Study on identification method of line density of the elastic beam under unknown boundary conditions

Abstract

In numerical simulation, dynamic model is necessary to predict the product performance such as strength of structure, noise, and vibration. The prediction accuracy depends on the accuracy of parameter identification. For installed or completed products, an experiment must be done to identify structural properties such as Young's modulus or density. This experiment allows us to accurately predict the product performance regardless of product dispersion and aging deterioration. Hence there are many studies about identification methods of the structural parameters of beams. In these studies, the structural parameters were derived from natural frequencies of a beam with/without an additional mass. However, no study can obtain the parameters under unknown boundary conditions. In this study, we proposed a new simple method to identify line density of beams. This method assumes that mode shapes of a beam do not change regardless of additional masses. This study proposes an experimental method for arrangements of additional masses, which can keep mode shapes unchanged. In the numerical analysis, a finite element method is used to obtain the natural frequencies of a beam with/without additional masses. The natural frequencies and the weight of the additional masses are used to identify line density of the beams. We also verify the method through experiment.