Modeling the elastic support properties of Bernoulli-Euler beams

Abstract

Considering the transverse vibration problem of a machine rotor, the authors deal with the free vibration of elastically restrained Bernoulli-Euler beams. Based upon Rayleigh's quotient, an iterative strategy is developed to identify the approximated torsional stiffness coefficients, which allows to bringing together experimental results obtained through impact tests and the ones of the theoretical model. The proposed algorithm treats the vibration of continuous beams taking into account different stiffness coefficients at the left end side and intermediate supports and the effect of attached mass with inertia at the free beam tip, not just on the energetic terms of the Rayleigh's quotient but also on the mode shapes, considering the shape functions defined in branches. A number of loading cases are studied and examples are given to illustrate the validity of the model and the accuracy of the obtained natural frequencies. ©2010 Society for Experimental Mechanics Inc.