Influence of Hygrothermal Environment and FG Material on Natural Frequency and Parametric Instability of Plates

In this article, vibration characteristics and the parametric instability of functionally graded material (FGM) plates with cyclic loading in a hygrothermal field are discussed. The plate element is modeled in a finite element by applying the third-order shear deformation hypothesis. The mathematical formulation of the FGM plate is made with two material constituents by applying the power rule to vary in association with the thickness path of the plate. Hamilton’s principle is employed to develop the arbitrary equation of motion, which is converted into periodic constants using the Mathieu Hill equation. The derived equation of movement with the help of Floquet’s theorem is applied to generate the instability and stability separations of the FGM plate in the hygrothermal environment. The current proposed results are compared with existing literature results to assess its validity. The free vibration characteristics are reduced by the rise of moisture absorption and the temperature of the FGM plates in the hygrothermal atmosphere. Hence, the influence of increased parameters increases the parametric instability of FGM plates. Temperature rise and moisture absorption regarding the parametric stability and the uncertainty region of the FGM plates are also observed.