Modified couple stress-based geometrically nonlinear oscillations of porous functionally graded microplates using NURBS-based isogeometric approach

Abstract

In this work, porosity-dependent nonlinear large-amplitude oscillation responses of rectangular microplates with and without a central square cutout made of a porous functionally graded material (PFGM) is explored using modified couple stress theory of elasticity (MCSTE). The associated nonlinear size-dependent modified couple stress-based differential motion equations are obtained based on third-order shear deformation plate model (TSDPM). A new power-law function incorporating simultaneously the material gradient and porosity dependency is employed for the extraction of the effective mechanical characteristics of PFGM microplates. Afterwards, the non-uniform rational B-spline (NURBS)-based isogeometric technique is put to use as an efficient discretization method taking the C−1 continuity satisfaction into account. It is observed that among various patterns of porosity distribution, the lowest and greatest effects of couple stress size dependency are observed on the nonlinear frequencies of microplates in which the porosity from top and down surfaces to center is increased and decreased, respectively. Also, it was observed that increase of the material property gradient index as well as plate deflection reduces couple stress size effect on the nonlinear oscillations of PFGM microplates. It was shown that there is a specific length to thickness ratio, corresponding to which the modified couple stress-based frequency ratio becomes minimum. This minimum value enhances with the increase of the porosity index of PFGM microplates.