Vibration analysis of new cosine functionally graded microplates using isogeometric analysis

This paper investigates the free vibration characteristics of a novel functionally graded (FG) porous microplate using isogeometric analysis (IGA). The study incorporates two types of FG microplates, FG-A and FG-B, with material properties varying continuously through thickness as defined by a new cosine function. Modified couple stress theory and higher-order shear deformation plate theory are employed to formulate the governing equations, incorporating size-dependent effects under various boundary conditions. A numerical model based on IGA is used to compute fundamental frequencies. To validate the proposed solution model, a comparison study with existing literature is conducted. The results indicate that increasing the size-dependent ratio enhances plate rigidity and vibration frequencies, while higher porosity reduces plate stiffness, and dimensionless frequencies decrease with an increasing aspect ratio and a decreasing thickness ratio. These findings underscore the model's robustness and its accuracy in capturing the effects of material and geometric parameters on vibration behavior.