Geometrically nonlinear dynamic analysis of a damped porous microplate resting on elastic foundations under transverse patch loadings

This is a unique study in which a damped porous microplate's nonlinear vibration and response are analyzed semi-analytically using MSGT and HSDT under localized loading. The substrate is modeled using the Winkler-Pasternak elastic foundation. Partial differential equations are obtained using Hamilton's principle and solved by Galerkin's method. IHB and Newmark's methods are used to trace the nonlinear vibration and response. The results show that uniform porosity leads to lower stiffness compared to symmetric porosity distribution. Pasternak foundation parameter has a larger impact on stiffness compared to Winkler parameter. The effect of geometric nonlinearity is weakened while using MSGT.