A nonlinear semi-continuum model for silicon micro/nanosheets and its application in bending and vibration

Abstract

Background: This paper is concerned with a nonlinear semi-continuum model for an ultrathin structure. The basic equations of the theoretical model for silicon micro/nanosheets are derived, and the geometric nonlinearity is introduced in the model. Methods: From two different approaches including the new strain energy and the new external potential energy, we establish the nonlinear semi-continuum theoretical model of silicon micro/nanosheets, respectively. A new dimensionless nonlinear semi-continuum parameter is defined. Based on the theoretical model, the characteristics of bending deformation and free vibration are revealed. Results: The relationships between bending deflection and atomic layers in thickness direction as well as the relaxation coefficient between atomic layers are analyzed. The resonance frequencies of free vibration and their relationship with atomic layers are calculated. By introducing the specific property parameters of silicon micro/nanomaterials, several numerical calculations have been carried out. Conclusion: The theoretical results are compared with other studies in the literature, such as nonlinear finite element method (FEM), experimental and classical results, to validate the semi-continuum model established in the present research. This work can provide new ideas for the mechanical analyses of micro/nanomaterials and structures, and the results could be foundations for the design and application of silicon micro/nanosheets.