Polygonal plate element method for free vibration analysis using an efficient alpha (α)-assumed rotations and shear strains

• An efficient polygonal plate element is extended to free vibration analysis • Alpha (α)-assumed rotations and shear strains approach is applied • Its performance is superior compared to the original polygonal element • Lowest frequencies closely approximate to reference solutions This paper investigates the performance of a recently proposed polygonal plate element with alpha ( α )-assumed rotations and shear strains, referred to as α ARS-Poly, in free vibration analysis . The α ARS-Poly element utilizes a simple and efficient approach involving a scaling factor ( α ) to enhance the accuracy of assumed rotations and shear strains. To fully explore the advantages of this element, we undertake a comprehensive analysis of free vibration in plate structures using a range of models with complex geometries. Numerical results demonstrate that the α ARS-Poly element offers stability and reliability within smooth mode shapes. Furthermore, it significantly outperforms the previous polygonal Reissner-Mindlin plate element with piecewise-linear shape functions (PRM n -PL), achieving frequencies that closely match reference solutions, thereby validating its accuracy and robustness for dynamic applications.