understanding the effects of point liquid loading on transversely isotropic poroelastic media is crucial for advancing geomechanics and biomechanics, where precise modeling of fluid-structure interactions is essential. This paper presents a comprehensive analysis of infinite transversely isotropic poroelasticity under a fluid source, based on Biot's theory, aiming to uncover new and previously unexplored insights in the literature. We begin our study by deriving a general solution for fluid-saturated, transversely isotropic poroelastic materials in terms of harmonic functions that satisfy sixth-order homogeneous partial differential equations, using potential theory and Almansi's theorem. Based on these general solutions and potential functions, we construct a Green's function for a point fluid source, introducing three new harmonic functions with undetermined constants. These constants are determined by enforcing continuity and equilibrium conditions. Substituting these into the general solution yields fundamental solutions for poroelasticity that provide crucial support for a wide range of project problems. Numerical results and comparisons with existing literature are provided to illustrate physical mechanisms through contour plots. Our observations reveal that all components tend to zero in the far field and become singular at the concentrated source. Additionally, the contours exhibit rapid changes near the point fluid source but display gradual variations at a distance from it. These findings highlight the intricate behavior of the system under point liquid loading, offering valuable insights for further research and practical applications.
基金supported by Shanghai 2021“Science and Technology Innovation Action Plan”:Social Development Science and Technology Research Project(Grant No.21DZ1202703).
文摘The numerical simulation of the fluid flow and the flexible rod(s)interaction is more complicated and has lower efficiency due to the high computational cost.In this paper,a semi-resolved model coupling the computational fluid dynamics and the flexible rod dynamics is proposed using a two-way domain expansion method.The gov-erning equations of the flexible rod dynamics are discretized and solved by the finite element method,and the fluid flow is simulated by the finite volume method.The interaction between fluids and solid rods is modeled by introducing body force terms into the momentum equations.Referred to the traditional semi-resolved numerical model,an anisotropic Gaussian kernel function method is proposed to specify the interactive forces between flu-ids and solid bodies for non-circle rod cross-sections.A benchmark of the flow passing around a single flexible plate with a rectangular cross-section is used to validate the algorithm.Focused on the engineering applications,a test case of a finite patch of cylinders is implemented to validate the accuracy and efficiency of the coupled model.
文摘In this paper, the Adomian decomposition method with Green’s function (Standard Adomian and Modified Technique) is applied to solve linear and nonlinear tenth-order boundary value problems with boundary conditions defined at any order derivatives. The numerical results obtained with a small amount of computation are compared with the exact solutions to show the efficiency of the method. The results show that the decomposition method is of high accuracy, more convenient and efficient for solving high-order boundary value problems.
文摘We study the nonlinear parabolic equations for travelling wave solutions of Burger’s equations. The purpose of the present work is to study various types of Burger’s equations describing waves and those are based on nonlinear equations. We focus on to describe the analytic solution in the special pattern of travelling wave solutions using tan-cot function method. We discuss about inviscid and viscous version of Burger’s equation for fluid flow and investigate the effects of internal friction of a fluid via Reynolds number. By changing the velocity amplitude, the nature of flows with shock wave and disturbance are observed. For numerical solutions, the Crank-Nicolson scheme is introduced to establish the wave solutions.
文摘This study evaluates the effectiveness of a new technique that transforms doma in integrals into boundary integrals that is applicable to the boundary element method.Si mulations were conducted in which two-dimensional surfaces were approximated by inter polation using radial basis functions with full and compact supports.Examples involving Poisson’s equation are presented using the boundary element method and the proposed te chnique with compact radial basis functions.The advantages and the disadvantages are e xamined through simulations.The effects of internal poles,the boundary mesh refinemen t and the value for the support of the radial basis functions on performance are assessed.
