CALCULATING THE NATURAL FREQUENCY OF HOLLOW STEPPED CANTILEVER BEAM

Stepped or non-prismatic beams are widely used in many engineering applications and the calculation of their natural frequency is one of the most important problem. Several methods were used to calculate the natural frequency of stepped beam. In this work, the Rayleigh methods (Classical and Modified) and finite element method using ANSYS software were used for calculating the natural frequency of Hollow stepped cantilever beam with circular and square cross section area. The comparison between the results of natural frequency and frequency ratio due to the increasing the length of the small part for these types of beams and for these three methods were made. The agreement between ANSYS the classical Rayleigh results was better than the agreement between ANSYS the Modified Rayleigh results for the two types of cross section area. The maximum error of MRM was greater than that of CRM and the maximum error of circular C.S.A. Was greater than that of square C.S.A. At the same dimensions. The natural frequency of circular C.S.A was smaller than that of square C.S.A. for the same dimensions