Analysis on Bistable Response of a Disk-Rod-Fastening Rotor

2011 ◽  
Vol 199-200 ◽  
pp. 983-987
Author(s):  
Li Cheng ◽  
Zheng Wen Qian ◽  
Wei Chen
Keyword(s):  
Contact Surface ◽  
Harmonic Balance ◽  
Harmonic Balance Method ◽  
Equation Of Motion ◽  
Simplified Model ◽  
Nonlinear Stiffness ◽  
Contact Effect ◽  
Bending Resistance ◽  
Rod Fastening Rotor ◽  
Rotor Stiffness

In the view of the fault of bistable response appeared in the disk-rod-fastening rotor, the peculiar structure of this kind rotor was taken into account in this paper. By considering the influence of contact effect of discontinuous interfaces on the rotor stiffness, the tie-rod and the contact surface between the wheel disks were equated to a bending resistance spring with nonlinear stiffness. Then the equation of motion of the disk-rod-fastening rotor was put forward according to this simplification. The vibration characteristics of rotor was calculated by the harmonic balance method that combined with the predict-correct and homotopy arithmetic. The bistable response behaviors recurred in this simplified model was much closer to the measured results in flying. The study showed that the nonlinear factor of stiffness, resulted from the contact effect of discontinuous interfaces, was the main reason which led to the appearance of bistable response in the disk-rod-fastening rotor.

Stability Analysis of an Articulated Loading Platform in Regular Sea

2007 ◽  
Vol 3 (1) ◽  
Author(s):  
A. K. Banik ◽  
T. K. Datta
Keyword(s):  
Harmonic Balance ◽  
Harmonic Wave ◽  
Harmonic Balance Method ◽  
Equation Of Motion ◽  
Damping Term ◽  
Incremental Harmonic Balance Method ◽  
Left Hand ◽  
Hydrodynamic Damping ◽  
Incremental Harmonic Balance ◽  
The Right

Stability of the response of an articulated loading platform under regular wave, modeled as a SDOF nonlinear oscillator, is investigated. Relative velocity square drag force for harmonic wave appearing in the right hand side of the equation of motion is mathematically treated to bring the velocity dependent nonlinear hydrodynamic damping term to the left hand side of the equation of motion. Use of these two techniques makes the equation of motion amenable to the application of method IHBC. In order to trace different branches of the response curve and investigate different instability phenomena that may exist, the commonly used incremental harmonic balance method (IHB) is modified and integrated with an arc-length continuation technique to develop into incremental harmonic balance continuation (IHBC) method. Further, a technique for treating the nonlinear hydrodynamic damping term using a concept of distribution theory has been developed. The stability of the solution is investigated by the Floquet theory using Hsu’s scheme. The stable solutions obtained by the IHBC method are compared with those obtained by the numerical integration of equation of motion wherever applicable.

Dynamical analysis of vibratory feeder and feeding parts considering interactions by an improved increment harmonic balance method

2014 ◽  
Vol 229 (6) ◽  
pp. 1029-1040 ◽  
Author(s):  
Xiangxi Kong ◽  
Xueliang Zhang ◽  
Qinliang Li ◽  
Bangchun Wen
Keyword(s):  
Discrete Element Method ◽  
Nonlinear Dynamic ◽  
Dynamic Problem ◽  
Harmonic Balance ◽  
Harmonic Balance Method ◽  
Balance Method ◽  
Dynamical Analysis ◽  
Simplified Model ◽  
Vibratory Feeder ◽  
Nonlinear Dynamic Problem

Vibratory feeder is known as one of major machines in various industries. The feeding parts in a vibratory feeder are experiencing repeated discontinuous friction that can be considered as a typical strong nonlinear dynamic problem. It is very significant to obtain the motion of parts under different alternating loads for the design of vibratory feeder. An analytical model of parts’ motion in sliding regime was constructed and verified with a simplified model based on discrete element method. An improved increment harmonic balance method was proposed to obtain the dynamic behaviors of vibratory feeder and the motion of feeding parts. In contrast to previous researches, we considered the interactions between vibratory feeder and parts in detail, not only containing the effects of the dynamics of vibratory feeder on the motion of parts but also the motion of parts on vibratory feeder. Finally, studying the interactions for various parts’ masses in different frequencies, the motion of parts had a significant effect on the dynamics of vibratory feeder. In reverse, the alterations of the dynamics of vibratory feeder influenced the motion of parts and conveying speed. In the design of vibratory feeder, the interactions between vibratory feeder and parts should not be neglected.

Stability Analysis of TLP Tethers Under Vortex-Induced Oscillations

2008 ◽  
Vol 131 (1) ◽  
Author(s):  
A. K. Banik ◽  
T. K. Datta
Keyword(s):  
Harmonic Balance ◽  
Harmonic Balance Method ◽  
Equation Of Motion ◽  
Incremental Harmonic Balance Method ◽  
Incremental Harmonic Balance ◽  
The Stability ◽  
Lock In ◽  
Continuation Technique ◽  
Mode Response ◽  
Stability Of The Solution

The vortex-induced oscillation of TLP tether is investigated in the vicinity of lock-in condition. The vortex shedding is caused purely due to current, which may vary across the depth of the sea. The vibration of TLP is modeled as a SDOF problem by assuming that the first mode response of the tether dominates the motion. Nonlinearity in the equation of motion is produced due to the relative velocity squared drag force. In order to trace different branches of the response curve and investigate different instability phenomena that may exist, an arc-length continuation technique along with the incremental harmonic balance method (IHBC) is employed. A procedure for treating the nonlinear term using distribution theory is presented so that the equation of motion is transformed to a form amenable to the application of IHBC. The stability of the solution is investigated by the Floquet theory using Hsu’s scheme.

scholarly journals Prediction of Transient Pressure Fluctuations within a Low-Pressure Turbine Cascade Using a Lanczos-Filtered Harmonic Balance Method

2021 ◽  
Vol 6 (3) ◽  
pp. 25
Author(s):  
Jan Philipp Heners ◽  
Stephan Stotz ◽  
Annette Krosse ◽  
Detlef Korte ◽  
Maximilian Beck ◽  
...  
Keyword(s):  
Turbulence Model ◽  
Harmonic Balance ◽  
Separation Bubble ◽  
Pressure Fluctuations ◽  
Harmonic Balance Method ◽  
Low Pressure ◽  
Filter Method ◽  
Turbine Cascade ◽  
Transient Pressure ◽  
Low Pressure Turbine

Unsteady pressure fluctuations measured by fast-response pressure transducers mounted in a low-pressure turbine cascade are compared to unsteady simulation results. Three differing simulation approaches are considered, one time-integration method and two harmonic balance methods either resolving or averaging the time-dependent components within the turbulence model. The observations are used to evaluate the capability of the harmonic balance solver to predict the transient pressure fluctuations acting on the investigated stator surface. Wakes of an upstream rotor are generated by moving cylindrical bars at a prescribed rotational speed that refers to a frequency of f∼500 Hz. The excitation at the rear part of the suction side is essentially driven by the presence of a separation bubble and is therefore highly dependent on the unsteady behavior of turbulence. In order to increase the stability of the investigated harmonic balance solver, a developed Lanczos-type filter method is applied if the turbulence model is considered in an unsteady fashion.

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