Surface elasticity and size effect on the vibrational behavior of silicon nanoresonators

• MD simulation of nano-beams using SW potential and study of beam natural frequency.
• Study of the boundary conditions, the beam dimensions and crystalline directions.
• Calibrating Euler–Bernoulli and Timoshenko beam models, incorporating surface elasticity.
• Comparison of results of different models in prediction of nano-beam frequency.
• Developing a continuum model capable of predicting vibrational behavior of nanobeams.

Predominance of nano-scale effects observed in material behavior at small scales requires implementation of new simulation methods which are not merely based on classical continuum mechanic. On the other hand, although the atomistic modeling methods are capable of modeling nano-scale effects, due to the computational cost, they are not suitable for dynamic analysis of nano-structures. In this research, we aim to develop a continuum-based model for nano-beam vibrations which is capable of predicting the results of molecular dynamics (MD) simulations with considerably lower computational effort. In this classical-based modeling, the surface and core regions are taken to have different mechanical properties, where core atoms are assumed to have macroscale properties whereas surface layer is showing a different elastic modulus from the core components. By estimating physical parameters of proposed classical model using molecular dynamics results and the genetic algorithm, calibrated classical Euler–Bernoulli and Timoshenko beam models are developed. The results demonstrates that a Timoshenko beam model incorporating surface effects and having calibrated parameters, is able to provide almost the same results as molecular dynamics method which can be used to predict the vibrational behavior of nano-beams at different scales from nano to macro.