NONLINEAR RANDOM VIBRATION ANALYSIS USING TAIL EQUIVALENT LINEARIZATION METHOD

Abstract

A new non-parametric linearization method for nonlinear random vibration analysis is created. This method works on a discrete representation of the stochastic inputs and the ideas from the first order reliability method (FORM). For a specifiedzresponse thresholdzof theznonlinear system, thezequivalent linearzsystem is characterizedxby matchingzthe "design points" of the linear and nonlinearzresponses in the space of thezstandard normalzvariables acquiredzfrom the discretizationzof thezexcitation. Because of thiszdefinition, the tail probabilityzofzthe linearzsystem is equalzto the firstzorder approximation ofzthe tailzprobability of theznonlinear system, this propertyzmotivating the namezTail- EquivalentzLinearization Method (TELM).This leads to the identification of the TELS in terms of a unit-impulse response function for each component of the input excitation,tail equivalent linearization method is a new,non-parametric linearization method for nonlinear random vibration analysis.This method is to overcome 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 as well as computation of certain nonlinear response characteristics. Further more 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).It is demonstratedzthat the equivalentzlinear systemzis determined in termszof its impulsezresponse functionzin the non-parametriczform fromzthe knowledgezof design point. This examination lookszatzthe impacts of differentzparameters onzthe tail-equivalentzlinear system, presentszan algorithmzfor findingzthe design points. Design point in FORM is the point on a limit-state surface that is nearest to the origin when the random variables are transformed to the standard normal space.Linearization of the limit-state surface at this point uniquely defines a linear system, denoted as Tail-Equivalent Linear System, TELS.Previous study shows that design point shows that design point on limit state surface of linear system and nonlinear system is same. Once the TELS is defined for a specific response threshold, methods of linear random vibrational analysis are used to compute various response statistics, such as the mean crossing rate and tail probabilities of local and extreme peaks. The method has been developed for application in both time, and frequency domain and it has been applied to inelastic structures as well as structures experiencing geometric nonlinearities.