Abstract
ДЛИННОВОЛНОВЫЕ МОДЫ КОЛЕБАНИЙ СИЛЬНО НЕОДНОРОДНЫХ УПРУГИХ СЛОИСТЫХ КОНСТРУКЦИЙ
Highlights
INTRODUCTIONThe classical theory for thin homogeneous elastic structures governing bending, extensional and torsional-shear vibration modes, e.g. see [1–3], is asymptotically consistent over the low-frequency range
The classical theory for thin homogeneous elastic structures governing bending, extensional and torsional-shear vibration modes, e.g. see [1–3], is asymptotically consistent over the low-frequency range. It does not take into consideration any of high-frequency modes with the cut-off frequencies related to thickness resonances
In this paper we extend the framework of the cited publication [6] on thin strongly inhomogeneous plates to multi-layered structures with arbitrary number of layers
Summary
The classical theory for thin homogeneous elastic structures governing bending, extensional and torsional-shear vibration modes, e.g. see [1–3], is asymptotically consistent over the low-frequency range. It does not take into consideration any of high-frequency modes with the cut-off frequencies related to thickness resonances. Multi-parametric analysis of strongly vertical inhomogeneous three-layered plates in [6], see [8] and [9], indicates that for certain combination of problem parameters the lowest thickness shear resonance frequency becomes asymptotically small, resulting in an extra low-frequency vibration mode in comparison with the traditional layout. The order of the aforementioned equation coincides with the number of strong layers undergoing almost rigid body motion [9] In this case the weaker layers are subject to nearly homogeneous thickness deformation.
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