The dynamic response of a beam-tip mass-pendulum system subjected to a sinusoidal excitation is investigated. A simple pendulum mounted to a tip mass of a beam is used as a vibration absorber. The nonlinear equations of motion are developed to investigate the autoparametric interaction between the first two modes of the system. The nonlinear terms appear due to the curvature of the beam and the coupling effect between the beam and pendulum. Complete energy transfer between modes is shown to occur when the beam frequency is twice the pendulum frequency. Experimental results are compared with a theoretical solution obtained using numerical integration. The experimental results are in qualitative agreement with the theory.
Issue Section:
Research Papers
1.
Arnold, F. R., 1955, “Steady-State Behavior of Systems Provided with Nonlinear Dynamic Vibration Absorbers,” ASME Journal of Applied Mechanics, pp. 487–492.
2.
Banerjee, B., Bajaj, K. A., and Davies, P., 1993, “Second Order Averaging Study of an Autoparametric System,” 1993 ASME Design Technical Conferences-14th Biennial Conference on Mechanical Vibration and Noise, DE-Vol. 54, pp. 127–138.
3.
Crossley, F. R. E., and Conn, N. H., 1953, “The Forced Oscillation of the Centrifugal Pendulum with Wide Angles,” ASME Journal of Applied Mechanics, pp. 41–47.
4.
Ertas
A.
Chew
E. K.
1990
, “Nonlinear Dynamic Response of a Rotating Machine
,” International Journal of Nonlinear Mechanics
, Vol. 25
, pp. 241
–251
.5.
Ertas
A.
Mustafa
G.
1992
, “Real-Time Response of the Simple Pendulum: An Experimental Technique
,” Experimental Techniques
, Vol. 16
, No. 4
, pp. 33
–35
.6.
Eugene, S., 1961, “On the Parametric Excitation of Pendulum Type Vibration Absorber,” ASME Journal of Applied Mechanics, pp. 330–334.
7.
Gurgoze
M.
1986
, “On the Approximate Determination of the Fundamental Frequency of a Restrained Cantilever Beam Carrying a Tip Heavy Body
,” Journal of Sound and Vibration
, Vol. 105
, No. 3
, pp. 443
–449
.8.
Haddow
A. G.
Barr
A. D. S.
Mook
D. T.
1984
, “Theoretical and Experimental Study of Modal Interaction in a Two Degree of Freedom Structure
,” J. Sound Vib.
, Vol. 97
, No. 3
, pp. 451
–473
.9.
Hatwal
H.
1982
, “Notes on an Autoparametric Vibration Absorber
,” Journal of Sound and Vibration
, Vol. 83
, No. 3
, pp. 440
–443
.10.
Hatwall
H.
Mallik
A. K.
Ghosh
A.
1983
a, “Forced Nonlinear Oscillations of an Autoparametric Systems—Part 1: Periodic Response
,” ASME Journal of Applied Mechanics
, Vol. 50
, pp. 657
–662
.11.
Hatwall
H.
Mallik
A. K.
Ghosh
A.
1983
b, “Forced Nonlinear Oscillations of an Autoparametric Systems—Part 2: Chaotic Response
,” ASME Journal of Applied Mechanics
, Vol. 50
, pp. 663
–668
.12.
Haxton, R. S., and Barr, A. D. S., 1972, “The Autoparametric Vibration Absorber,” ASME Journal of Engineering for Industry, pp. 119–125.
13.
Hunt
J. B.
Nissen
J-C.
1982
, “The Broadband Dynamic Vibration Absorber
,” J. Sound Vib.
, Vol. 83
, No. 4
, pp. 573
–578
.14.
Ibrahim
R. A.
1975
, “Autoparametric Resonance in a Structure Containing Liquid—Part 1: Two mode Interaction
,” J. Sound Vib.
, Vol. 42
, No. 2
, pp. 159
–179
.15.
Ibrahim
R. A.
Barr
A. D. S.
1978
, “Parametric Vibration—Part 2: Mechanics of Nonlinear Problems
,” Shock Vib. Digest
, Vol. 10
, No. 2
, pp. 41
–57
.16.
