Vibration and Small Scale Effects of Skew Graphene Sheets Using Nonlocal Elasticity Theory

Abstract

Nonlocal elasticity theory is a popularly growing technique for the realistic analysis of nano structures. In the present work nonlocal elasticity plate theory has been employed and vibration analyses of skew graphene sheets are carried out. Relevant governing differential equations are reformulated using the nonlocal differential constitutive relations suggested by Eringen. The equations of motion including the nonlocal theory are derived. All edges of the skew graphene sheets are assumed to be simply supported. Naviers approach has been employed to solve the governing differential equations. Bauers skew plate analysis has been extended to include the nonlocal elasticity plate theory. Vibration response of the skew graphene sheets is studied. Effects of the (i) size of the graphene sheets (ii) modes of vibration (iii) nonlocal parameter and (iv) skew angle of graphene sheet on nonlocal vibration frequencies are investigated. It has been observed that the vibration response of the skew graphene sheets are influenced significantly by the nonlocal parameter.