Abstract
This paper treats the problem of analysis of steady-state vibration of a frame structure with breathing cracks. The breathing crack opens and closes during vibration. Since the opening and closing of the breathing crack depends on the sign of the bending moment and tensile force in the axial direction, the key point to this problem is explicit treatment of the bending moment and tensile force. In a previous paper, one of the authors presented a method to analyze vibration of a beam with breathing cracks. The presented method is based on the mixed variational principle which allows one to use deflection as well as bending moment as primary variables in the governing equation. In this paper the presented method is generalized so that it becomes applicable to frame structures. First the governing equations of a frame structure with breathing cracks are derived by the finite element procedure based on the mixed variational principle. Then a method to solve the derived governing equations by combining the iteration method and the harmonic balance method is presented.
