Natural mode analysis of a telescopic boom system with multiple sections using the Rayleigh-Ritz method

Abstract

A truck crane, a type of construction machine, contains a boom consisting of several strips with different cross-sectional data. A set of the overall natural frequencies of each mode should be obtained for a boom body with multiple sections to analyze vibrational characteristics. The proposed tool for analysis is Rayleigh-Ritz, which is an energy method that employs the calculus of variations. We develop a general computer code for a set of sub-beam structures with a symbolic expression in MATLAB and compare the result with that of a numerical analysis using the finite element method (FEM) with COMSOL, a commercial code. Results of the boom model show that the first-mode natural frequency shows an error of 4.6 % between the Rayleigh-Ritz method and 3D FEM. The solution reaches stable convergence after increasing the terms of base functions, and the present application produces reasonable results.