The 1：2 subharmonic resonance of the labyrinth seals-rotor system is inves- tigated, where the low-frequency vibration of steam turbines can be caused by the gas exciting force. The empirical parameters of gas exciti...The 1：2 subharmonic resonance of the labyrinth seals-rotor system is inves- tigated, where the low-frequency vibration of steam turbines can be caused by the gas exciting force. The empirical parameters of gas exciting force of the Muszynska model are obtained by using the results of computational fluid dynamics （CFD）. Based on the multiple scale method, the 1：2 subharmonic resonance response of the dynamic system is gained by truncating the system with three orders. The transition sets and the local bifurcations diagrams of the dynamics system are presented by employing the singular theory analysis. Meanwhile, the existence conditions of subharmonic resonance non-zero solutions of the dynamic system are obtained, which provides a new theoretical basis in recognizing and protecting the rotor from the subharmonic resonant failure in the turbine machinery.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
基金supported by the National Natural Science Foundation of China (No. 10632040)
文摘The 1：2 subharmonic resonance of the labyrinth seals-rotor system is inves- tigated, where the low-frequency vibration of steam turbines can be caused by the gas exciting force. The empirical parameters of gas exciting force of the Muszynska model are obtained by using the results of computational fluid dynamics （CFD）. Based on the multiple scale method, the 1：2 subharmonic resonance response of the dynamic system is gained by truncating the system with three orders. The transition sets and the local bifurcations diagrams of the dynamics system are presented by employing the singular theory analysis. Meanwhile, the existence conditions of subharmonic resonance non-zero solutions of the dynamic system are obtained, which provides a new theoretical basis in recognizing and protecting the rotor from the subharmonic resonant failure in the turbine machinery.
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.
