Measurement of the elastic modulus of nanowires based on resonant frequency and boundary condition effects

Abstract

The elastic modulus of nanowires can be measured by resonant frequency method, in which the elastic modulus is determined using the classical theory of beam deflection. However, the measurement accuracy of the elastic modulus obtained from the resonant frequency can be largely affected by theoretical models and boundary conditions. In the present paper, a theoretical model is developed by considering nonlocal interactions and boundary condition effects of cantilever support. Based on the proposed model, we investigate the influence of nonlocal parameter and elastic foundation on the elastic modulus of carbon nanotubes (CNTs). The results show that the resonant frequency of CNTs is affected by the clamped cantilever condition. Support stiffness and clamped length of CNTS cannot be ignored in determining the elastic modulus of CNTs, especially for CNTs with low stiffness support. After considering the boundary conditions, the influence of cantilever support on the frequency is effectively removed, and the elastic modulus can be precisely determined by measuring the resonant frequency.