Free vibration characteristics of sigmoid-functionally graded plates reinforced by longitudinal and transversal stiffeners

The main objective of this research paper is to investigate the positive influence of the stiffeners on the vibration of functionally graded plates based on an exact approach via Navier solution. The plate is reinforced by stiffeners in both longitudinal and transversal directions. The material properties of functionally graded materials (FGMs) media are distributed across the thickness based on a sigmoid-law form and are assumed to be temperature-dependent. By using the Hamilton's principle and the classical plate theory (CPT), the governing equations of motion are obtained. Based on the Navier solution, an exact solution is proposed for natural frequencies of simply supported rectangular plates. In addition, the effects of related parameters on natural frequencies are also addressed in detail. Finally, numerical examples are presented and compared with existing results.