Fluctuation Characteristics And Vibrational Power Flow Analysis Of Cracked Beam

Engineering structures will confront problems of structure cracks or cracks accumulation. If structure cracks can be analyzed thoroughly to identify cracks on line and real time, not only quality of engineering structures can be improved, but structure cracks can be known well in time. And thus, we can take appropriate maintaining measures to reduce extents of structure cracks accumulation, and avoid unnecessary losses and disasters. This paper studies preliminarily and analyzes numerically fluctuation characteristics about infinite cracked beam based on theory of vibrational power flow. First, flexibility matrix of cracked beam element is induced considering all coupling effects. However with regard to slender beam, flexural torque is predominant in flexibility matrix, so flexibility of crack is verified and computed under condition of pure flexural torque. Then, inputted power flow and transmitted power flow are computed when two cracks exist on the same side of excitation point and on each side respectively applying the point transfer matrix and element transfer matrix. Using Matlab software, the change of inputted power flow and transmitted power flow corresponding to the variation of crack parameters is visualized. Cracks can be simulated as many models according to different theories. Here, damage is simulated as a small part of constant cross section, diminished inertia moment to compare with the results of a rotational spring model. However, assumption of that crack is always open in vibration is not realistic, so in this paper, a simple non-linear fatigue crack model is developed and compared with the results of a rotational spring model. Through this paper, the vibrational power flow has relations with crack parameters, i.e. position and depth of crack, for this reason, it is practical to identify cracks' position and depth using this paper's analysis and combining measured results of vibrational power flow.