Size-dependent frequency and stability characteristics of axially moving microbeams based on modified couple stress theory

作者：Dehrouyeh Semnani Amir Mehdi; Dehrouyeh Mohammad; Zafari Koloukhi Hamid; Ghamami Mehdi

来源：International Journal of Engineering Science, 2015, 97: 98-112.

DOI：10.1016/j.ijengsci.2015.09.003

• Axially moving microbeam
• Timoshenko beam theory
• Natural frequency
• Divergence bifurcation
• Critical velocity
• Modified couple stress theory

This investigation aims to explore dynamic characteristics of axially moving Timoshenko microbeams by taking into account size-dependency based on a modified couple stress theory. Size-dependent motion equations and associated boundary conditions are established via Hamilton's principle. In addition, size-dependent axially moving Euler-Bernoulli beam model can be recovered from the present Timoshenko beam model by reinstating the normality assumption. Galerkin method is applied to discretize the partial differential equations into a set of ordinary differential equations, and then the size-dependent dynamic characteristics of axially moving microbeams with simply supported and doubly clamped boundary conditions are numerically determined. It is observed that the microbeams losestability via a divergence bifurcation in the first mode. The results illustrate that the critical velocity in which the instability occurs and also the natural frequencies significantly increase when the role of size-dependency is of great importance. Finally, the sensitivity of frequencies to velocity and also the influence of size-dependent shear deformation on frequencies and critical velocities are examined.

• 出版日期2015-12