Nonlinear random vibration using updated tail equivalent linearization method

Tail equivalent linearization method is based on first order reliability method, which obtains an equivalent linear system for the considered nonlinear problem with equal tail probability related to a specified threshold and time. This method has been applied only to nonlinear non-degrading single- and multi-degrees of freedom shear beam two-dimensional models and three-dimensional one-story rigid diaphragm supported by frames with in-plane uni-axial stiffness which is subjected to independent random excitation along the structural axes. To use TELM for more practical problems it is required to extend this method to cover more realistic material and excitation characteristics. In this paper, some of these developments have been presented. Application of TELM for bi-directional excitation with bi-axial material subjected to different incidence angles of excitation and using TELM for degrading material which has been presented in the previous works of the authors have been reviewed briefly. In addition a new method for defining rotational dependent component of earthquake excitation in terms of independent translational components in the standard normal random variable space is proposed, and TELM has been used for this kind of excitation. Three examples related to these extensions have been presented; the comparison of the TELM results with Mote-Carlo simulation results shows good agreement.