Kojima
H.
Nagaya
K.
Shiraishi
H.
Yamashita
A.
1985
, “Nonlinear Vibration of a Beam with a Mass Subjected to Alternating Electromagnetic Force
,” Bulletin of JSME
, Vol. 28
, pp. 468
–474
.17.
Laura
P. A. A.
Pombo
J. L.
Susemihl
E. A.
1974
, “A Note on the Vibrations of a Clamped-Free Beam with a Mass at the Free End
,” Journal of Sound and Vibration
, Vol. 37
, No. 2
, pp. 161
–168
.18.
Liu
W. H.
Huang
C. C.
1988
, “Vibrations of a Constrained Beam Carrying a Heavy Tip Body
,” Journal of Sound and Vibration
, Vol. 123
, No. 1
, pp. 15
–29
.19.
Ludeke
C. A.
1942
, “Resonance
,” Journal of Applied Physics
, Vol. 13
, pp. 418
–423
.20.
Masri, S. F., and Caughey, T. K., 1966, “On the Stability of the Impact Damper,” ASME Journal of Applied Mechanics, pp. 586–592.
21.
Masri, S. F., 1972, “Theory of the Dynamic Vibration Neutralizer with Motion-Limiting Stops,” ASME Journal of Applied Mechanics, pp. 563–568.
22.
Nageswara Rao, B., Shastry, B. P., and Venkateswara Rao, G., 1986, “Large Deflections of a Cantilevered Beam Subjected to a Tip Concentrated Rotational Load,” Aeronautical Journal, pp. 262–266.
23.
Nissen
J.-C.
Popp
K.
Schmalhorst
B.
1985
, “Optimization of a Nonlinear Dynamic Vibration Absorber
,” Journal of Sound and Vibration
, Vol. 99
, No. 1
, pp. 149
–154
.24.
Sato
K.
Saito
H.
Otomi
K.
1978
, “The Parametric Response of a Horizontal Beam Carrying a Concentrated Mass Under Gravity
,” ASME Journal of Applied Mechanics
, Vol. 45
, pp. 643
–648
.25.
Shaw
J.
Shaw
S. W.
1989
, “The Onset of Chaos in a Two Degree of Freedom Impacting System
,” ASME Journal of Applied Mechanics
, Vol. 56
, pp. 168
–174
.26.
Struble, R. A., and Heinbockel, J. H., 1963, “Resonant Oscillation of a Beam-Pendulum System,” ASME Journal of Applied Mechanics, pp. 181–188.
27.
Storch
J.
Gates
S.
1985
, “Transverse Vibration and Buckling of a Cantilever Beam with Tip Body Under Axial Acceleration
,” Journal of Sound and Vibration
, Vol. 99
, No. 1
, pp. 43
–52
.28.
Szemplinska-Stupnica
W.
1969
, “On the Phenomenon of the Combination Type Resonance in Nonlinear Two Degree of Freedom Systems
,” Intl. J. Nonlinear Mech.
, Vol. 4
, No. 4
, pp. 336
–359
.29.
Tomas, J., 1967, “The Contribution to the Problem of Internal Resonance in a Nonlinear System with Two Degrees of Freedom,” Proc. 4th Conf. Nonlinear Oscill., Prague, pp. 503–508.
30.
Tondl
A.
1963
, “On the Combination Resonance of a Nonlinear Systems with Two Degrees of Freedom
,” Rev. Mech. Appl.
, Vol. 8
, No. 4
, pp. 573
–588
.31.
Verma
M. K.
Murthy
A. V. Krishna
1978
, “Non-linear Vibration of Non-uniform Beams with Concentrated Masses
,” Journal of Sound and Vibration
, Vol. 100
, pp. 487
–491
.32.
Zavodney
L. D.
Nayfeh
A. H.
1989
, “The Nonlinear Response of a Slender Beam Carrying a Lumped Mass to a Principal Parametric Excitation: Theory and Experiment
,” Int. J. Non-Linear Mechanics
, Vol. 24
, No. 2
, pp. 105
–125
.
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