What is it about?

Using tWe use the two-phase model of nonlocal elasticity to describe free vibrations of nonlocal rods. Assuming the exponential attenuation kernel in the nonlocal integral models, the governing integro-differential equation is reduced to more simple differential equation of the forth order with additional boundary conditions. Using the asymptotic approuch, we find the natural frequencies for different variants of boundary conditions. As a limitting case, we obtain the natural frequencies in the fraimwork of purely nonlocal model of Eringen and its so-called the equivalent differential model.

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Why is it important?

We prove that the purely nonlocal and equivalent differential models lead to ill-posed problems. On the ather hand, we consider that the two-phase model of nonlocality is consistent and may be effectively used to study dynamic response of nanoscale structures


The analytical and asymptotic solutions constructed in this work for the simplest case of a nanorod may be considered as a benchmark for subsequent investigations of vibrations of nanosized beams, plates and shells.

Professor Gennadi Mikhasev
Belarusian State University

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This page is a summary of: Free vibrations of nonlocally elastic rods, Mathematics and Mechanics of Solids, July 2018, SAGE Publications, DOI: 10.1177/1081286518785942.
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