A computational and experimental study of a uniform cantilever beam with a tip mass under base excitation was performed. The beam was excited at various levels of base displacement to provoke tip displacements greater than 15% of the beam length. Damping and yield stress of the beam were both considered. It was found that a large tip displacement causes nonlinear inertial (NLI) and structural (NLS) effects to arise. Each of the structural and inertial nonlinearities has an opposite effect on the resulting resonance frequency, which are nearly mutually canceling. The result was that resonant frequency calculated using the full nonlinear (FNL) model was essentially equal to the value calculated by linear (LIN) theory, and the tip displacement amplitude varied only modestly from the LIN value. It was also observed that the damping in this system is likely nonlinear, and depends on tip displacement amplitude. A theoretical model for fluid damping is suggested. Initial investigation shows encouraging agreement between the theoretical fluid damping and the measured values.

References

1.
Tang
,
D.
,
Zhao
,
M.
, and
Dowell
,
E. H.
,
2014
, “
Inextensible Beam and Plate Theory: Computational Analysis and Comparison With Experiment
,”
ASME J. Appl. Mech.
,
81
(
6
), p.
061009
.
2.
Dowell
,
E.
, and
McHugh
,
K.
,
2016
, “
Equations of Motion for an Inextensible Beam Undergoing Large Deflections
,”
ASME J. Appl. Mech.
,
83
(
5
), p.
051007
.
3.
Herişanu
,
N.
, and
Marinca
,
V.
,
2010
, “
Explicit Analytical Approximation to Large-Amplitude Non-Linear Oscillations of a Uniform Cantilever Beam Carrying an Intermediate Lumped Mass and Rotary Inertia
,”
Meccanica
,
45
(
6
), pp.
847
855
.
4.
Das
,
D.
,
Sahoo
,
P.
, and
Saha
,
K.
,
2012
, “
A Numerical Analysis of Large Amplitude Beam Vibration Under Different Boundary Conditions and Excitation Patterns
,”
J. Vib. Control
,
18
(
12
), pp.
1900
1915
.
5.
Novozhilov
,
V.
,
1953
,
Foundations of the Nonlinear Theory of Elasticity
,
Graylock Press
, Mineola, NY.
6.
Qian
,
Y.
,
Lai
,
S.
,
Zhang
,
W.
, and
Xiang
,
Y.
,
2011
, “
Study on Asymptotic Analytical Solutions Using Ham for Strongly Nonlinear Vibrations of a Restrained Cantilever Beam With an Intermediate Lumped Mass
,”
Numer. Algorithms
,
58
(
3
), pp.
293
314
.
7.
Qaisi
,
M. I.
,
1993
, “
Application of the Harmonic Balance Principle to the Nonlinear Free Vibration of Beams
,”
Appl. Acoust.
,
40
(
2
), pp.
141
151
.
8.
Pillai
,
S.
, and
Rao
,
B. N.
,
1992
, “
On Nonlinear Free Vibrations of Simply Supported Uniform Beams
,”
J. Sound Vib.
,
159
(
3
), pp.
527
531
.
9.
Azrar
,
L.
,
Benamar
,
R.
, and
White
,
R.
,
1999
, “
Semi-Analytical Approach to the Non-Linear Dynamic Response Problem of S–S and C–C Beams at Large Vibration Amplitudes—Part I: General Theory and Application to the Single Mode Approach to Free and Forced Vibration Analysis
,”
J. Sound Vib.
,
224
(
2
), pp.
183
207
.
10.
Tang
,
D.
,
Yamamoto
,
H.
, and
Dowell
,
E.
,
2003
, “
Flutter and Limit Cycle Oscillations of Two-Dimensional Panels in Three-Dimensional Axial Flow
,”
J. Fluids Struct.
,
17
(
2
), pp.
225
242
.
11.
Paidoussis
,
M.
,
2004
,
Fluid-Structure Interactions: Slender Structures and Axial Flow
, Vol.
2
,
Academic Press
, London.
12.
Simmonds
,
J.
, and
Libai
,
A.
,
1979
, “
Exact Equations for the Inextensional Deformation of Cantilevered Plates
,”
ASME J. Appl. Mech.
,
46
(
3
), pp.
631
636
.
13.
Simmonds
,
J.
, and
Libai
,
A.
,
1979
, “
Alternate Exact Equations for the Inextensional Deformation of Arbitrary, Quadrilateral, and Triangular Plates
,”
ASME J. Appl. Mech.
,
46
(
4
), pp.
895
900
.
14.
Simmonds
,
J.
,
1981
, “
Exact Equations for the Large Inextensional Motion of Elastic Plates
,”
ASME J. Appl. Mech.
,
48
(
1
), pp.
109
112
.
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