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A micro scale beam of rectangular cross-section, for which the rate of twist introduced a bending bending coupling effect, is considered.
The presented governing equation of motion is used to address the effects of the rate of twist and the material length scale on the bending wave propagation characteristics of the micro scale beam.
Results are presented for the spectrum curve, the cut-off frequency, the phase speed and the group velocity of a propagating harmonic wave profile in the twisted micro scale beam.
It is observed that the rate of twist bifurcates the spectrum curve of the micro scale beam within a given frequency range, while the material length scale improves the dispersion of the traveling wave.
In this paper, starting with the modified couple stress theory, the elastodynamics governing partial differential equations of motion for the transverse dynamics of a twisted micro scale beam is derived.
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Thermoelastic damping is recognized as a significant loss mechanism at room temperature in micro-scale beam resonators.
Our next step is to use the data from the micro-scale beam models in order to parametrize a macroscopic, Cosserat-type continuum model.
In such scale transitions, normally either bottom-up homogenization approaches or top-down reverse modeling strategies are used in order to match the macro-scale Cosserat continuum to the micro-scale beam network.
For validation we use a direct comparison between averaged results from our micro-scale beam model and a finite element implementation of the Cosserat continuum that uses the material parameters of Fig. 4, averaged over all loading modes and system sizes.
For strongly disordered cellular structures, the thus parametrized Cosserat continuum produces results that reproduce the behavior of the micro-scale beam models both in view of the observed strain patterns and in view of the macroscopic response, including its size dependence.
The aim is mainly focused on the static and dynamical responses of micro-scale beams under consideration in both prebuckling and postbuckling cases.
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