Vibration analysis of two-dimensional structures using micropolar elements

doi:10.1007/s10483-021-2746-8

Abstract

Abstract: Based on the micropolar theory (MPT), a two-dimensional (2D) element is proposed to describe the free vibration response of structures. In the context of the MPT, a 2D formulation is developed within the ABAQUS finite element software. The user-defined element (UEL) subroutine is used to implement a micropolar element. The micropolar effects on the vibration behavior of 2D structures with arbitrary shapes are studied. The effect of micro-inertia becomes dominant, and by considering the micropolar effects, the frequencies decrease. Also, there is a considerable discrepancy between the predicted micropolar and classical frequencies at small scales, and this difference decreases when the side length-to-length scale ratio becomes large.

Key words: finite element method (FEM), quadrilateral element, micropolar theory (MPT), user-defined element (UEL) subroutine, free vibration

2010 MSC Number:

74S05
70J30

M. KOHANSAL-VAJARGAH, R. ANSARI, M. FARAJI-OSKOUIE, M. BAZDID-VAHDATI. Vibration analysis of two-dimensional structures using micropolar elements. Applied Mathematics and Mechanics (English Edition), 2021, 42(7): 999-1012.

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URL: https://www.amm.shu.edu.cn/EN/10.1007/s10483-021-2746-8

https://www.amm.shu.edu.cn/EN/Y2021/V42/I7/999

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Vibration analysis of two-dimensional structures using micropolar elements

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