scholarly journals Application of Multiple Scale Analysis on the Parametric Resonance of Continuous Gyroscopic Systems

1998 ◽  
Vol 120 (1) ◽  
pp. 303-305 ◽  
Author(s):  
Jen-San Chen ◽  
Yu-Ran Lin
Keyword(s):  
Parametric Resonance ◽  
Degrees Of Freedom ◽  
Multiple Scale ◽  
Scale Analysis ◽  
Complex State ◽  
Multiple Degrees Of Freedom ◽  
First Order ◽  
Rayleigh Beam ◽  
Gyroscopic Systems ◽  
Multiple Scale Analysis

Nayfeh and Mook (1977) presented a multiple scale analysis on the parametric resonance of a non-gyroscopic system with multiple degrees of freedom. This Note extends their method to the case of continuous gyroscopic systems Orthogonality properties among the eigenfunctions of the unloaded system in the complex state space are used to discretize the equation of motion into a set of first order differential equations. Multiple scale method is then employed to study the parametric resonance of the loaded system up to the second order perturbation. A spinning Rayleigh beam under pulsating axial load is studied as an example.

Multiple scale analysis of factors influencing the distribution of an invasive aquatic grass

2008 ◽  
Vol 11 (8) ◽  
pp. 1903-1912 ◽  
Author(s):  
Sarina E. Loo ◽  
Ralph Mac Nally ◽  
Dennis J. O’Dowd ◽  
James R. Thomson ◽  
P. S. Lake
Keyword(s):  
Multiple Scale ◽  
Scale Analysis ◽  
Factors Influencing ◽  
Multiple Scale Analysis

scholarly journals Experiment and Theory on the Nonlinear Vibration of a Shallow Arch Under Harmonic Excitation at the End

2005 ◽  
Vol 74 (6) ◽  
pp. 1061-1070 ◽  
Author(s):  
Jen-San Chen ◽  
Cheng-Han Yang
Keyword(s):  
Steady State ◽  
Excitation Frequency ◽  
Multiple Scale ◽  
Steady State Response ◽  
Scale Analysis ◽  
Jump Phenomenon ◽  
Shallow Arch ◽  
State Response ◽  
Geometrical Imperfection ◽  
Multiple Scale Analysis

In this paper we study, both theoretically and experimentally, the nonlinear vibration of a shallow arch with one end attached to an electro-mechanical shaker. In the experiment we generate harmonic magnetic force on the central core of the shaker by controlling the electric current flowing into the shaker. The end motion of the arch is in general not harmonic, especially when the amplitude of lateral vibration is large. In the case when the excitation frequency is close to the nth natural frequency of the arch, we found that geometrical imperfection is the key for the nth mode to be excited. Analytical formula relating the amplitude of the steady state response and the geometrical imperfection can be derived via a multiple scale analysis. In the case when the excitation frequency is close to two times of the nth natural frequency two stable steady state responses can exist simultaneously. As a consequence jump phenomenon is observed when the excitation frequency sweeps upward. The effect of geometrical imperfection on the steady state response is minimal in this case. The multiple scale analysis not only predicts the amplitudes and phases of both the stable and unstable solutions, but also predicts analytically the frequency at which jump phenomenon occurs.

scholarly journals Multiple-scale analysis of quantum systems

1996 ◽  
Vol 54 (12) ◽  
pp. 7710-7723 ◽  
Author(s):  
Carl M. Bender ◽  
Luís M. A. Bettencourt
Keyword(s):  
Multiple Scale ◽  
Quantum Systems ◽  
Scale Analysis ◽  
Multiple Scale Analysis
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