Longitudinal vibration of cracked beams under magnetic field

Longitudinal vibration of a cracked beam subjected to the transverse magnetic field is addressed. One dimensional wave theory is used and the crack part of the beam is modelled as by a linear spring, in this analysis. The obtained explicit solution, for clamped-free and clamped-clamped boundary conditions, is illustrated as graphically. It is generally seen that the longitudinal frequencies increase with increase of the intensity of magnetic field. However, the results of the analysis reveal that the transverse magnetic field has a more significant effect on the variation of longitudinal vibration frequency under the clamped-clamped boundary conditions.