An experimental and theoretical investigation into the first- and second-mode responses of a parametrically excited slender cantilever beam is presented. Inclusion of quadratic damping in the analytical model significantly improves the agreement between the experimental and theoretical results. In addition, the experimental results verify that the often ignored nonlinear curvature terms play a dominant role in the response of the first mode and that the nonlinear inertia terms play a dominant role in the response of the second mode.

1.
Bolotin, V. v., 1964, The Dynamic Stability of Elastic Systems, Translated by V. I. Weingarten et al., Holden-Day, CA.
2.
Crespo da Silva
M. R. M.
, and
Glynn
C. C.
,
1978
a, “
Non-Linear Flexural-Flexural-Torsional Dynamics of Inextensional Beams—I. Equations of Motion
,”
J. Struct. Mech.
, Vol.
6
, No.
4
, pp.
437
448
.
3.
Crespo da Silva
M. R. M.
, and
Glynn
C. C.
,
1978
b, “
Non-Linear Flexural-Flexural-Torsional Dynamics of Inextensional Beams—II. Forced Motion
,”
J. Struct. Mech.
, Vol.
6
, No.
4
, pp.
449
461
.
4.
Dugundji
J.
, and
Mukhopadhyay
V.
,
1973
, “
Lateral Bending-Torsion Vibrations of a Thin Beam Under Parametric Excitation
,”
ASME Journal of Applied Mechanics
, Vol.
40
, pp.
693
698
.
5.
Evan-Iwanowski
R. M.
,
Sanford
W. F.
, and
Kehagioglou
T.
,
1970
, “
Nonstationary Parametric Response of a Non-Linear Column
,”
Dev. Theor. Appl. Mech.
, Vol.
5
pp.
715
743
.
6.
Evensen
H. A.
, and
Evan-Iwanowski
R. M.
,
1966
, “
Effects of Longitudinal Inertia upon the Parametric Response of Elastic Columns
,”
ASME Journal of Applied Mechanics
, Vol.
33
, pp.
141
148
.
7.
Haight
E. C.
, and
King
W. W.
,
1971
, “
Stability of Parametrically Excited Vibrations of an Elastic Rod
,”
Dev. Theor. Appl. Mech.
, Vol.
5
pp.
677
714
.
8.
Moody
M. L.
,
1967
, “
The Parametric Response of Imperfect Columns
,”
Developments in Mechanics
, Vol.
4
, Proceedings of the Tenth Midwestern Mechanics Conference, pp.
329
346
.
9.
Nayfeh, A. H., 1981, Introduction to Perturbation Techniques, Wiley, New York.
10.
Nayfeh, A. H., and Balachandran, B., 1995, Applied Nonlinear Dynamics, Wiley, New York.
11.
Nayfeh, A. H., and Mook, D. T., 1979, Nonlinear Oscillations, Wiley, New York.
12.
Nayfeh
A. H.
, and
Pai
P. F.
,
1989
, “
Non-Linear Non-Planar Parametric Responses of an Inextensional Beam
,”
Int. J. Non-lin. Mech.
, Vol.
24
, No.
2
, pp.
139
158
.
This content is only available via PDF.
You do not currently have access to this content.