A novel size-dependent finite strip based on Carrera unified formulation and micropolar theory for the free vibration analysis of microplates

Abstract

In this article, a novel size-dependent finite strip approach based on Carrera unified formulation (CUF) and micropolar elasticity is developed and introduced to investigate the free vibration analysis of micro-plate structures. The micropolar theory, through taking the micro-rotational degrees of freedom and micropolar couple stress effects into account, is a suitable elasticity theory for analysis of the microstructures. The finite strip method (FSM) allows for the division of a plate into some finite strips that are connected through the so-called nodal lines. The present higher-order refined finite strip model is more advanced and allows for the expression of all displacement and micro-rotation variables in each nodal line as a set of thickness functions that solely rely on the thickness coordinate, and the corresponding variable that depends on the in-plane coordinates, which involve continuously harmonic series and polynomial shape functions. Thanks to the CUF, the three-dimensional displacement and micro-rotation field are approximated compactly as a generic N-order expansion model. Therefore, the governing equations are obtained in terms of a few fundamental nuclei in a compact and explicit unified manner and presented here. The results obtained by the proposed method are compared with those available in the literature.