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
The problem of nonlinear forced oscillations for elliptical sandwich plates is dealt with. Based on the governing equations expressed in terms of five displacement components, the nonlinear dynamic equation of an elli...The problem of nonlinear forced oscillations for elliptical sandwich plates is dealt with. Based on the governing equations expressed in terms of five displacement components, the nonlinear dynamic equation of an elliptical sandwich plate under a harmonic force is derived. A superpositive-iterative harmonic balance (SIHB) method is presented for the steady-state analysis of strongly nonlinear oscillators. In a periodic oscillation, the periodic solutions can be expressed in the form of basic harmonics and bifurcate harmonics. Thus, an oscillation system which is described as a second order ordinary differential equation, can be expressed as fundamental differential equation with fundamental harmonics and incremental differential equation with derived harmonics. The 1/3 subharmonic solution of an elliptical sandwich plate is investigated by using the methods of SIHB. The SIHB method is compared with the numerical integration method. Finally, asymptotical stability of the 1/3 subharmonic oscillations is inspected.展开更多
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.
文摘The problem of nonlinear forced oscillations for elliptical sandwich plates is dealt with. Based on the governing equations expressed in terms of five displacement components, the nonlinear dynamic equation of an elliptical sandwich plate under a harmonic force is derived. A superpositive-iterative harmonic balance (SIHB) method is presented for the steady-state analysis of strongly nonlinear oscillators. In a periodic oscillation, the periodic solutions can be expressed in the form of basic harmonics and bifurcate harmonics. Thus, an oscillation system which is described as a second order ordinary differential equation, can be expressed as fundamental differential equation with fundamental harmonics and incremental differential equation with derived harmonics. The 1/3 subharmonic solution of an elliptical sandwich plate is investigated by using the methods of SIHB. The SIHB method is compared with the numerical integration method. Finally, asymptotical stability of the 1/3 subharmonic oscillations is inspected.
