In engineering practice, tubular X-joints have been widely used in offshore structures. The fatigue failure of tubular X-joints in offshore engineering is mainly caused by axial tensile stress. In this study, the stre...In engineering practice, tubular X-joints have been widely used in offshore structures. The fatigue failure of tubular X-joints in offshore engineering is mainly caused by axial tensile stress. In this study, the stress concentration factor distribution along the weld toe in the hot spot stress region for tubular X-joints subject to axial loads have been analyzed by use of finite element method. Through numerical analysis, it has been found that the peak stress concentration factor is located at the saddle position. Thereafter, 80 models have been analyzed, and the effect of the geometric parameters of a tubular X-joint on the stress concentration factor has been investigated. Based on the experimental values of the numerical stress concentration factor, a parametric equation to calculate the stress concentration factor of tubular X-joints has been proposed. The accuracy of this equation has been verified against the requirement of the Fatigue Guidance Review Panel, and the proposed equation is found capable of producing reasonably accurate stress concentration factor values for tubular X-joints subject to axial loads.展开更多
The dynamical and physical behavior of a complex system can be more accurately described by using the fractional model.With the successful use of fractional calculus in many areas of science and engineering,it is nece...The dynamical and physical behavior of a complex system can be more accurately described by using the fractional model.With the successful use of fractional calculus in many areas of science and engineering,it is necessary to extend the classical theories and methods of analytical mechanics to the fractional dynamic system.Birkhoffian mechanics is a natural generalization of Hamiltonian mechanics,and its core is the Pfaff-Birkhoff principle and Birkhoff′s equations.The study on the Birkhoffian mechanics is an important developmental direction of modern analytical mechanics.Here,the fractional Pfaff-Birkhoff variational problem is presented and studied.The definitions of fractional derivatives,the formulae for integration by parts and some other preliminaries are firstly given.Secondly,the fractional Pfaff-Birkhoff principle and the fractional Birkhoff′s equations in terms of RieszRiemann-Liouville fractional derivatives and Riesz-Caputo fractional derivatives are presented respectively.Finally,an example is given to illustrate the application of the results.展开更多
The problem of transforming autonomous systems into Birkhoffian systems is studied. A reasonable form of linear autonomous Birkhoff equations is given. By combining them with the undetermined tensor method, a necessar...The problem of transforming autonomous systems into Birkhoffian systems is studied. A reasonable form of linear autonomous Birkhoff equations is given. By combining them with the undetermined tensor method, a necessary and sufficient condition for an autonomous system to have a representation in terms of linear autonomous Birkhoff equations is obtained. The methods of constructing Birkhoffian dynamical functions are given. Two examples are given to illustrate the application of the results.展开更多
In this paper, we present a new integration algorithm based on the discrete Pfaff-Birkhoff principle for Birkhoffian systems. It is proved that the new algorithm can preserve the general symplectic geometric structure...In this paper, we present a new integration algorithm based on the discrete Pfaff-Birkhoff principle for Birkhoffian systems. It is proved that the new algorithm can preserve the general symplectic geometric structures of Birkhoffian systems. A numerical experiment for a damping oscillator system is conducted. The result shows that the new algorithm can better simulate the energy dissipation than the R-K method, which illustrates that we can numerically solve the dynamical equations by the discrete variational method in a Birkhoffian framework for the systems with a general symplectic structure. Furthermore, it is demonstrated that the results of the numerical experiments are determined not by the constructing methods of Birkhoffian functions but by whether the numerical method can preserve the inherent nature of the dynamical system.展开更多
This paper focuses on studying the generalized geometry theory of constrained rotating relativistic Birkhoffian systems. Based on the fact that relativistic rotating inertia is embedded in the Birkhoffian systems, the...This paper focuses on studying the generalized geometry theory of constrained rotating relativistic Birkhoffian systems. Based on the fact that relativistic rotating inertia is embedded in the Birkhoffian systems, the Pfaff action of rotating relativistic Birkhoffian systems was defined. The Pfaff-Birkhoff principles and Birkhoff's equations of the constrained rotating relativistic systems were obtained. The geometrical description, the exact properties and their forms on R T^*M for the constrained rotating relativistic Birkhoffian systems are given. The global analyses of the autonomous, semi-autonomous and non-autonomous constrained relativistic Birkhoff's equations as well as the geometrical properties of energy change for the constrained rotating relativistic Birkhoffian systems were also conducted.展开更多
The fractional Pfaffian variational problem and Noether’s theorems were investigated in terms of Riemann-Liouville derivatives on the basis of El-Nabulsi fractional model.The problem of the calculus of variations wit...The fractional Pfaffian variational problem and Noether’s theorems were investigated in terms of Riemann-Liouville derivatives on the basis of El-Nabulsi fractional model.The problem of the calculus of variations with fractional derivatives is a hot topic recently.Firstly,within Riemann-Liouville derivatives,the ElNabulsi Pfaffian variational problem was presented,the fractional Pfaff-Birkhoff-d’Alembert principle was established,and the fractional Birkhoff equations and the corresponding transversality conditions were obtained.Then,the Noether’s theorems in terms of Riemann-Liouville derivatives for the Birkhoffian system on the basis of El-Nabulsi fractional model are investigated under the special and the general transformations respectively.Finally,an example is given to illustrate the methods and results appeared in this paper.展开更多
