Constructing resonance calabashes of Hill's equations using step potentials

2000 ◽  
Vol 129 (1) ◽  
pp. 153-164 ◽  
Author(s):  
MEIRONG ZHANG ◽  
SHAOBO GAN
Keyword(s):  
Hill’S Equations

On a family of Hill's equations in the complex field

1991 ◽  
Vol 52 (3) ◽  
pp. 277-291 ◽  
Author(s):  
Amar Makhlouf ◽  
Fernand Nahon
Keyword(s):  
Complex Field ◽  
Hill’S Equations

Stability and Vibration of a Rotating Circular Plate Subjected to Stationary In-Plane Edge Loads

1996 ◽  
Vol 63 (1) ◽  
pp. 121-127 ◽  
Author(s):  
I. Y. Shen ◽  
Y. Song
Keyword(s):  
Circular Plate ◽  
Rotational Speed ◽  
Multiple Scales ◽  
Method Of Multiple Scales ◽  
Parametric Instability ◽  
Single Mode ◽  
Equation Of Motion ◽  
Asymmetric Membrane ◽  
Parametric Resonances ◽  
Hill’S Equations

This paper predicts transverse vibration and stability of a rotating circular plate subjected to stationary, in-plane, concentrated edge loads. First of all, the equation of motion is discretized in a plate-based coordinate system resulting in a set of coupled Hill’s equations. Through use of the method of multiple scales, stability of the rotating plate is predicted in closed form in terms of the rotational speed and the in-plane edge loads. The asymmetric membrane stresses resulting from the stationary in-plane edge loads will transversely excite the rotating plates to single-mode parametric resonances as well as combination resonances at supercritical speed. In addition, introduction of plate damping will suppress the parametric instability when normalized edge loads are small. Moreover, the radial in-plane edge load dominates the rotational speed at which the instability occurs, and the tangential in-plane edge load dominates the width of the instability zones.

Resonance Pockets of Hill's Equations with Two-Step Potentials

2000 ◽  
Vol 32 (3) ◽  
pp. 651-664 ◽  
Author(s):  
Shaobo Gan ◽  
Meirong Zhang
Keyword(s):  
Hill’S Equations
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