The effect of boundary conditions on the lowest vibration modes of strongly inhomogeneous beams

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.