Model Validation and Vibration Analysis of Cosserat Plates

TL;DR

This paper validates a mathematical model for Cosserat elastic plates by comparing eigenfrequency computations with exact 3D solutions, revealing micro-macro vibration frequency splitting.

Contribution

It introduces a validated Cosserat plate model capable of distinguishing micro and macro vibration frequencies through eigenfrequency analysis.

Findings

High agreement of eigenfrequencies with exact solutions

Detection of micro vibration frequency splitting

Tool for micro-macro vibration differentiation

Abstract

In this paper we present the validation of our recently published mathematical model for the dynamics of Cosserat elastic plates. The validation is based on the comparison with the exact solution of the 3-dimensional Cosserat elastodynamics. The preliminary computations of eigenfrequencies show the high agreement with the exact values. The computations allow us to detect the splitting of the frequencies of vibrations (micro vibration) depending on the orientation of micro elements. This provided us with a powerful tool for distinguishing between the frequencies of the micro and macro vibrations of the plate.