Based on the elastic fracture mechanics, we establish a continuous model of one-dimensional Euler–Bernoulli cracked beam using the traveling wave method, and analyze the damage characteristics of cracked beam through the changes of deflection and power flow response. First, the control equation of bending vibration of healthy beam is deduced by traveling wave method. Then, the reflection and transmission matrices of waves at force point, constraint point, crack point are derived. The analytic solutions of deflection and power flow are expressed explicitly as the function of crack location and size. The effects of crack width and depth on deflection and power flow response of cracked beam are revealed. Finally, the numerical example illustrates the effectiveness of the proposed method.
Soliton dynamics in optical fibers using the generalized traveling-wave method