Lateral Bending-Torsion Vibrations of a Thin Beam Under Parametric Excitation,
Abstract
A thin plate-like cantilever beam, well below static lateral buckling under gravity, is subjected to vertical harmonic excitation of its base. The governing equations reduce to systems of two Mathieu equations coupled mainly by symmetric, off-diagonal parametric excitation terms. For such cases, the primary instability regions are shown to occur near forcing frequencies (omega sub F) = (omega sub i) + (omega sub j), with each mode oscillating at its own natural frequency, omega sub i. Experiments performed on an actual beam confirm this behavior. Since the beam had nonlinear damping, the instability regions settled down to steady limit cycles whose frequencies and amplitudes were well predicted by theory. The simultaneous excitation of two modes, each oscillating at its own natural frequency, may be of considerable interest in vibration testing of actual structures. (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- Jun 01, 1972
- Accession Number
- AD0750546
Entities
People
- John Dugundji
- Vivekananda Mukhopadhyay
Organizations
- Massachusetts Institute of Technology