Free vibration analysis of a functionally graded porous triangular plate with arbitrary shape and elastic boundary conditions using an isogeometric approach

This paper presents a comprehensive analysis of the free vibrations of functionally graded porous (FGP) triangular plates with arbitrary shapes and elastic boundary conditions using Isogeometric Analysis (IGA). We express the triangular shapes by using non-uniform rational B-splines (NURBS). The impact of porosity, geometry, and boundary conditions on the natural frequencies is investigated, with a focus on three key factors: porosity coefficient, geometric shape, and type of boundary conditions. Results show that increasing porosity generally leads to an increase in natural frequencies for thin plates, while thicker plates exhibit the opposite trend. The effect of geometric shape, characterized by different angles, is investigated and reveals distinct trends in natural frequencies. The study also investigates both classical and elastic boundary conditions, illustrating the impact of arbitrary boundary conditions on the natural frequency response. Validation against previous references and finite element methods establishes the accuracy of the presented results. The paper concludes with an extension of the analysis to various scenarios, offering valuable insights into the intricate interplay of porosity, geometry, and boundary conditions on the vibrational behavior of FGP triangular plates.