We study the symmetries admitted by the amplitude equations governing the nonlinear nonplanar parametric responses of an inextensional beam (Nayfeh and Pai, 1989). As a result of these symmetries, the differential equations can be integrated in two limiting cases.

Issue Section:
Brief Notes
Topics:
Differential equations, Resonance
1.
Feng
Z. C.
, and
Sethna
P. R.
,
1990
, “
Global bifurcation and chaos in parametrically forced systems with one-one resonance
,”
Dynamics and Stability of Systems
, Vol.
5
, pp.
201
–
225
.
2.
Feng
Z.
, and
Wiggins
S.
,
1993
, “
On the existence of chaos in a class of two-degree-of-freedom, damped, strongly parametrically forced mechanical systems with broken O(2) symmetry
,”
ZAMP
, Vol.
44
, pp.
201
–
248
.
3.
Nayfeh
A. H.
, and
Pai
P. F.
,
1989
, “
Non-linear non-planar parametric responses of an inextensional beam
,”
International Journal of Nonlinear Mechanics
, Vol.
24
, pp.
139
–
158
.
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