ON THE NUMERICAL CONVERGENCE OF DISCRETIZATION METHODS FOR THE FREE-VIBRATIONS OF BEAMS WITH ATTACHED INERTIA ELEMENTS

This paper is concerned with a numerical convergence study of three discretization methods, Rayleigh-Ritz, Galerkin and finite element, as applied to the analysis of free bending linear vibrations of a uniform Bernoulli-Euler beam carrying inertia elements at intermediate points. A cantilever beam carrying a lumped mass with rotary inertia at an arbitrary intermediate point and another at the beam tip is used as a case study. The first five frequency parameters of this beam obtained by using the Rayleigh-Ritz method in conjunction with broadly admissible base beam eigenfunctions, Galerkin’s method in conjunction with strictly admissible base beam eigenfunctions, and the classical finite element method, are compared with the exact ones over a wide range of values of the system parameters. Conclusions are drawn regarding the effects of the various system parameters on the accuracy and convergence characteristics of the above three discrete methods, and on the mode shapes and the first five frequency parameters of the beam system. © 1994 Academic Press Limited.