A general nonlocal stress-strain gradient theory for forced vibration analysis of heterogeneous porous nanoplates

Dynamic modeling of nanoplates constructed from porous functionally graded (FG) and metal foam materials is presented based on nonlocal strain gradient theory (NSGT). In this model, both stiffness-softening and stiffness-hardening effects are considered for more reliable forced vibration analysis of nanoplates. The present nano-resonator is based on a vibrating higher order nanoscale plate subjected to transverse uniform dynamic load. Porosities inside FG material are incorporated to the model based on a modified rule of mixture. Also, porosities inside metal foam nanoplate are non-uniformly distributed thorough the thickness. Applying Galerkin's method, the resonance frequencies and dynamic deflections are obtained. It is indicated that the forced vibration characteristics of the nanoplate are significantly influenced by the excitation frequency, porosities, nonlocal parameter, strain gradient parameter, elastic foundation and dynamic load characteristics.