Lateral Bending-Torsion Vibrations of a Thin Beam Under Parametric Excitation

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 ω_F = Ω_i + Ω_j, and each mode oscillates at its own natural frequency, Ω_i. 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.