Size-dependent free vibration analysis of first-order shear-deformable orthotropic nanoplates via the nonlocal strain gradient theory

In this study, the free vibration analysis of first-order shear-deformable orthotropic nanoplates are conducted in the frameworks of the nonlocal strain gradient elasticity theory. The equations of motion and also the associated boundary conditions are derived using the extended Hamilton's principle. The multi-term extended Kantorovich method (MTEKM) in conjunction with the generalized differential quadrature method (GDQM) is employed to solve the equations of motion. For clamped and simply supported boundary conditions the problem is solved. In addition, a modified Mindlin plate model is introduced by excluding the nonlocality in the shear constitutive equations. Numerical results have shown that the two material length scale parameters have opposite effects on the frequency response of the nanoplate. Also, the excluding the nonlocality in the shear constitutive equations is associated with the stiffness-softening phenomenon.