Correction in the continuity conditions for beams with structure governed by the Timoshenko–Ehrenfest equation

Abstract

We develop a theory that significantly improves the correspondence between theoretical and experimental results in beams with structures excited with bending waves. We use beam theory and Timoshenko-Ehrenfest continuity conditions with the transfer matrix method to solve the fourth-order differential equation. First, we analyze the continuity conditions to understand the deformation in the cross-section between the notch-body interface. Then, using analytical and numerical methods, we determine an effective cross-section between the notch-body interface that, when included in the continuity conditions of the Timoshenko–Ehrenfest beam theory, brings the theoretical results into a high agreement with the experimental results with a relative error of less than 12%.