Abstract:
The problem of natural vibrations of a five-layer symmetrical in thickness rod with two fillers is considered.
The bearing layers are assumed to be thin, high-strength. The Bernoulli hypotheses on cross-sections of flat and perpendicular
to the deformed axial line, after load application, are accepted for them. In relatively thick lightweight aggregates,
the Timoshenko hypothesis is fulfilled, according to which the cross-section remains flat and incompressible, but is rotated
by some additional angle. The differential equations of the vibrations are obtained with the variational method, taking into
account transverse forces of inertia. A transcendental equation for the eigenvalues of a rod with rigidly sealed ends is is derived,
and its numerical solutions are obtained. The dependence of the natural frequencies of vibrations on the thickness of external
bearing layers for different materials of the rod layers is investigated.
Keywords:symmetric five-layer rod, two fillers, eigenvalues, vibration frequencies, numerical results.
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