Nonlinear surface and nonlocal piezoelasticity theories for vibration of embedded single-layer boron nitride sheet using harmonic differential quadrature and differential cubature methods

Abstract

Surface stress and small-scale effects on nonlinear vibration analysis of a single-layer boron nitride sheet are investigated based on theories of nonlocal and surface piezoelasticity. The single-layer boron nitride sheet is embedded in an elastic medium which is simulated by Pasternak model. Considering electromechanical coupling, the discretize governing equations of motion are obtained by Hamilton’s principal. Two numerical methods, harmonic differential quadrature and differential cubature, are employed to determine the nondimensional nonlinear frequency of single-layer boron nitride sheet. The detailed study parameters are conducted to investigate the influences of the small-scale, temperature change, surface effects, elastic medium, vibrational mode, aspect ratio, and smartness of sheet on the nonlinear nonlocal vibration characteristics of single-layer boron nitride sheet. It is concluded that ignoring surface and small-scale effects lead to inaccurate results in vibrational response of the single-layer boron nitride sheet. Furthermore, differential cubature method yields accurate results with less computational effort with respect to harmonic differential quadrature method. The obtained results of this study may be useful for designing of nano-electro mechanical system or micro-electro mechanical system and other nano-/micro-smart structures.