Abstract: The complex Mode Theorem and Matrix Perturbation Method are applied to execution of the modal sensitivity analysis and the Fourier Series Method for calculation of the vibration responses.The dynamic characteristics of a complicated aerogear system,so-called star gear system,are elaborated thoroughly.The damping enhancement and modifications of other structural parameters for the vibration depression of the system are also considered in order to find the most efficient measures to minimize the vibration responses of the whole gear system.As a result,an accurate and efficient procedure for the dynamic analysis and redesign of viscously damped linear vibration system is developed,and some practically useful conclusions are drawn out.