基金National Natural Science Foundation of China under grant No.51578373 and 51578372the Natural Science Foundation of Tianjin Municipality under Grant No.16JCYBJC21600
文摘The dynamic stiffness method combined with the Fourier transform is utilized to derive the in-plane Green’s functions for inclined and uniformly distributed loads in a multi-layered transversely isotropic（TI）half-space.The loaded layer is fixed to obtain solutions restricted in it and the corresponding reactions forces,which are then applied to the total system with the opposite sign.By adding solutions restricted in the loaded layer to solutions from the reaction forces,the global solutions in the wavenumber domain are obtained,and the dynamic Green’s functions in the space domain are recovered by the inverse Fourier transform.The presented formulations can be reduced to the isotropic case developed by Wolf（1985）,and are further verified by comparisons with existing solutions in a uniform isotropic as well as a layered TI halfspace subjected to horizontally distributed loads which are special cases of the more general problem addressed.The deduced Green’s functions,in conjunction with boundary element methods,will lead to significant advances in the investigation of a variety of wave scattering,wave radiation and soil-structure interaction problems in a layered TI site.Selected numerical results are given to investigate the influence of material anisotropy,frequency of excitation,inclination angle and layered on the responses of displacement and stress,and some conclusions are drawn.
基金Aeronautical Science Foundation of China （2008ZC52024）
文摘The accurate analyses for a plate fin heat sink with the ability to control the temperature of the avionics devices within a pre-set controllable temperature range are required both in the process of circuit design and for the real-time temperature monitoring purposes. In order to provide an insight into the behavior of the temperature of a plate fin heat sink subjected non-uniform heat density on the surfaces, it is necessary to obtain accurate analytical solutions yielding explicit formulas relating the dissipated power to the temperature rise at any point of avionics devices. This paper presents a method for thermal simulation of a plate fin heat sink using an analytical solution of the three-dimensional heat equation resulting from an appropriate plate fin heat sink transient thermal model. The entire solution methodology is illustrated in detail on the particular examples of the plate fin heat sink subjected non-uniform heat density on the surfaces. The transient temperature profiles are obtained for different positions at the surface of the plate fin heat sink. The analytical results are compared with measurements made on the surface of the cold plate and it is found that they are in good agreement with an error of less than 3 K.
文摘A new algorithm is presented for solving Troesch’s problem. The numerical scheme based on the sinc-collocation technique is deduced. The equation is reduced to systems of nonlinear algebraic equations. Some numerical experiments are made. Compared with the modified homotopy perturbation technique (MHP), the variational iteration method and the Adomian decomposition method. It is shown that the sinc-collocation method yields better results.
基金This work was supported by Young Scientists Fundamental Research Program of Shandong Province of China (No. 031B5147).
文摘In heating, ventilating and air-conditioning （HVAC） systems, there exist severe nonlinearity, time-varying nature, disturbances and uncertainties. A new predictive functional control based on Takagi-Sugeno （T-S） fuzzy model was proposed to control HVAC systems. The T-S fuzzy model of stabilized controlled process was obtained using the least squares method, then on the basis of global linear predictive model from T-S fuzzy model, the process was controlled by the predictive functional controller. Especially the feedback regulation part was developed to compensate uncertainties of fuzzy predictive model. Finally simulation test results in HVAC systems control applications showed that the proposed fuzzy model predictive functional control improves tracking effect and robustness. Compared with the conventional PID controller, this control strategy has the advantages of less overshoot and shorter setting time, etc.
基金supported by National Engineering School of Tunis (No.13039.1)
文摘To reduce computational costs, an improved form of the frequency domain boundary element method（BEM） is proposed for two-dimensional radiation and propagation acoustic problems in a subsonic uniform flow with arbitrary orientation. The boundary integral equation（BIE） representation solves the two-dimensional convected Helmholtz equation（CHE） and its fundamental solution, which must satisfy a new Sommerfeld radiation condition（SRC） in the physical space. In order to facilitate conventional formulations, the variables of the advanced form are expressed only in terms of the acoustic pressure as well as its normal and tangential derivatives, and their multiplication operators are based on the convected Green＇s kernel and its modified derivative. The proposed approach significantly reduces the CPU times of classical computational codes for modeling acoustic domains with arbitrary mean flow. It is validated by a comparison with the analytical solutions for the sound radiation problems of monopole,dipole and quadrupole sources in the presence of a subsonic uniform flow with arbitrary orientation.
