A Parametric Study of the Free Undamped Torsional Vibration of One-Dimensional Structural Elements using the Differential Quadrature Method (DQM)

Abstract

Recently, structures prone to torsional vibration have grabbed the interest of the structural engineering field whose aim has become to design structures with increased torsional stiffness. To the author’s limited knowledge, studies researching this topic couldn’t provide a simplified method to obtain the natural torsional frequencies and the corresponding mode shapes of structures providing ease of use by structural engineers having limited mathematical backgrounds. The purpose of this study is to establish a simplified numerical model of the torsional vibration of rods with non-uniform geometry and material with classical boundary conditions using the differential quadrature method (DQM). To account for geometric and material non- uniformity, any space varying functions in the longitudinal direction of a one- dimensional structural element can be used in the model. The numerical results obtained are compared with previously obtained analytical results in cases of rods with uniform cross sections and linearly non-uniform ones. The comparison proved significant agreement with the analytical results. The illustrated use of the DQM showed efficiency and acceptable accuracy that made it legible to create an alternative to the time-consuming analytical solutions that require a unique solution technique for every type of structural variation where a strong mathematical background of the user is needed.