Dynamic instability analysis for S-FGM plates embedded in Pasternak elastic medium using the modified couple stress theory

The modified couple stress-based third-order shear deformation theory is presented for sigmoid functionally graded materials (S-FGM) plates. The advantage of the modified couple stress theory is the involvement of only one material length scale parameter which causes to create symmetric couple stress tensor and to use it more easily. Analytical solution for dynamic instability analysis of S-FGM plates on elastic medium is investigated. The present models contain two-constituent material variation through the plate thickness. The equations of motion are derived from Hamilton\'s energy principle. The governing equations are then written in the form of Mathieu-Hill equations and then Bolotin\'s method is employed to determine the instability regions. The boundaries of the instability regions are represented in the dynamic load and excitation frequency plane. It is assumed that the elastic medium is modeled as Pasternak elastic medium. The effects of static and dynamic load, power law index, material length scale parameter, side-to-thickness ratio, and elastic medium parameter have been discussed. The width of the instability region for an S-FGM plate decreases with the decrease of material length scale parameter. The study is relevant to the dynamic simulation of micro structures embedded in elastic medium subjected to intense compression and tension.