Bending and vibration of a discontinuous beam with a curvic coupling under different axial forces

Abstract

The transverse stiffness and vibration characteristics of discontinuous beams can significantly differ from those of continuous beams given that an abrupt change in stiffness may occur at the interface of the former. In this study, the equations for the deflection curve and vibration frequencies of a simply supported discontinuous beam under axial loads are derived analytically on the basis of boundary, continuity, and deformation compatibility conditions by using equivalent spring models. The equation for the deflection curve is solved using undetermined coefficient methods. The normal function of the transverse vibration equation is obtained by separating variables. The differential equations for the beam that consider moments of inertia, shearing effects, and gyroscopic moments are investigated using the transfer matrix method. The deflection and vibration frequencies of the discontinuous beam are studied under different axial loads and connection spring stiffness. Results show that deflection decreases and vibration frequencies increase exponentially with increasing connection spring stiffness. Moreover, both variables remain steady when connection spring stiffness reaches a considerable value. Lastly, an experimental study is conducted to investigate the vibration characteristics of a discontinuous beam with a curvic coupling, and the results exhibit a good match with the proposed model.

Linear and nonlinear vibrations of variable cross‐section beams using shear deformation theory

“…[42] investigated the nonlinear vibrations and dynamic response of a FG beam within the framework of the improved TSDT and a new numerical technique. Liu et al [26], investigated the deflection and frequencies of a simply supported discontinuous beam under axial loads by using the equivalent spring models. They solved the equation using undetermined coefficient methods.…”