Three-to-one Internal Resonance in The Non Linear Oscillation of Shallow Arch

2005 ◽  
Vol 72 (6) ◽  
pp. 439-450 ◽  
Author(s):  
A F El-Bassiouny
Keyword(s):  
Internal Resonance ◽  
Shallow Arch ◽  
Non Linear ◽  
Linear Oscillation

Non-Linear Effects of Vibration in Gas Turbine Engines With Two or Three Rotors

2002 ◽  
Author(s):  
J. Pismenny ◽  
Y. Levy
Keyword(s):  
Complex System ◽  
Gas Turbine ◽  
Turbine Engines ◽  
Gas Turbine Engines ◽  
Practical Application ◽  
Turbine Engine ◽  
Non Linear ◽  
Linear Elements ◽  
Linear Effects ◽  
Linear Oscillation

The dependence of the vibration characteristics of gas turbine engines on the rotor speeds becomes highly complicated in engines with two and three rotors, both because of the simultaneous dynamic action of the multiple rotors and the ambiguous relationships between their speeds. In this paper, the gas turbine engine is analyzed in the context of the theory of non-linear oscillation — as a complex system comprising a large number of non-linear elements and multiple periodical forces of different frequencies (defined by the rotor speeds). This paper presents results, which indicate that the level of vibration can obtain critical values at certain relationships between the rotor speeds. As a practical application of this phenomena it is shown that the number of three-spool engines returns from the aircraft to the engine manufacturer, due to different kinds of malfunctions, for example due to activation of the “intensified vibration” alarm, may be approximately three times that of returns of analogous two-rotor engines.

scholarly journals Generalized Theory of Shell Flash and Accreting White Dwarfs

1981 ◽  
Vol 93 ◽  
pp. 191-206
Author(s):  
Daiichiro Sugimoto ◽  
Shigeki Miyaji
Keyword(s):  
White Dwarfs ◽  
Dissipative System ◽  
Finite Amplitude ◽  
Recurrence Time ◽  
Near Surface ◽  
Giant Stars ◽  
Deep Interior ◽  
Non Linear ◽  
Red Giant ◽  
Linear Oscillation

Shell flashes take place both in deep interior of red giant stars and near surface of accreting white dwarfs. Theories of shell flashes have been thus far presented piece by piece in different papers. It is the purpose of the present review to construct and generalize them in order to reach better understanding. A non-linear yet almost analytical theory is presented which treats the development of the shell flash in finite amplitude. Recurrence of the shell flashes is also shown to be well understood as a non-linear oscillation in dissipative system which tends to be its limit cycle. As a result strength of the peak energy-generation and recurrence time of the shell flashes are related with mass of the accreting white dwarfs, accretion rate, etc.

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