damage detection of axially loaded beam: a frequency-based method

the present study utilizes an analytical method to formulate the three lowest modal frequencies of axially-loaded notched beam through both crack location and load level in a specific format that can be used in existing frequency-based crack-identification methods. the proposed formula provides a basis to shift into two states, one with axial loading and the other without any loading whatsoever. when any two natural frequencies in simply-supported beam with an open crack, subjected to axial load, are measured, crack position and extent can be determined, using a characteristic equation, which is a function of crack location, sectional flexibility, and eigenvalue (natural frequency). theoretical results show high accuracy for service axial loads. in this range, errors for crack location and extent are less than 12% and 10%, respectively.