Dynamic Behaviors of Couple Stress Quadrilateral Thick Microplates within a Refined DQFE Framework

Abstract

This study proposes a novel refined differential quadrature finite element (DQFE) framework for the size-dependent dynamic analysis of thick quadrilateral microplates, incorporating couple-stress effect and two kinematic variables. The proposed methodology addresses inter-element compatibility through fifth-order differential quadrature geometric mapping while achieving geometric adaptability via global-local coordinate transformation. Detailed procedures for assembling element matrices and imposing boundary conditions are provided. Validation through representative quadrilateral plate configurations confirms the efficacy of the proposed framework, with particular success in modeling asymmetric trapezoidal plates through experimental correlation. The enhanced DQFE framework further elucidates fundamental mechanisms governing cyclic quadrilateral microplate dynamics by systematically investigating three critical factors: material length scale parameters (MLSP), thickness-to-length ratios, and boundary constraint configurations. Mode localization characteristics are quantitatively assessed using the mode assurance criterion. The principal conclusions reveal: (1) Superior convergence characteristics of the fifty-degree-of-freedom DQFE formulation compared to conventional lower-order implementations; (2) Emergence of mode-transition phenomena driven by central angle variations; (3) Differential sensitivity of critical mode-transition angles to MLSP variations under contrasting boundary constraint intensities; (4) Characteristic modification of vibration mode contours induced by size-dependent effects.