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.

Issue Section:
Technical Briefs
Topics:
Resonance, Degrees of freedom, Differential equations, Eigenfunctions, Equations of motion, Spin (Aerodynamics), Spinning (Textile), Stress
1.
Chen
J.-S.
, and
Bogy
D. B.
,
1992
, “
Mathematical Structure of Modal Interactions in a Spinning Disk-Stationary Load System
,”
ASME Journal of Applied Mechanics
, Vol.
39
, No.
2
, Part 1, pp.
390
–
397
.
2.
Nayfeh
A. H.
, and
Mook
D. T.
,
1977
, “
Parametric Excitations of Linear Systems Having Many Degrees of Freedom
,”
Journal of Acoustical Society of America
, Vol.
62
, pp.
375
–
381
.
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