Free vibration of a cantilevered beam with multiple steps: Comparison of several theoretical methods with experiment

The flexural-free vibration of a cantilevered beam with multiple cross-section steps is investigated theoretically and experimentally. Experimental results are compared against Euler-Bernoulli beam theory solutions from Rayleigh-Ritz and component modal analyses, as well as finite element results using the commercial package ANSYS. Finite elements are also used to investigate a Timoshenko beam, a two-dimensional shell, and a three-dimensional solid element model. A detectable difference in the first in-plane bending natural frequency is noted between the beam theory results and those of the higher-dimensional finite element models and experimental observation. The convergence of the several theoretical multiple-stepped beams are also discussed. approaches and their effectiveness as analysis and design methods for (c) 2007 Elsevier Ltd. All rights reserved.