A thin platelike cantilever beam, well below static lateral buckling under gravity, is subjected to vertical harmonic excitation of its base. The governing equations indicate combination resonance possible, where the primary instability regions occur near forcing frequencies ωF = Ωi + Ωj, and each mode oscillates at its own natural frequency, Ωi. Experimental results are given for an actual beam showing this behavior. Since the beam had nonlinear damping, the instability regions settled down to steady nonlinear limit cycles whose frequencies and also amplitudes were well predicted by theory. This example of simultaneous excitation of two modes, each oscillating steadily at its own natural frequency, may be of considerable interest in vibration testing of actual structures.
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September 1973
Research Papers
Lateral Bending-Torsion Vibrations of a Thin Beam Under Parametric Excitation
J. Dugundji,
J. Dugundji
Department of Aeronautics and Astronautics, Massachusetts Institute of Technology, Cambridge, Mass.
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V. Mukhopadhyay
V. Mukhopadhyay
Department of Aeronautics and Astronautics, Massachusetts Institute of Technology, Cambridge, Mass.
Search for other works by this author on:
J. Dugundji
Department of Aeronautics and Astronautics, Massachusetts Institute of Technology, Cambridge, Mass.
V. Mukhopadhyay
Department of Aeronautics and Astronautics, Massachusetts Institute of Technology, Cambridge, Mass.
J. Appl. Mech. Sep 1973, 40(3): 693-698 (6 pages)
Published Online: September 1, 1973
Article history
Received:
May 1, 1972
Revised:
August 1, 1972
Online:
July 12, 2010
Citation
Dugundji, J., and Mukhopadhyay, V. (September 1, 1973). "Lateral Bending-Torsion Vibrations of a Thin Beam Under Parametric Excitation." ASME. J. Appl. Mech. September 1973; 40(3): 693–698. https://doi.org/10.1115/1.3423075
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