In this paper, by using of the theory of coincidence degree ,we obtain the new conditions which guarantee the existence of harmonic solutions for Lienard Systems our resuls do not require that the damping must be pos...In this paper, by using of the theory of coincidence degree ,we obtain the new conditions which guarantee the existence of harmonic solutions for Lienard Systems our resuls do not require that the damping must be positire.展开更多
Fluid-solid interaction problems have been studied q uite extensively in the past years. Rotor-bearing system is a typical example. Fluid field is changed under the exciting of rotor vibration. On the same ti me, a ne...Fluid-solid interaction problems have been studied q uite extensively in the past years. Rotor-bearing system is a typical example. Fluid field is changed under the exciting of rotor vibration. On the same ti me, a net force caused by fluid pressure exerts on rotor, which will change roto r vibration. So, the fluid-solid coupled analysis method must be used. Traditionally, numerical difference method was used to solve fluid problems. The coupled fluid-solid equation could not be set up based on the method. It is no t until finite element method was used in fluid dynamics area then can the coupl ed dynamics be researched. Recently many experimental, analytical and numerical studies have been used in the area . But in these investigations, it is a ssumed that the solid vibration could not be influenced by fluid. In the other w ords, the force exerted on solid from fluid was neglected in the papers. So, the models built were some kinds of semi-coupled model only. In this paper, the Galerkin finite-element method, two-dimension vibration equ ation of rigid body and Navier-Stokes equations are used to build a full-coupl ed fluid-solid model in rotor-bearing system. Some assumptions are taken: 1) In fluid equation, the nonlinear terms are relatively small and neglected. 2) The gravity takes no effect on this system. 3) The bearing and the rotor are long. Flow and leakage along the axis is neglec ted. 4) The fluid is a kind of Newtonian incondensable viscous fluid. 5) The rotor is considered to be a rigid body. Using the model established, we calculated all the examples given by paper , results show the error are less than 7%. So the full-coupled model is built c orrectly. Examples are given in the end of the paper. After analyzing the examples, we get some conclusions: 1) In rotor-bearing system, while being taken under two conditions that whether coupled method is taken or not, difference of pressure and vibration amplitude could reach 76% and 120%. Therefore coupled method must be taken to investigate fluid-solid system. 1) Amplitude of fluid pressure can be more or less influenced by rotor unbalance , gap, eccentricity and other factors. 2) By using coupling method, results show that the amplitudes of vibration and p ressure are greater than ignoring the method. It should be paid more attention t o.展开更多
A famous model, the chemical reaction-Brussel model with periodic force, is investigated.We study the regilar Hopf bifurcation and singular Hopf bifurcation from a basic equilibrium, and show the existence of the subh...A famous model, the chemical reaction-Brussel model with periodic force, is investigated.We study the regilar Hopf bifurcation and singular Hopf bifurcation from a basic equilibrium, and show the existence of the subharmonic solutions by using the averaging method and perturbed methods and bifurcation equations. By our analysis it can be shown that the homoclinic orbits do not occur, so we can conjecture that the harmonic oscillation can make successive subharmonic bifurcations, until a chaotic state ultimately develops. The results and methods in this paper are our first step in theoretically treating the transition to a chaotic state in the Brussel model and are appropriate to investigating the general nonlinear oscillation with periodic force.展开更多
文摘In this paper, by using of the theory of coincidence degree ,we obtain the new conditions which guarantee the existence of harmonic solutions for Lienard Systems our resuls do not require that the damping must be positire.
文摘Fluid-solid interaction problems have been studied q uite extensively in the past years. Rotor-bearing system is a typical example. Fluid field is changed under the exciting of rotor vibration. On the same ti me, a net force caused by fluid pressure exerts on rotor, which will change roto r vibration. So, the fluid-solid coupled analysis method must be used. Traditionally, numerical difference method was used to solve fluid problems. The coupled fluid-solid equation could not be set up based on the method. It is no t until finite element method was used in fluid dynamics area then can the coupl ed dynamics be researched. Recently many experimental, analytical and numerical studies have been used in the area . But in these investigations, it is a ssumed that the solid vibration could not be influenced by fluid. In the other w ords, the force exerted on solid from fluid was neglected in the papers. So, the models built were some kinds of semi-coupled model only. In this paper, the Galerkin finite-element method, two-dimension vibration equ ation of rigid body and Navier-Stokes equations are used to build a full-coupl ed fluid-solid model in rotor-bearing system. Some assumptions are taken: 1) In fluid equation, the nonlinear terms are relatively small and neglected. 2) The gravity takes no effect on this system. 3) The bearing and the rotor are long. Flow and leakage along the axis is neglec ted. 4) The fluid is a kind of Newtonian incondensable viscous fluid. 5) The rotor is considered to be a rigid body. Using the model established, we calculated all the examples given by paper , results show the error are less than 7%. So the full-coupled model is built c orrectly. Examples are given in the end of the paper. After analyzing the examples, we get some conclusions: 1) In rotor-bearing system, while being taken under two conditions that whether coupled method is taken or not, difference of pressure and vibration amplitude could reach 76% and 120%. Therefore coupled method must be taken to investigate fluid-solid system. 1) Amplitude of fluid pressure can be more or less influenced by rotor unbalance , gap, eccentricity and other factors. 2) By using coupling method, results show that the amplitudes of vibration and p ressure are greater than ignoring the method. It should be paid more attention t o.
文摘A famous model, the chemical reaction-Brussel model with periodic force, is investigated.We study the regilar Hopf bifurcation and singular Hopf bifurcation from a basic equilibrium, and show the existence of the subharmonic solutions by using the averaging method and perturbed methods and bifurcation equations. By our analysis it can be shown that the homoclinic orbits do not occur, so we can conjecture that the harmonic oscillation can make successive subharmonic bifurcations, until a chaotic state ultimately develops. The results and methods in this paper are our first step in theoretically treating the transition to a chaotic state in the Brussel model and are appropriate to investigating the general nonlinear oscillation with periodic force.
