Prediction of mechanical properties of microstructures through a nonlocal stress field theory

Abstract

The gradient type of nonlocal stress field theory has been one of the most popular theoretical approaches to study some size-dependent mechanical properties of microstructures. In this work, the nonlocal elasticity field theory is employed to investigate transverse bending vibration of the microbeams subjected to a pair of initial axial tensions, and the dynamical responses of such microstructures are determined and discussed in detail. The governing equation of motion containing a small length–scale parameter is derived according to the mechanical model constructed at microscale. Subsequently, two different methods, including the method of separation of variables and the multiple-scales analysis, are applied in the equation of motion to reveal the nonlocal elastic effects in vibrational behaviors of microstructures. It shows that the results by the two methods are in good agreement. Furthermore, the critical axial tension is also obtained, and it is observed to decrease with an increase in microscale parameter, which means an increase in nonlocal elastic effects causes the critical axial tension to decrease. By comparing with the results provided by the classical continuum vibration theory, inherent frequencies of the microbeams are lower or the bending stiffness is weakened in such a nonlocal stress model presented in this article.