Vibration characteristics of two DOF system designed by modal vectors

Abstract

The dynamic absorber must have the desired natural frequency which is determined by the condition of vibration suppression. For example, the Frahm damper has the natural frequency which is just same as the target frequency for vibration suppression. For two DOF system, we have shown that there are two combination of the parameters for specified natural frequencies. In the vibration theory of MDOF system, natural frequency and modal vector are a set and inseparable. Then, there is the question whether modal vector determines the parameters of two DOF system. In this study, we pick up mass ratio and stiffness ratio as parameters of two DOF system. and examine the relationship between these parameters and their modal vectors. It is shown that each of the mass ratio and the stiffness ratio mainly affects the second and the first modal vector, respectively. The transition of natural frequencies by the mass ratio and the stiffness ratio is also considered. Moreover, the mass ratio and the stiffness ratio from modal vectors are successfully derived. The modal vectors affect the mass ratio and the stiffness ratio in the almost similar way. In addition, the relationship between the modal vectors and natural frequencies are almost same as the mass ratio and the stiffness ratio.