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 approaches and their effectiveness as analysis and design methods for multiple-stepped beams are also discussed.