Exact vibration modes of multiple-stepped beams with arbitrary steps and supports using elemental impedance method

Abstract

A novel numerical method has been developed and applied to the prediction of vibration modes of general stepped beams with arbitrary steps and general elastic supports. Each beam section is modelled as an element with input impedance at one end and output impedance at the other. These impedances are then coupled when the beam sections are joined to form an overall stepped beam structure. General elastic supports are modelled and their effects on impedance are examined. The method is theoretically exact assuming each beam section can be modelled as Euler-Bernoulli beam and is computationally very efficient since it does not involve any matrix operations of large dimension. Vibration modes of a number of stepped beams of different configurations have been computed using the proposed method and are compared with existing results in literature. Experimental investigations have also been carried out to validate the practical usefulness of the method. The method is also ideally suited for forced vibration applications since it not only establishes vibration modes, but also frequency response functions. In addition, a general purpose software has since been developed based on the method which can be very useful for structural dynamics design of general stepped beam structures.