Vibration Characteristics and Power Flow Analysis of a Constant Cracked Beam with General Boundary Conditions

Abstract

The vibration analysis of beams with cracks is an important problem in the structural dynamics community. In this study, a general model for the vibration analysis of a cracked beam with general boundary conditions was developed and investigated, emphasizing its vibration and power flow characteristics. The beam crack was introduced via torsional and translational coupling springs, which separated the beam structure into two segments, and the corresponding vibration characteristics were investigated via an energy-based formulation in conjunction with the Lagrangian procedure. A boundary-smoothed Fourier series was employed to construct the beam displacement field to avoid boundary differential discontinuities. Various crack statuses, including their depths or positions can be easily considered by adjusting the stiffness coefficient of the artificial springs. Several examples were presented to validate the effectiveness and accuracy of the proposed model. The modal characteristics and forced response of a cracked beam were predicted and analyzed, respectively, with a detailed depiction of the power flow around the crack. The results indicate that the presence of a crack has an important effect on the modal characteristics of an elastically restrained beam, as well as on the power flow distribution across the beam structure. This study can provide an effective tool for the dynamic analysis and power flow mechanism of beam structures with various cracks and complex boundary conditions.