Size-dependent torsion of functionally graded bars

In this paper, size-dependent static and dynamic behavior of functionally graded microbars is investigated on the basis of the modified couple stress theory. The equation of motion and corresponding boundary conditions are derived using Hamilton's principle and presented in the dimensionless form. Equivalent mechanical properties (i.e. shear modulus, density and length scale) are extracted for the functionally graded microbar based on the mechanical properties of the material constituents. In this work, it is shown that without any simplifying assumption, two equivalent length scale parameters can be defined for functionally graded bars and the size-dependent mechanical behavior of these components can be explained using these parameters. As an example, static and dynamic behavior of a functionally graded microbar with fixed-free boundary conditions is analyzed and the effect of size-dependency on mechanical behavior of this structure is discussed.