Vibration analysis of multiple-stepped beams with the composite element model

A new approach to analyze the free and forced vibrations of beams with multiple cross-section steps is proposed using a composite element method in this paper. The results are compared to receptance function method and classical Rayleigh–Ritz method and finite element results. The natural frequencies obtained from the composite element method are found to be in close agreement with other methods mentioned above and finite element method. The forced vibration responses of the stepped beam are also calculated from the composite element method and compared with those obtained from the finite element method. Time histories from both methods are found to match very well. This indicates the correctness of the proposed method for vibration analyses of the stepped beam. The proposed method can be extended easily to deal with beams consisting of an arbitrary number of nonuniform segments.