Free vibration of axially loaded multi-cracked Timoshenko beams

In this paper, the free vibration of axially-loaded, multi-cracked Timoshenko beams with differing boundary conditions, namely, hinged-hinged, fixed-fixed, fixed-hinged, and fixed-free is studied. The cracked beam system is represented as several beam segments connected by massless rotational springs with sectional flexibility. Each segment is assumed to obey the Timoshenko beam theory. A simple transfer matrix method is used to derive the characteristic equation of the axially-loaded, multi-cracked beam with differing boundary conditions. The characteristic equation and corresponding mode shapes are a function of natural frequency, crack size and location, and physical parameters of the beam. In this paper, the effects of crack depth, number of cracks, position of cracks, axial load, shear deformation and rotary inertia on the dynamic behavior of multi-cracked beams are studied in detail. It is found that there is good agreement between the results obtained in this study and results available in the literature. Additionally, interesting observations overlooked by other researchers are obtained.