Sensitivity Analysis and Robust Assignment of Natural Frequencies for Vibrating Systems Using the Receptance Method

Abstract

This paper presents a new receptance-based method for the robust assignment of natural frequencies. This method aims to address the deviation of the actually achieved natural frequencies for target natural frequencies when assigning natural frequencies, which usually arises due to uncertainties in passive structural modifications (i.e. mass and stiffness modifications). The mathematical expression is derived for the sensitivity of the target natural frequency to the uncertainties in modification parameters, which are subsequently employed to characterize the potential deviations of the target natural frequencies in the total differential form. The obtained deviation expression is integrated into the optimization calculation of the natural frequency assignment as an extra penalty term to boost the acquisition of highly robust modification parameters. The proposed robust assignment method, as a non-probabilistic technique, can be employed without any knowledge of the probabilistic distribution of uncertainty in modification parameters. Moreover, it uses only the measured frequency response functions (FRFs), preserving the advantage of the receptance method not needing a numerical model. Two numerical examples and a comparison with a typical eigenstructure assignment method (reported in the literature) demonstrate that the proposed method can provide highly robust modification parameter solutions. The application of the proposed method to the natural frequency assignment of a laboratory water-filled pipeline system gives experimental evidence of its effectiveness.