Theoretical analysis of coupled torsional, warping and distortional waves in a straight thin-walled box beam by higher-order beam theory

When a thin-walled box beam is subjected to a dynamic torsional load, warping and distortional deformations of its cross section are coupled with torsional deformation. Due to the coupling, the wave propagation along the beam axis becomes considerably complicated. However, there appears no in-depth investigation on dispersion phenomena. It is difficult to see the intriguing interconnection of branches of the dispersion curves by means of numerical solutions of three-dimensional elastodynamic equations. Thus, we aim to analytically investigate the dispersion relation and wave reflection phenomena by using a one-dimensional higher-order beam theory that is capable of representing the three aforementioned deformations. Through this study, the interconnections of real, imaginary and complex branches of the dispersion relation for low frequencies are revealed and reflection and transmission phenomena occurring at a joint of two beams of different cross-sectional dimensions are also investigated.