
Accession Number : AD0750546
Title : Lateral BendingTorsion Vibrations of a Thin Beam Under Parametric Excitation,
Corporate Author : MASSACHUSETTS INST OF TECH CAMBRIDGE AEROELASTIC AND STRUCTURES RESEARCH LAB
Personal Author(s) : Dugundji,John ; Mukhopadhyay,Vivekananda
Report Date : JUN 1972
Pagination or Media Count : 41
Abstract : A thin platelike 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, offdiagonal 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)
Descriptors : (*CANTILEVER BEAMS, *VIBRATION), BENDING, TORSION, RESONANCE, EQUATIONS OF MOTION
Subject Categories : Structural Engineering and Building Technology
Mechanics
Distribution Statement : APPROVED FOR PUBLIC RELEASE