Natural frequencies of transversely vibrating cracked simple beams

Structural elements may be subjected to a transverse vibration caused by some external effect along its service life. The governing equation of motion is well known and is expressed in terms of transverse displacements, longitudinal distances, time, kind of transverse load and element properties. Natural frequencies of simply supported beams, for example, can be easily derived mathematically when the bending rigidity is being constant along their spans. In this paper the effect of cracking on natural frequencies of transversely vibrating simply supported beams under uniform gravity loads is studied. Different forms of inertia variation along middle parts of these beams, where cracks initiate and propagate, are considered. Modified finite integral method is used in solving for the natural frequencies of such beams numerically covering a range of cracking propagation length, inertia variation being constant, linear and of second degree order forms. Results are discussed and compared with natural frequencies of such beams with non-cracked beams, and a conclusion about the subject is drafted.