Linearization of non-linear stochastically excited dynamic systems

A “second order” linearization method for non-linear stochastically excited dynamic systems is described. Second order probabilistic functions are used to evaluate the linearized stiffness or damping coefficients of the non-linear elements. The values of these coefficients are frequency dependent, in contrast to the nowadays generally used “first order” linearization methods. Principles of both “first order” and “second order” methods are discussed. So-called “linearization functions” of typical non-linearities greatly simplifying practical computations are introduced. The actual linearization procedure is discussed. A simple approximate criterion for the validity of the linearization is established.