According to theoretical predictions one can change the effective stiffness or natural frequency of an elastic structure by employing harmonic excitation of very high frequency. Here we examine this effect for a hinged-hinged beam subjected to longitudinal harmonic excitation. A simple analytical expression is presented, that relates the effective natural frequencies of the beam to the intensity of harmonic excitation. Experiments performed with a laboratory beam confirm the general tendency of this prediction, though there are discrepancies that cannot be explained in the framework of the linear Galerkin-discretized beam model. [S0021-8936(00)01302-7]

1.
Chelomei
,
V. N.
,
1956
, “
On the Possibility of Increasing the Stability of Elastic Systems by Using Vibration
,”
Dokl. Akad. Nauk
,
110
, pp.
345
347
(in Russian).
2.
Stephenson
,
A.
,
1908
, “
On a New Type of Dynamical Stability
,”
Mem. Proc. Manch. Lit. Philos. Soc.
,
52
, pp.
1
10
.
3.
Kapitza
,
P. L.
,
1951
, “
Dynamic Stability of a Pendulum With an Oscillating Point of Suspension
,”
Zh. Eksp. Teor. Fiz. Pis'ma Red.
,
21
, pp.
588
597
(in Russian).
4.
Blekhman, I. I., 2000, Vibrational Mechanics, World Scientific Publishing Company, Singapore.
5.
Chelomei
,
V. N.
,
1983
, “
Mechanical Paradoxes Caused by Vibrations
,”
Sov. Phys. Dokl.
,
28
, pp.
387
390
.
6.
Blekhman, I. I., 2000, “Forming the Properties of Nonlinear Mechanical Systems by Means of Vibration,” Proceedings of the IUTAM/IFToMM Symposium on Synthesis of Nonlinear Dynamical Systems, Riga, Latvia, 1998, Kluwer, Dordrecht, The Netherlands.
7.
Jensen, J. S., 1996, “Transport of Continuous Material in Vibrating Pipes,” Proceedings of the EUROMECH 2nd European Nonlinear Oscillation Conference, Vol. 1, Czech Technological University, Prague, Czech Republic, pp. 211–214.
8.
Jensen
,
J. S.
,
1997
, “
Fluid Transport due to Nonlinear Fluid-Structure Interaction
,”
J. Fluids Struct.
,
11
, pp.
327
344
.
9.
Thomsen, J. J., 1996, “Vibration Induced Sliding of Mass: Non-trivial Effects of Rotatory Inertia,” Proceedings of the EUROMECH 2nd European Nonlinear Oscillation Conference, Vol. 1, Czech Technological University, Prague, Czech Republic, pp. 455–458.
10.
Thomsen
,
J. J.
,
1996
, “
Vibration Suppression by Using Self-Arranging Mass: Effects of Adding Restoring Force
,”
J. Sound Vib.
,
197
, pp.
403
425
.
11.
Thomsen, J. J., 1997, Vibrations and Stability, Order and Chaos, McGraw-Hill, London.
12.
Miranda
,
E. C.
, and
Thomsen
,
J. J.
,
1998
, “
Vibration Induced Sliding: Theory and Experiments for a Beam With a Spring-Loaded Mass
,”
Nonlinear Dyn.
,
16
, pp.
167
186
.
13.
Thomsen
,
J. J.
,
1999
, “
Using Fast Vibrations to Quench Friction-Induced Oscillations
J. Sound Vib.
, ,
228
, No.
5
, pp.
1079
1102
.
14.
Thomsen, J. J., 2000, “Vibration-Induced Displacement Using High-Frequency Resonators and Friction Layers,” Proceedings of the IUTAM/IFToMM Symposium on Synthesis of Nonlinear Dynamical Systems, Riga, Latvia, 1998, Kluwer, Dordrecht, The Netherlands.
15.
Blekhman
,
I. I.
, and
Malakhova
,
O. Z.
,
1986
, “
Quasiequilibrium Positions of the Chelomei Pendulum
,”
Sov. Phys. Dokl.
,
31
, pp.
229
231
.
16.
Chelomei
,
S. V.
,
1981
, “
Dynamic Stability Upon High-Frequency Parametric Excitation
,”
Sov. Phys. Dokl.
,
26
, pp.
390
392
.
17.
Hansen, M. H., 2000, “Non-trivial Effects of High-Frequency Excitation of Spinning Disks,” J. Sound Vib., accepted for publication.
18.
Jensen
,
J. S.
,
1998
, “
Non-linear Dynamics of the Follower-Loaded Double Pendulum With Added Support-Excitation
,”
J. Sound Vib.
,
215
, pp.
125
142
.
19.
Jensen
,
J. S.
,
1999
, “
Articulated Pipes Conveying Fluid Pulsating With High Frequency
,”
Nonlinear Dyn.
,
19
, pp.
171
191
.
20.
Jensen
,
J. S.
,
1999
, “
Buckling of an Elastic Beam With Added High-Frequency Excitation
,”
Int. J. Non-Linear Mech.
,
32
, pp.
43
54
.
21.
Jensen, J. S., 2000, “Effects of High-Frequency Bi-directional Support-Excitation of the Follower-Loaded Double Pendulum,” Proceedings of the IUTAM/IFToMM Symposium on Synthesis of Nonlinear Dynamical Systems, Riga, Latvia, 1998, Kluwer, Dordrecht, The Netherlands.
22.
Schmitt
,
J. M.
, and
Bayly
,
P. V.
,
1998
, “
Bifurcations in the Mean Angle of a Horizontally Shaken Pendulum: Analysis and Experiment
,”
Nonlinear Dyn.
,
15
, pp.
1
14
.
23.
Shapiro
,
B.
, and
Zinn
,
B. T.
,
1997
, “
High-Frequency Nonlinear Vibrational Control
,”
IEEE Trans. Autom. Control
,
42
, pp.
83
89
.
24.
Tcherniak
,
D. M.
,
1999
, “
The Influence of Fast Excitation on a Continuous System
J. Sound Vib.
, ,
227
, No.
2
, pp.
343
360
.
25.
Tcherniak, D. M., 2000, “Using Fast Vibration to Change the Nonlinear Properties of Mechanical Systems,” Proceedings of the IUTAM/IFToMM Symposium on Synthesis of Nonlinear Dynamical Systems, Riga, Latvia, 1998, Kluwer, Dordrecht, The Netherlands.
26.
Tcherniak
,
D. M.
, and
Thomsen
,
J. J.
,
1998
, “
Slow Effects of Fast Harmonic Excitation for Elastic Structures
,”
Nonlinear Dyn.
,
17
, pp.
227
246
.
27.
Weibel
,
S.
,
Kaper
,
T. J.
, and
Baillieul
,
J.
,
1997
, “
Global Dynamics of a Rapidly Forced Cart and Pendulum
,”
Nonlinear Dyn.
,
13
, pp.
131
170
.
28.
Nayfeh, A. H., and Mook, D. T., 1979, Nonlinear Oscillations, John Wiley and Sons, New York.
You do not currently have access to this content.