Nonlinear Coupling Vibration Research Articles

Nonlinear Vibration Analysis for a Jeffcott Rotor with Seal and Air-Film Bearing Excitations

The nonlinear coupling vibration and bifurcation of a high-speed centrifugal compressor with a labyrinth seal and two air-film journal bearings are presented in this paper. The rotary shaft and disk are modeled as a rigid Jeffcott rotor. Muszynska's model is used to express the seal force with multiple parameters. For air-film journal bearings, the model proposed by Zhang et al. is adopted to express unsteady bearing forces. The Runge-Kutta method is used to numerically determine the vibration responses of the disk center and the bearings. Bifurcation diagrams for transverse motion of the rotor are presented with parameters of rotation speed and pressure drop of the seal. Multiple subharmonic, periodic, and quasiperiodic motions are presented with two seal-pressure drops. The bifurcation characteristics show inherent interactions between forces of the air-film bearings and the seal, presenting more complicated rotor dynamics than the one with either of the forces alone. Bifurcation diagrams are obtained with parameters of pressure drop and seal length determined for the sake of operation safety.

Solid-liquid Coupling Analysis of Valveless Micropumps Dynamic Characteristics

According to the working principle of valveless micropumps,the theoretical analysis of membrane-fluid coupling vibration process is carried out and a non-linear coupling vibration equation is developed.The approximate solution is obtained by using Galerkin weighted minimum residual method.And the relations among the damping coefficient,the driving force,the natural frequency of membrane and the amplitude of membrane,phase difference,and the flow rate of valveless pumps ate discussed. Theoretical analysis shows that when the damping coefficient is small,the amplitude increases near the first order natural frequency. With the increasing of damping coefficient,the resistance of fluid increases gradually on the membrane.At the same time,the amplitude decreases rapidly and phase difference tends to 90°faster with the increasing frequency.When the driving force is certain, the lower the first order frequency of the membrane is,the greater the amplitude can achieve in low frequency.As for the flow rate,it will reach the maximum value quickly in low frequency.Moreover,the greater the damping coefficient is,the lower the natural frequency of pump membrane is,the greater the driving force is,the flux will reach its maximum value more quickly.

Analyses of Hopf Bifurcation Characteristics in Longitudinal Power Systems by Using a Nonlinear Coupled Vibration Model

Power system is a large dynamic system, which includes a lot of nonlinear elements. According to the nonlinear analyses using Hopf bifurcation theory, it can be detected that a limit cycle exists around an operating point, which may affect the global stability of power system significantly. The authors have proposed a numerical method to analyze the nonlinear characteristics in power systems by observing the power swing after some perturbation where the coefficients of nonlinear terms are determined by the least squares method. In this paper the method is modified for the application to a longitudinally interconnected power system including an excitation system to consider the inuence of the modal interaction on the nonlinear phenomena. In this method the system is approximated by a nonlinear coupled vibration model. Then the bifurcation characteristics are evaluated numerically based on the approximate model. The method has been applied to the low-frequency oscillation in IEEJ WEST10-machine system.

1001 リード線により生じる非線形連成振動を考慮した変電機器の振動応答特性(GS-10 振動)

1001 リード線により生じる非線形連成振動を考慮した変電機器の振動応答特性(GS-10 振動)

Nonlinear Coupled Vibration Response of Serpentine Belt Drive Systems

This theoretical and experimental study identifies a key nonlinear mechanism that promotes strongly coupled dynamics of serpentine belt drive systems. Attention is focused on a prototypical three-pulley system that contains the essential features of automotive serpentine drives having automatic (spring-loaded) tensioners. A theoretical model is presented that describes pulley and tensioner arm rotations, and longitudinal and transverse belt vibration response. A recent investigation demonstrates that infinitesimal belt stretching creates a linear mechanism that couples transverse belt vibration to tensioner arm rotation. Here, it is further demonstrated that finite belt stretching creates a nonlinear mechanism that may lead to strong coupling between pulley/tensioner arm rotation and transverse belt vibration, in the presence of an internal resonance. Theoretical and experimental results confirm the existence of this nonlinear coupling mechanism. In particular, it is shown that very large transverse belt vibrations can result from small resonant torque pulses applied to the crankshaft or accessory pulleys. These large amplitude transverse vibrations are particularly sensitive to seemingly small changes in the rotational mode characteristics.

Random responses of a two-degree-of-freedom structure with strongly nonlinear coupling and parametric interaction

This paper investigates the random responses of a TDOF structure with strongly nonlinear coupling and parametric vibration. With the nonlinear coupling of inertia in the equations of motion of the system being removed by successive elimination, the non-Gaussian moment equation method (NGM) is applied and 69 moment equations are integrated with central cumulative truncation technique. The stochastic central difference-cum-statistical linearization method(SCD-SL) and the digital simulation method(DSM) are also used. A comparison of results by different methods are given and the SCD-SL method is the most efficient method.

断面の楕円化に伴う : 円筒殼の非線型振動に関する研究

Up to this time, some characteristic phenomenon about sway of thin circular cylindrical shells had been reported by J. S. M. E. (Genshiro Taishin Sekkeiho Kenkyu Bunkakai). Considering this characteristic phenomenon as nonlinear coupling vibration originated from periodical change (ovalization) of the form of cylinder section and parametric oscillation, we have explained this phenomena theoretically in this report. Here, in analyzing this problem, the new-assumptions was introduced, that there are simultaneously two kinds of mode in the circumferential direction for the former and two kinds of frequency for the latter. Analyzing the sway of cylindrical shell, Galerkins method was used for coupled mode and method of averaging for coupled frequency. In this reports the purpose of considering nonlinearity in strain displacement relation lies not in explanating effects of large amplitude so far thought of, but in the effect of coupling vibration for two mode and two frequency. It has been shown that the analytical result based on the above stated assumption and method coincided well with the experimental observation.