The(un)forced(un)damped parametric pendulum oscillator(PPO)is analyzed analytically and numerically using some simple,effective,and more accurate techniques.In the first technique,the ansatz method is employed for ana...The(un)forced(un)damped parametric pendulum oscillator(PPO)is analyzed analytically and numerically using some simple,effective,and more accurate techniques.In the first technique,the ansatz method is employed for analyzing the unforced damped PPO and for deriving some optimal and accurate analytical approximations in the form of angular Mathieu functions.In the second approach,some approximations to(un)forced damped PPO are obtained in the form of trigonometric functions using the ansatz method.In the third approach,He’s frequency-amplitude principle is applied for deriving some approximations to the(un)damped PPO.In the forth approach,He’s homotopy technique is employed for analyzing the forced(un)damped PPO numerically.In the fifth approach,the p-solution Method,which is constructed based on Krylov–Bogoliúbov Mitropolsky method,is introduced for deriving an approximation to the forced damped PPO.In the final approach,the hybrid Padé-finite difference method is carried out for analyzing the damped PPO numerically.All proposed techniques are compared to the fourth-order Runge–Kutta(RK4)numerical solution.Moreover,the global maximum residual distance error is estimated for checking the accuracy of the obtained approximations.The proposed methodologies and approximations can help many researchers in studying and investigating several nonlinear phenomena related to the oscillations that can arise in various branches of science,e.g.waves and oscillations in plasma physics.展开更多
Parametric Polynomial Method is used to analyze the three dimensional viscous flow through multistage turbomachines. Three high pressure stages in a 20MW steam turbine are calculated at design flow rate and small llow...Parametric Polynomial Method is used to analyze the three dimensional viscous flow through multistage turbomachines. Three high pressure stages in a 20MW steam turbine are calculated at design flow rate and small llow rate (G/G0 = 0.3). Large separated flow is predicted in the passage at small flow rate. The result shows that the upstream flow has a conspicuous effect on the downstream flow, so the multbetage fiow calculating is展开更多
基金The research work was financially supported by the National Natural Scientice Foundation of China(Grant No.10142001)by the Shandong Provincial Natural Scientice Foundation(Grant No.Y2006F46)
文摘In engineering practice, tubular X-joints have been widely used in offshore structures. The fatigue failure of tubular X-joints in offshore engineering is mainly caused by axial tensile stress. In this study, the stress concentration factor distribution along the weld toe in the hot spot stress region for tubular X-joints subject to axial loads have been analyzed by use of finite element method. Through numerical analysis, it has been found that the peak stress concentration factor is located at the saddle position. Thereafter, 80 models have been analyzed, and the effect of the geometric parameters of a tubular X-joint on the stress concentration factor has been investigated. Based on the experimental values of the numerical stress concentration factor, a parametric equation to calculate the stress concentration factor of tubular X-joints has been proposed. The accuracy of this equation has been verified against the requirement of the Fatigue Guidance Review Panel, and the proposed equation is found capable of producing reasonably accurate stress concentration factor values for tubular X-joints subject to axial loads.
基金Supported by the National Natural Science Foundation of China(10972151,11272227)the Innovation Program for Postgraduate in Higher Education Institutions of Jiangsu Province(CXZZ11_0949)the Innovation Program for Postgraduate of Suzhou University of Science and Technology(SKCX11S_050)
文摘The dynamical and physical behavior of a complex system can be more accurately described by using the fractional model.With the successful use of fractional calculus in many areas of science and engineering,it is necessary to extend the classical theories and methods of analytical mechanics to the fractional dynamic system.Birkhoffian mechanics is a natural generalization of Hamiltonian mechanics,and its core is the Pfaff-Birkhoff principle and Birkhoff′s equations.The study on the Birkhoffian mechanics is an important developmental direction of modern analytical mechanics.Here,the fractional Pfaff-Birkhoff variational problem is presented and studied.The definitions of fractional derivatives,the formulae for integration by parts and some other preliminaries are firstly given.Secondly,the fractional Pfaff-Birkhoff principle and the fractional Birkhoff′s equations in terms of RieszRiemann-Liouville fractional derivatives and Riesz-Caputo fractional derivatives are presented respectively.Finally,an example is given to illustrate the application of the results.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.10932002,11172120,and 11202090)
文摘The problem of transforming autonomous systems into Birkhoffian systems is studied. A reasonable form of linear autonomous Birkhoff equations is given. By combining them with the undetermined tensor method, a necessary and sufficient condition for an autonomous system to have a representation in terms of linear autonomous Birkhoff equations is obtained. The methods of constructing Birkhoffian dynamical functions are given. Two examples are given to illustrate the application of the results.
