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 αARS-Poly, in free vibration analysis. The αARS-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 αARS-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 (PRMn-PL), achieving frequencies that closely match reference solutions, thereby validating its accuracy and robustness for dynamic applications.