Analysis of Stress Wave Interaction with a 180° Bend Junction Between Two Square Bars

Abstract

An analytical model for wave propagation through an unrestrained 180° bend junction connecting two long bars of rectangular cross-section is developed and the results are validated using experimental and numerical analyses. Upon arrival of a longitudinal stress wave, the bend junction is assumed to undergo rigid translation followed by rotation. By analyzing the normal and shear forces as well as the bending moments acting at the intersection of the bend junction, a set of 15 equations consisting of fifteen variables has been derived. Solving the system of equations in Laplace domain leads to transfer functions that relate the incident pulse to reflected and transmitted wave characteristics, as well as to the translation and rotation of the bend junction. These results in Laplace domain are converted back to time domain using the convolution integral. Concurrently, finite element analysis and experimental validation of the bend junction behavior were carried out to verify the results obtained from the analytical model. In addition to revealing the influence of individual parameters explicitly, the model revealed that the efficiency of the unrestrained bend junction for transmission of the longitudinal waves is at most ∼70% for a long duration stress pulse. This limitation is a result of the rotation of the bend junction which emanates flexural waves into both the bars. Thus, further increase in transmission efficiency of longitudinal wave is possible if the bend junction is restrained to move only in the axial direction with no rotation.