Frequency analysis of carbon and silicon nanosheet with surface effects

Silicon-based microelectromechanical system (MEMS) and nanoelectromechanical systems (NEMS) have been used to design and fabricate sensitive sensors and actuators. Recent research trends show that graphene and carbon nanotubes (CNTs) have been used to change the surface properties of silicon-based MEMS and NEMS to improve different mechanical, optical and electrical properties of silicon-based composites. In this paper, we focus on analyzing the vibrational characteristics of silicon-based devices when the surface of silicon is coated with single-layer graphene and horizontally aligned carbon nanotubes (HACNTs). To perform the analysis, we use multi-scale finite element approach for developing graphene–silicon nanocomposites (GSNCs) and carbon nanotube-silicon nanocomposites (CSNC) composites in which interface layer of silicon with graphene or CNT is modeled using bonded contact element. Subsequently, we performed modal analysis to find the first transverse mode frequency of GSNC and CSNC composites for beam with smaller as well as longer lengths. The numerical model is compared with classical beam theory with and without surface effect. For GSNCs composites, we take a fixed-free case with lengths in the range of (20 Å–120 Å) and (400 Å–2000 Å), respectively. For CSNC composites, CNT diameter is varied from (5 Å–30 Å) for single walled nanotube. Subsequently, we analyze the influence of HACNTs-on-silicon on its vibrational characteristics. The analysis presented in the paper demonstrate that GSNCs offer a higher bending stiffness compared to single layer graphene (SLGs) and isolated silicon nanosheet which lead to higher natural frequency. A similar trend is found in the case of HACNTs on silicon NS when the number of tubes increases.