Accuracy enhancement of modal analysis using higher-order residual terms

Abstract

This study proposes a method to improve the computational accuracy of modal analysis by considering higher-order residual terms in addition to the residual stiffness. Conventionally, the effect of the residual stiffness of higher-order eigenmodes has been considered using the Hansteen and Bell method. However, it is insufficient to consider only the effect of the residual stiffness in the frequency range near the natural frequencies of the omitted eigenmodes. The proposed method improves computational accuracy by considering lower-order residual terms in addition to the residual mass when low-order eigenmodes are omitted rather than high-order eigenmodes. Furthermore, assuming that a continuous body is analyzed, we also present an approach to evaluate the residual stiffness of the eigenmodes of the degrees of freedom (DOF) excluded from the equations of motion by using the exact solution of the static displacement. The concept and essence of the proposed method were theoretically described using a 1-DOF vibration system. Then, higher-order and lower-order residual terms were theoretically formulated in a multi-DOF vibration system. Furthermore, we also describe the approach used to evaluate the residual stiffness of the degrees of freedom excluded from the equations of motion by using static displacement. The effectiveness of the proposed method was verified by comparing the exact solution with the simulation results of modal analysis using the proposed method.