Effect of Timoshenko Coefficient in Wave Propagation Analysis of a Three-Dimensional Frame Structure

Abstract

The Timoshenko theory is usually used in the vibration analysis of a beam because it can yield a relatively good approximation in the high-frequency domain. This theory uses the so-called Timoshenko coefficient to couple the bending and shear deformations. This coefficient is calculated using the shear deformation distribution within the cross section that arises from the bending deformation of a beam. The shear deformation distribution is calculated based on certain assumptions. In this study, we reexamine Cowper's theory that introduces the least assumptions in computing the Timoshenko coefficient in the view point of dynamic behavior. The relationship between the Timoshenko coefficient and the dispersion relation is investigated. The evaluation of the shear stress distribution within this cross section is attempted using numerical simulation. Finally the effect of the Timoshenko coefficient on the wave propagation analysis of a beam is examined.