Constant energy control by time-varying gain for steady-state oscillation of thermoacoustic engines to estimate critical temperature ratio

2016 ◽  
Author(s):  
Yasuhide Kobayashi ◽  
Kazuaki Sakurai ◽  
Noboru Yamada
Keyword(s):  
Steady State ◽  
Critical Temperature ◽  
Time Varying ◽  
Temperature Ratio ◽  
Energy Control ◽  
Constant Energy ◽  
Thermoacoustic Engines ◽  
Steady State Oscillation

On Stability of a Nonlinear, Periodically Time Varying, Rotating Blade

2011 ◽  
Author(s):  
Fengxia Wang
Keyword(s):  
Steady State ◽  
Differential Equations ◽  
Nonlinear Partial Differential Equations ◽  
Multiple Time ◽  
Time Varying ◽  
Rotating Blade ◽  
Stability And Bifurcation ◽  
Geometric Stiffening ◽  
Rotational Motions ◽  
The Stability

This paper discusses the stability of a periodically time-varying, spinning blade with cubic geometric nonlinearity. The modal reduction method is adopted to simplify the nonlinear partial differential equations to the ordinary differential equations, and the geometric stiffening is approximated by the axial inertia membrane force. The method of multiple time scale is employed to study the steady state motions, the corresponding stability and bifurcation for such a periodically time-varying rotating blade. The backbone curves for steady-state motions are achieved, and the parameter map for stability and bifurcation is developed. Illustration of the steady-state motions is presented for an understanding of rotational motions of the rotating blade.

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