Dynamic analysis of extensible beam with multiple cracks

We present the governing equation and study vibrations of multiple crack beams undergoing large deflections subject to transverse loads. First, the primary motion equation is derived using Hamilton’s principle applied to energy functions accounting for cracks. Then we derive a normalized equation governing the vibration of the extensible cracked beam. Single and multiple crack beam examples are considered and analyzed numerically to verify the validity of the derived equations. We propose a modified cracked extensible beam model accounting for the axial force by considering the reduced cross-sectional area. It is expressed by a new reduction parameter. Using the proposed model, we numerically investigate how the cracked extensible beam’s natural frequencies change depending on various model parameters.