A modal-energy based equivalent lumped model for open cracks

Two modeling methods are proposed for open notch-like cracks in beam structures. In exact modeling method, the cracked beam is divided into 3 parts – two beams and one crack parts – and its natural frequency analysis is done by assuming that shear beam theory governs the dynamic behavior of the structure. In equivalent modeling method, an equivalent lumped model composed of a set of lateral, torsional and lateral-torsional springs is considered for crack part. The stiffness coefficients of the equivalent lumped model are obtained by comparing the two modeling methods in a modal-energy based approach. The accuracy of the proposed modeling methods are verified by numerous numerical and experimental case studies.