The transfer matrix method for modal analysis of cracked multistep beam

Abstract

The present study addresses the modal analysis of multistep beam with arbitrary number of cracks by using the transfer matrix method and modal testing technique. First, there is conducted general solution of free vibration problem for uniform beam element with arbitrary number of cracks that allows one to simplify the transfer matrix for cracked multistep beam. The transferring beam state needs to undertake only at the steps of beam but not through crack positions. Such simplified the transfer matrix method makes straightforward to investigate effect of cracks mutually with cross-section step in beam on natural frequencies. It is revealed that step-down and step-up in beam could modify notably sensitivity of natural frequencies to crack so that the analysis provides useful indication for crack detection in multistep beam. The proposed theory was validated by an experimental case study