Approximate solution for nonlinear random vibration problems by partial stochastic linearization

The accuracy of the stochastic linearization methods is improved by the proposed method of partial stochastic linearization, in which only the nonlinear damping force in the original system is replaced by a linear viscous damping, while the nonlinear restoring force remains unchanged. The replacement is based on the criterion of equal mean work, performed by the nonlinear damping force in the original system and its linear counterpart. The resulting nonlinear stochastic differential equation is then solved exactly, keeping the equivalent damping coefficient as a parameter, which can be determined for a specific system by solving a nonlinear algebraic equation.