Vibration frequency analysis of new rectangular finite element for thin plate bending

Purpose This paper aims to address a new rectangular thin plate finite element for vibration frequency analysis. This element has a computationally efficient formulation and integrates linear elastic behavior. The system has twelve degrees of freedom and is made up of four nodes with three degrees of freedom: two normal rotations (θx, θy) and one transverse displacement (w). Design/methodology/approach In this paper, MATLAB programming is used for the mathematical formulations, and the methodology’s novel approach combines the use of a displacement formulation with the application of analytical integration techniques for basic stiffness matrix computation. Findings Comprehensive validation studies were performed through vibration frequency analyses. The element demonstrates superior accuracy and computational efficiency performance. The numerical results show excellent convergence characteristics and robust performance across various boundary conditions and loading scenarios. Originality/value Vibration frequency analyses were used to conduct thorough validation studies. Excellent convergence characteristics and reliable performance under a range of loading scenarios and boundary conditions are demonstrated by the numerical results.