The solution of Nekrasov’s integral equation is described. By means of this solution the wave kinetic, potential, and full mechanical energies are defined as functions of fluid depth and wavelength. The wave obeys th...The solution of Nekrasov’s integral equation is described. By means of this solution the wave kinetic, potential, and full mechanical energies are defined as functions of fluid depth and wavelength. The wave obeys the laws of mass and energy conservation. It is found that for any constant depth of fluid the wavelength is bounded from above by a value denoted as maximal wavelength. At maximal wavelength 1) the maximum slope of the free surface of the wave exceeds 38o and the value 45o is supposed attainable,2) the wave kinetic energy vanishes. The stability of a steady wave considered as a compound pendulum is analyzed.展开更多
The micro turbine(MT)is scheduled to address wind power uncertainties and thus lead to greater variations in the state of natural gas system(NGS).To meet this challenge,first,a dynamic model of a gas-electricity combi...The micro turbine(MT)is scheduled to address wind power uncertainties and thus lead to greater variations in the state of natural gas system(NGS).To meet this challenge,first,a dynamic model of a gas-electricity combined system with wind power is established,the dynamic model of the NGS is based on differential equations,so that it can easily connect with the MT model;and a droop control module is added to the Rowen's MT model,so that the improved model can adjust the output power according to the scheduling instructions.Then,a stability control method based on the variable regulation ratio gas pressure regulator is proposed,the essence of this method is to reduce the variation of natural gas storage in the gas pipeline,so as to ensure the stability of pressure.The simulation results show that the dynamic model is correct and the stability control method is effective.展开更多
In this paper,the stability of three classes of steady basic states in the two-dimensional compressible adiabatic and non-dissipation atmosphere is discussed,and the following property is exactly demonstrated that the...In this paper,the stability of three classes of steady basic states in the two-dimensional compressible adiabatic and non-dissipation atmosphere is discussed,and the following property is exactly demonstrated that the stability of these basic states is decided by their engine matrix A in two ways:(a)the basic states are stable if A is positively definite in set,and(b)the basic states are unstable if A is negatively definite in set.展开更多
This paper presents an efficient time-integration method for obtaining reliable solutions to the second-order nonlinear dynamic problems in structural engineering. This method employs both the backward-acceleration di...This paper presents an efficient time-integration method for obtaining reliable solutions to the second-order nonlinear dynamic problems in structural engineering. This method employs both the backward-acceleration differentiation formula and the trapezoidal rule, resulting in a self-starting, single step, second-order accurate algorithm. With the same computational effort as the trapezoidal rule, the proposed method remains stable in large deformation and long time range solutions even when the trapezoidal rule fails. Meanwhile, the proposed method has the following characteristics: (1) it is applicable to linear as well as general nonlinear analyses; (2) it does not involve additional variables (e.g. Lagrange multipliers) and artificial parameters; (3) it is a single-solver algorithm at the discrete time points with symmetric effective stiffness matrix and effective load vectors; and (4) it is easy to implement in an existing computational software. Some numerical results indicate that the proposed method is a powerful tool with some notable features for practical nonlinear dynamic analyses.展开更多
With the natural splitting of a Hamiltonian system into kinetic energy and potential energy,we construct two new optimal thirdorder force-gradient symplectic algorithms in each of which the norm of fourth-order trunca...With the natural splitting of a Hamiltonian system into kinetic energy and potential energy,we construct two new optimal thirdorder force-gradient symplectic algorithms in each of which the norm of fourth-order truncation errors is minimized.They are both not explicitly superior to their no-optimal counterparts in the numerical stability and the topology structure-preserving,but they are in the accuracy of energy on classical problems and in one of the energy eigenvalues for one-dimensional time-independent Schrdinger equations.In particular,they are much better than the optimal third-order non-gradient symplectic method.They also have an advantage over the fourth-order non-gradient symplectic integrator.展开更多
文摘The solution of Nekrasov’s integral equation is described. By means of this solution the wave kinetic, potential, and full mechanical energies are defined as functions of fluid depth and wavelength. The wave obeys the laws of mass and energy conservation. It is found that for any constant depth of fluid the wavelength is bounded from above by a value denoted as maximal wavelength. At maximal wavelength 1) the maximum slope of the free surface of the wave exceeds 38o and the value 45o is supposed attainable,2) the wave kinetic energy vanishes. The stability of a steady wave considered as a compound pendulum is analyzed.
基金supported by the National Natural Science Foundation of China(51977012).
文摘The micro turbine(MT)is scheduled to address wind power uncertainties and thus lead to greater variations in the state of natural gas system(NGS).To meet this challenge,first,a dynamic model of a gas-electricity combined system with wind power is established,the dynamic model of the NGS is based on differential equations,so that it can easily connect with the MT model;and a droop control module is added to the Rowen's MT model,so that the improved model can adjust the output power according to the scheduling instructions.Then,a stability control method based on the variable regulation ratio gas pressure regulator is proposed,the essence of this method is to reduce the variation of natural gas storage in the gas pipeline,so as to ensure the stability of pressure.The simulation results show that the dynamic model is correct and the stability control method is effective.
基金This work is supported by the National Natural Science Foundation of China.
文摘In this paper,the stability of three classes of steady basic states in the two-dimensional compressible adiabatic and non-dissipation atmosphere is discussed,and the following property is exactly demonstrated that the stability of these basic states is decided by their engine matrix A in two ways:(a)the basic states are stable if A is positively definite in set,and(b)the basic states are unstable if A is negatively definite in set.
基金sponsored by the Scientific Foundation for Returned Oversea Scholars of China (Grant No.20101020044)the State Key Laboratory of Hydro–Science and Engineering (Grant Nos. 2008Z6 and 2009-TC-2)
文摘This paper presents an efficient time-integration method for obtaining reliable solutions to the second-order nonlinear dynamic problems in structural engineering. This method employs both the backward-acceleration differentiation formula and the trapezoidal rule, resulting in a self-starting, single step, second-order accurate algorithm. With the same computational effort as the trapezoidal rule, the proposed method remains stable in large deformation and long time range solutions even when the trapezoidal rule fails. Meanwhile, the proposed method has the following characteristics: (1) it is applicable to linear as well as general nonlinear analyses; (2) it does not involve additional variables (e.g. Lagrange multipliers) and artificial parameters; (3) it is a single-solver algorithm at the discrete time points with symmetric effective stiffness matrix and effective load vectors; and (4) it is easy to implement in an existing computational software. Some numerical results indicate that the proposed method is a powerful tool with some notable features for practical nonlinear dynamic analyses.
基金supported by the NationalNatural Science Foundation of China (Grant No.10873007)supported by the Science Foundation of Jiangxi Education Bureau (Grant No.GJJ09072)the Program for Innovative Research Team of Nanchang University
文摘With the natural splitting of a Hamiltonian system into kinetic energy and potential energy,we construct two new optimal thirdorder force-gradient symplectic algorithms in each of which the norm of fourth-order truncation errors is minimized.They are both not explicitly superior to their no-optimal counterparts in the numerical stability and the topology structure-preserving,but they are in the accuracy of energy on classical problems and in one of the energy eigenvalues for one-dimensional time-independent Schrdinger equations.In particular,they are much better than the optimal third-order non-gradient symplectic method.They also have an advantage over the fourth-order non-gradient symplectic integrator.
