Dynamic stability of viscoelastic porous FG nanoplate under longitudinal magnetic field via a nonlocal strain gradient quasi-3D theory

This research is devoted to analyze the dynamic instability of viscoelastic porous functionally graded (FG) nanoplates under biaxially oscillating loading and longitudinal magnetic field using quasi-3D sinusoidal shear deformation plate theory as well as nonlocal strain gradient theory (NSGT). Modified power-law function is developed to show the effective material properties of the porous FG nanoplate that change uniformly from one surface to another. The motion equations are obtained by employing Hamilton's variational principle. In order to calculate the unstable region of the porous FG nanoplate, Navier as well as Bolotin's methods are utilized. The current theories and formulations are verified by comparing the obtained results with those available in literature. Then, the effects of several remarkable factors like magnetic field, nonlocal parameter (NP), internal damping, power-law index, static load factor, aspect ratio, porosity volume index and length scale parameter (LSP) on the unstable region of viscoelastic porous FG nanoplates are investigated via a comprehensive parametric study which could be utilized as reference results in future research. The numerical results indicated that increasing the porosity volume index, power-law index, internal damping parameter and NP leads to a reduction in the pulsation frequency and thus, unstable region moves to left, whereas magnetic field and LSP have a reverse effect.