Torsional static and free vibration analysis of noncircular short-fiber-reinforced microwires with arbitrary boundary conditions

Abstract

This study investigates the free torsional vibration response of short fiber-reinforced noncircular microwires by considering the size effect. Moreover, the formulation of Eigen value problem based on forced boundary conditions that consider warping function and small-scale parameter. The composite microwire has been considered to be composed of fiber reinforced by short particle distributed along the thickness direction based on different symmetric patterns. The partial differential equation with force boundary conditions of a microwire under the general boundary conditions are presented in a matrix form and are solved analytically via the modified couple stress theory. An analytical solution is obtained for a microwire with arbitrary boundary conditions using the Fourier sine series with Stokes' transformation and effect of different parameters including warping function and elastic springs at the ends, material length scale parameter, distribution of short fibers on the free torsional frequencies are investigated.