Substructure elimination method for evaluating bending vibration of beams

In this study, a vibration analysis method is presented based on the substructure elimination method for a Bernoulli-Euler beam. Vibration analysis using modal analysis is effective for reducing the degrees of freedom and enables the analysis of a beam on which actuators and sensors are installed. When mechanical impedances are installed at the boundaries or the beam is coupled to other structures, a free-free beam is employed for conventional modal analysis using continuous functions. However, conventional modal analysis provides inaccurate simulation results when the coupled mechanical impedances considering the characteristic impedances of the beam are large. To address this issue, the modal analysis of a beam using the substructure elimination method was proposed in this study. Because the substructure elimination method for beams was only briefly reported on by the first author, several problems currently exist. To solve these problems, a substructure elimination method is proposed using a simply supported beam in addition to a guided-guided beam. Additionally, a new formulation method based on constraint conditions was proposed as a versatile method for setting arbitrary boundary conditions. The appropriate length, line density, and bending stiffness of the elimination regions, and the highest order of the eigenmode, were determined through simulations. The effectiveness of the proposed method was then verified by comparing the simulation results of the proposed method and exact solutions obtained using the boundary conditions. Based on a comparison with the simulation results of conventional modal analysis using a free-free beam, the precision of the proposed method is significantly higher than that of conventional modal analysis.