Large amplitude free vibration of porous skew and elliptical nanoplates based on nonlocal elasticity by isogeometric analysis

Abstract

The current work presents an investigation on size-dependent nonlinear free vibration of porous skew and elliptical nanoplates. Formulations are based on a four-variable higher-order shear deformation plate theory to satisfy automatically the traction-free condition, von Kármán geometric nonlinearity to account for the mid-plane stretching, and Eringen's nonlocal elasticity theory to capture the scale effect. The isogeometric analysis and a displacement control strategy are employed synthetically to obtain large amplitude responses of the nanoplates. New results show the influences of porosity distribution pattern, porosity coefficient, and nonlocal parameter on the behaviors of vibration behaviors of the skew and elliptical nanoplates.