By using of extending order and modal transformation of dynamic equation

a Lyapunov equation was established

and the solution of the Lyapunov equation could be used to directly obtain stationary random vibration response variance of large-scale finite element structure.Duffing system was linearized by equivalent linearization method

and the Lyapunov equation was solved to get the variance of random vibration response of duffing system.The precision has been justified by simulation

showing that the presented method is efficient and precise.