Statistical and equivalent linearization techniques with probability density criteria

The concept of statistical and equivalent linearization with probability density criteria for dynamic systems under Gaussian excitations is considered in the paper. New criteria of linearization and two approximate approaches are proposed. In the first one (statistical linearization) in order to establish the linearization coefficients and response characteristics the output probability density functions of static nonlinear element and the corresponding static linearized element are used in an iterative procedure. In the second approach (equivalent linearization) the direct minimization of a criterion based on output probability density functions of dynamic nonlinear system and the corresponding dynamic linearized system is proposed. The detailed analysis and numerical results are given for the Duffing oscillator.