This paper investigates the influence of the boundary conditions on the lowest
vibration modes of strongly inhomogeneous beams. It is observed that the softer
component of the composite beams asymptotically contributes to an almost
rigid-body motion of the stiffer parts and gives rise to one or two nonzero
eigenfrequencies contrary to a single beam with free end conditions. An
asymptotic procedure is employed to derive the eigenfrequencies as well as the
eigenforms in the case of global low frequency regime. The developed model is
adapted for two and three-component beams with different end conditions. It is
also shown that all eigenforms corresponding to the stiffer components of
the beams perform almost rigid body motions. Comparisons of exact and
approximate solutions are presented, demonstrating the validity of the proposed
approach.
Keywords
composite beam, low frequency vibration, contrast,
perturbation, rigid body motion
