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On the lowest frequencies of strongly inhomogeneous multicomponent beams

The paper considers harmonic vibration modes of multicomponent beams having high‐contrast mechanical properties. The analysis is focused on the low frequencies because of their omnipresent characters. An asymptotic procedure is developed to obtain explicit expressions for the eigenfrequencies and eigenforms, which reveals that only under certain conditions on the ratios of material parameters, low‐frequency and rigid body motions are possible. Comparisons of the derived asymptotic formulae with exact ones are presented for examples of three‐ and five‐component beams, showing a remarkable agreement for high‐contrast beam components.