基金supported by the National Natural Science Foundation of China(Nos.11672071,11302046,and 11672072)the Fundamental Research Funds for the Central Universities(No.N150504003)
文摘Geometrically nonlinear oscillations are investigated on sigmoid functionally graded material （S-FGM） plates with a longitudinal speed. The material properties of the plates obey a sigmoid distribution rule along the thickness direction. Based on the D＇Alembert＇s principle, a nonlinear equation of motion is derived for the moving S-FGM plates, where the von K^rm^n nonlinear plate theory is adopted. Utilizing the Galerkin method, the equation of motion is discretized and solved via the method of harmonic bal- ance. The approximate analytical solutions are validated through the adaptive step-size fourth-order Runge-Kutta method. Besides, the stability of the steady-state solutions is examined. The results reveal that the mode interaction behavior can happen between the first two modes of the moving S-FGM plates, leading to a complex nonlinear frequency response. It is further found that the power-law index, the longitudinal speed, the exci- tation amplitude, and the in-plane pretension force can significantly affect the nonlinear frequency-response characteristics of longitudinally traveling S-FGM plates.
基金Project supported by the National Nature Science Foundation of China （Grant No 49894190） of the Chinese Academy of Science （Grant No KZCXI-sw-18）, and Knowledge Innovation Program.
文摘The extended F-expansion method or mapping method is used to construct exact solutions for the coupled KleinGordon Schr/Sdinger equations （K-G-S equations） by the aid of the symbolic computation system Mathematica. More solutions in the Jacobi elliptic function form are obtained, including the single Jacobi elliptic function solutions, combined Jacobi elliptic function solutions, rational solutions, triangular solutions, soliton solutions and combined soliton solutions.
基金Jointly supported by China Major Key Project for Basic Researcher and Provincial Natrual Science Foundation.
文摘In this paper we give an almost sharp error estimate of Halley’s iteration for the majorizing sequence. Compared with the corresponding results in [6,14], it is far better. Meanwhile,the convergence theorem is established .for Halley’s iteration in Banach spaces.
文摘Making an exact computation of added resistance in sea waves is of high interest due to the economic effects relating to ship design and operation. In this paper, a B-spline based method is developed for computation of added resistance. Based on the potential flow assumption, the velocity potential is computed using Green＇s formula. The Kochin function is applied to compute added resistance using Maruo＇s far-field method, the body surface is described by a B-spline curve and potentials and normal derivation of potentials are also described by B-spline basis functions and B-spline derivations. A collocation approach is applied for numerical computation, and integral equations are then evaluated by applying Gauss–Legendre quadrature. Computations are performed for a spheroid and different hull forms; results are validated by a comparison with experimental results. All results obtained with the present method show good agreement with experimental results.
基金support by Program for Changjing Schol-ars and Innovative Research Team in University(PSCIRT0720)
文摘Using a linear scaling self-consistent-charge density functional tight binding （SCC-DFTB） and an ab initio Omol method, the bonding characteristics and Young＇s modulus of （10, 0） and （10,10） single-walled carbon nanotubes are calculated. The structure of a graphene is also calculated. It is found that the C-C and C-H bond length, their distribution characteristics on the tube, and Young^s modulus of the tube by linear scaling SCC-DFTB are identical to those by ab initio, while the computing cost by the linear scaling SCC-DFTB is reduced by more than 30 times as compared with that by the Dmol for the （10,0） and （10,10） tubes. By computing the structure of a graphene it is also found that the linear scaling SCCDFTB is reliable and time-saving.
