International Journal of Sustainable Building Technology and Urban Development ISSN:2093-761X(Print) 2093-7628(Online)

In this paper, free vibration analysis of a cracked cantilever bar by an Approximate Analytical approach is investigated. The crack is modeled by an equivalent axial spring with stiffness Kx according to Castigliano’s theorem. The effect of different crack depth ratio on the longitudinal frequencies and mode shapes in the cracked bar has been analyzed. It is shown that an increase in the crack depth ratio produces a decrease in the fundamental longitudinal natural frequency of a cracked bar. On the other hand, approximate analytical results indicate that the variation of a normalized longitudinal natural frequency with respect to the crack depth ratio give comparable results with those obtained from the numerical solution of an analytical equation of a cracked beam.