Equivalent linearization method based on energy-to-cTH-power difference criterion in nonlinear stochastic vibration analysis of multi-degree-of-freedom systems

2001 ◽  
Vol 22 (8) ◽  
pp. 947-955 ◽  
Author(s):  
Guo-yan Wang ◽  
Min Dai
Keyword(s):  
Vibration Analysis ◽  
Linearization Method ◽  
Degree Of Freedom ◽  
Equivalent Linearization ◽  
Stochastic Vibration ◽  
Power Difference ◽  
Equivalent Linearization Method ◽  
Difference Criterion

scholarly journals Non-Gaussian Stochastic Equivalent Linearization Method for Inelastic Nonlinear Systems with Softening Behaviour, under Seismic Ground Motions

2014 ◽  
Vol 2014 ◽  
pp. 1-16 ◽  
Author(s):  
Francisco L. Silva-González ◽  
Sonia E. Ruiz ◽  
Alejandro Rodríguez-Castellanos
Keyword(s):  
Monte Carlo ◽  
Ground Motions ◽  
Joint Probability ◽  
Structural Response ◽  
Linearization Method ◽  
Degree Of Freedom ◽  
Structural Behavior ◽  
Equivalent Linearization ◽  
Equivalent Linearization Method ◽  
Non Gaussian

A non-Gaussian stochastic equivalent linearization (NSEL) method for estimating the non-Gaussian response of inelastic non-linear structural systems subjected to seismic ground motions represented as nonstationary random processes is presented. Based on a model that represents the time evolution of the joint probability density function (PDF) of the structural response, mathematical expressions of equivalent linearization coefficients are derived. The displacement and velocity are assumed jointly Gaussian and the marginal PDF of the hysteretic component of the displacement is modeled by a mixed PDF which is Gaussian when the structural behavior is linear and turns into a bimodal PDF when the structural behavior is hysteretic. The proposed NSEL method is applied to calculate the response of hysteretic single-degree-of-freedom systems with different vibration periods and different design displacement ductility values. The results corresponding to the proposed method are compared with those calculated by means of Monte Carlo simulation, as well as by a Gaussian equivalent linearization method. It is verified that the NSEL approach proposed herein leads to maximum structural response standard deviations similar to those obtained with Monte Carlo technique. In addition, a brief discussion about the extension of the method to muti-degree-of-freedom systems is presented.

Equivalent Linearization of Bladed Disk Assemblies with Friction Nonlinearities Under Random Excitation

2020 ◽  
Author(s):  
Alwin Förster ◽  
Lars Panning-von Scheidt ◽  
Jörg Wallaschek
Keyword(s):  
Degrees Of Freedom ◽  
Turbine Blades ◽  
Random Excitation ◽  
Linearization Method ◽  
Equivalent Linearization ◽  
Friction Damper ◽  
Bladed Disk ◽  
Stationary Stochastic Processes ◽  
Bladed Disk Assembly ◽  
Equivalent Linearization Method

Abstract The present article addresses the vibrational behaviour of bladed disk assemblies with nonlinear shroud coupling under random excitation. In order to increase the service life and safety of turbine blades, intense calculations are carried out to predict the vibrational behaviour. The use of friction dampers for energy dissipation and suppression of large amplitudes makes the mechanical system nonlinear, which complicates the calculations. Depending on the stage, different types of excitation can occur in a turbine, from clearly defined deterministic to random excitation. So far, the latter problem has only been dealt with to a limited extent in the literature on turbomachinery. Nevertheless, there are in general different approaches and methods to address this problem most of which are strongly restricted with regard to the number of degrees of freedom. The focus of this paper is the application of an equivalent linearization method to calculate the stochastic response of an academic model of a bladed disk assembly under random excitation. The nonlinear contact is modelled both with an elastic Coulomb-slider and a Bouc-Wen formulation to reproduce the hysteretic character of a friction nonlinearity occurring in the presence of a friction damper. Both the excitation and the response are limited to mean-free, stationary stochastic processes, which means that the stochastic moments, do not change over time. Unlike previous papers on this topic, the calculations are performed on a full bladed disk assembly in which each segment is approximated with several degrees of freedom.

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