Vibration Analysis of Size-Dependent Higher-Order Plates Based on Micropolar Theory

Articles in Press

Document Type : Article

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Department of Civil Engineering, Shahid Bahonar University of Kerman, Kerman, Iran

10.24200/sci.2024.61589.7388

Abstract

By considering micro-rotational degrees of freedom (DOFs), the micropolar continuum theory (MPT) can characterize the effect of micro-structures on the mechanical analysis of material particles, which classical theories (CT) of elasticity are unable to describe. The vibration behavior of the higher-order plates with a drilling DOF is discussed in this article to suggest a novel size-dependent rectangular element based on the micropolar elasticity theory. To do this, a new general formulation of the MPT, which can be employed with ease in the finite element method (FEM), is initially developed. The displacements and micro-rotations are therefore computed using quadratic shape functions on a rectangular plate element. In this element, the proper stiffness and mass matrices for the drilling DOF are derived, and to demonstrate the precision and application of the proposed element, several numerical examples of micropolar plates with various boundary conditions have been carried out. The current finite element formulation shown here is effectively used to take into account the micropolar efficiency for modeling microplates. This research contributes to advancing our understanding of the mechanical response of materials at the microscale.

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Scientia Iranica

Articles in Press, Accepted Manuscript
Available Online from 23 June 2024

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