Modelling of compound cantilevers for vibration analysis

This paper presents a method for investigating the vibration of a compound cantilever beam using the Assumed Mode Method. Here the compound beam refers to a beam having number of steps or connected sections, uniformly distributed and point loads, and carrying particles in the span. The static deflection curve for the beam was obtained and used as the shape function. Lagrange's equations were then applied to derive equations of motion. A systematic procedure was used to obtain static deflection curves and vibration calculations that facilitate the use of mathematical software for calculations. The method was then used to model and analyze a hydraulically driven boom. The deflection and natural frequency of the physical system were measured and compared with the assumed shape and the theoretical calculations. The fitted deflection curve is very close to the measured deflection. There is a discrepancy between the measured and calculated frequencies, which is mainly due to idealization of the physical system. The method can be used as a quick tool to find the natural frequency of a compound beam.