Calculating the free vibrations of functionally graded plates using the unlimited integral

This paper discusses the use of the infinite integral to calculate free vibrations of composite structures. This technique allows us to reduce the number of unknowns to four, resulting in simpler governing equations. This model is meant to look at the uncontrolled shaking of functionally graded plates (FGM), where the transverse shear stresses are spread out in a hyperbolic way and meet the requirements of free tension on both the top and bottom surfaces of the plate. The motion equations are based on Hamilton's principle and Navier-type analytical solutions for simply supported plates. The discovered solutions are compared to existing solutions to ensure the model's validity. The material's characteristics vary continuously over the plate's thickness according to a power law and an exponential function. We investigate the effects of the power law index and geometric ratio on natural frequencies using numerical data.