基金supported by the National Natural Science Foundation of China(Grant Nos.11301350,11172120,and 11202090)the Liaoning University Prereporting Fund Natural Projects(Grant No.2013LDGY02)
文摘In this paper, we present a new integration algorithm based on the discrete Pfaff-Birkhoff principle for Birkhoffian systems. It is proved that the new algorithm can preserve the general symplectic geometric structures of Birkhoffian systems. A numerical experiment for a damping oscillator system is conducted. The result shows that the new algorithm can better simulate the energy dissipation than the R-K method, which illustrates that we can numerically solve the dynamical equations by the discrete variational method in a Birkhoffian framework for the systems with a general symplectic structure. Furthermore, it is demonstrated that the results of the numerical experiments are determined not by the constructing methods of Birkhoffian functions but by whether the numerical method can preserve the inherent nature of the dynamical system.
基金Project supported by the National Natural Science Foundation of China (Grant Nos.10672143, 10372053), and the Natural Science Foundation of Henan Province (Grant Nos.03011011400, 05011022200)
文摘This paper focuses on studying the generalized geometry theory of constrained rotating relativistic Birkhoffian systems. Based on the fact that relativistic rotating inertia is embedded in the Birkhoffian systems, the Pfaff action of rotating relativistic Birkhoffian systems was defined. The Pfaff-Birkhoff principles and Birkhoff's equations of the constrained rotating relativistic systems were obtained. The geometrical description, the exact properties and their forms on R T^*M for the constrained rotating relativistic Birkhoffian systems are given. The global analyses of the autonomous, semi-autonomous and non-autonomous constrained relativistic Birkhoff's equations as well as the geometrical properties of energy change for the constrained rotating relativistic Birkhoffian systems were also conducted.
基金National Natural Science Foundations of China(Nos.11572212,11272227,10972151)the Innovation Program for Scientific Research of Nanjing University of Science and Technology,Chinathe Innovation Program for Postgraduate in Higher Education Institutions of Jiangsu Province,China(No.KYLX15_0405)
文摘The fractional Pfaffian variational problem and Noether’s theorems were investigated in terms of Riemann-Liouville derivatives on the basis of El-Nabulsi fractional model.The problem of the calculus of variations with fractional derivatives is a hot topic recently.Firstly,within Riemann-Liouville derivatives,the ElNabulsi Pfaffian variational problem was presented,the fractional Pfaff-Birkhoff-d’Alembert principle was established,and the fractional Birkhoff equations and the corresponding transversality conditions were obtained.Then,the Noether’s theorems in terms of Riemann-Liouville derivatives for the Birkhoffian system on the basis of El-Nabulsi fractional model are investigated under the special and the general transformations respectively.Finally,an example is given to illustrate the methods and results appeared in this paper.
基金The authors express their gratitude to Princess Nourah bint Abdulrahman University Researchers Supporting Project (Grant No. PNURSP2022R17)Taif University Researchers supporting project number (TURSP2020/275), Taif University, Taif, Saudi Arabia。
文摘The(un)forced(un)damped parametric pendulum oscillator(PPO)is analyzed analytically and numerically using some simple,effective,and more accurate techniques.In the first technique,the ansatz method is employed for analyzing the unforced damped PPO and for deriving some optimal and accurate analytical approximations in the form of angular Mathieu functions.In the second approach,some approximations to(un)forced damped PPO are obtained in the form of trigonometric functions using the ansatz method.In the third approach,He’s frequency-amplitude principle is applied for deriving some approximations to the(un)damped PPO.In the forth approach,He’s homotopy technique is employed for analyzing the forced(un)damped PPO numerically.In the fifth approach,the p-solution Method,which is constructed based on Krylov–Bogoliúbov Mitropolsky method,is introduced for deriving an approximation to the forced damped PPO.In the final approach,the hybrid Padé-finite difference method is carried out for analyzing the damped PPO numerically.All proposed techniques are compared to the fourth-order Runge–Kutta(RK4)numerical solution.Moreover,the global maximum residual distance error is estimated for checking the accuracy of the obtained approximations.The proposed methodologies and approximations can help many researchers in studying and investigating several nonlinear phenomena related to the oscillations that can arise in various branches of science,e.g.waves and oscillations in plasma physics.
文摘Parametric Polynomial Method is used to analyze the three dimensional viscous flow through multistage turbomachines. Three high pressure stages in a 20MW steam turbine are calculated at design flow rate and small llow rate (G/G0 = 0.3). Large separated flow is predicted in the passage at small flow rate. The result shows that the upstream flow has a conspicuous effect on the downstream flow, so the multbetage fiow calculating is