Perturbation methods for dynamic analysis of cracked beams

Structural perturbation method is used to analyze modal parameters of the damaged beam. Firstly, the modified crack model is proposed to consider damage's influence on structural stiffness and mass distribution functions. The governing vibration equations are derived using the first and second perturbation method. Then the natural frequencies and corresponding mode shapes of the cracked Euler-Bernoulli beam are calculated using the Fourier series method. Compared with experimental results of cracked cantilever beams, the computation results prove this method's precision.