Recursive expressions for time dependent means and mean square responses of a multi-degree-of-freedom non-linear system

Abstract

In this paper we present recursive expressions for time dependent means and mean square responses of a multi-degree-of-freedom (MDOF) system with non-symmetric non-linearities in its stiffness terms. Based on the stochastic central difference-cum-statistical linearization (SCD-SL) technique, four recursive schemes for this system are derived. These schemes are implemented in a digital computer program written in Fortran 77. The results of both the stationary and time dependent means and mean square responses obtained by using the computer program are compared with those employing the Monte Carlo simulation (MCS) technique. It is concluded that (a) the recursive expression schemes are easy to be implemented in a digital computer program, (b) the computed stationary and time dependent means and mean square responses are accurate, and (c) the schemes are far more economical to employ than the MCS technique.