Axial–Torsional Vibrational Modes of Braided and Trapezoidal Wires

Abstract

The coupled axial–torsional modes of vibration are examined for three common types of braided wires: the well-known (1 + 6) configuration, the trapezoidal configuration, and the so-called twisted-pair. Representative volume elements of these systems with angles of twist ranging from 0 deg to 30 deg are described using three-dimensional elasticity theory and subjected to pure axial deformation and then pure twist to determine the stiffness coefficients that are used to describe the force–displacement relationship. These are compared with the results of existing braided wire models for the (1 + 6) geometry. Both analytical and finite element models of all three wires are then introduced to determine the level of coupling between the axial and torsional modes of vibration for representative homogeneous and composite cables.