Size-dependent torsional oscillation of an elastic wire with circular cross-section

Abstract

Consistent couple stress theory (C-CST) provides the framework for the present investigation of size-dependent effects in the torsional oscillation of elastic circular wires. By using this form of couple stress theory, we are able to develop the first self-consistent size-dependent mechanics solution for this fundamental continuum dynamics problem that satisfies all boundary conditions without approximation. In addition, we derive the dispersion relations and characteristics for torsional waves in C-CST and the natural torsional modes for a finite length wire with fixed ends. Appendices provide a study of the general character of the C-CST eigensolutions and examine the torsional oscillation problem under classical and Mindlin-Tiersten-Koiter couple stress elastodynamics.