INVESTIGATION OF NONLINEAR SYSTEMS USING TAIL EQUIVALENT LINEARIZATION METHOD

Abstract

Development of a non-parametric linearization method to be used for analysis of nonlinear random vibration has been done. It operates on a discretized representation of the stochastic inputs and combines the ideas from the first order reliability method (FORM). For nonlinear system a particular response threshold is defined and the equivalent linear system is characterized by matching the "design points" of the nonlinear and linear responses in the space of the standard normal variables which is derived by discretizing the excitation. As a consequence of this definition, the first order approximation of tail probability of nonlinear system is equalized to tail probability of linear system. Thus, a unit-impulse response function of the input excitation is required for the representation of TELS. This system has been organized in order to tackle the inadequacy of conventional equivalent linearization method. Our objectives are investigation and thorough understanding of analysis of stochastic non-linear system by tail equivalent linearization method along with the calculations of certain nonlinear response characteristics. Furthermore study is presented on method of random vibrational analysis especially on equivalent linearization method and also gives brief review on reliability analysis of structure, first order reliability analysis (FORM). This purpose of this study is to look at the effects of different parameters on the system. At the design point, linearization of the limit-state surface is done in order to distinctly define a linear system, which is denoted as TELS.