Hardening and Softening Characteristics of a Piecewise Linear Isolator Under 1G Gravity

2013 ◽  
Author(s):  
X. Wang ◽  
G. T. Zheng
Keyword(s):  
Nonlinear System ◽  
Degrees Of Freedom ◽  
Piecewise Linear ◽  
Linearization Method ◽  
Equivalent Linearization ◽  
Frequency Responses ◽  
Flexible Base ◽  
Equivalent Linearization Method ◽  
System Frequency ◽  
Hardening And Softening

The frequency responses of a piecewise isolator mounted on a moving flexible base are investigated. A procedure, which is based on Equivalent Linearization method and transfer function, is proposed to study this two-degrees-of freedom nonlinear system. The influence of 1G gravity on the nonlinearity of the system frequency responses is investigated and presented in detail. It is shown that the piecewise stiffness may demonstrate both hardening and softening properties due to different amplitude, clearance and gravity.

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.

scholarly journals A weighted dual criterion for stochastic equivalent linearization method

2014 ◽  
Vol 36 (4) ◽  
pp. 307-320 ◽  
Author(s):  
N. D. Anh ◽  
N. N. Linh
Keyword(s):  
Piecewise Linear ◽  
Least Square Method ◽  
Piecewise Linear Function ◽  
Random Excitation ◽  
Linearization Method ◽  
Least Square ◽  
Weighting Coefficient ◽  
Equivalent Linearization ◽  
Mean Square ◽  
Equivalent Linearization Method

A weighted dual mean square criterion for stochastic equivalent linearization method is considered in which the forward and backward replacements are weighted. The normalized weighting coefficient is suggested as a piecewise linear function of the squared correlation coefficient and is defined by the least square method based on the data of Lutes-Sarkani oscillator. The application to two typical nonlinear systems subjected to random excitation shows accurate approximations when the nonlinearity varies from the weak to strong levels.

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 ◽  
Linear Part ◽  
Random Excitation ◽  
Linearization Method ◽  
System Response ◽  
Equivalent Linearization ◽  
Vibrational Behavior ◽  
Bladed Disk ◽  
Bladed Disk Assembly ◽  
Equivalent Linearization Method

Abstract The present article addresses the vibrational behavior 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 behavior. The use of friction dampers for energy dissipation and suppression of large amplitudes adds a nonlinearity to the mechanical system, which complicates the calculations. Depending on the stage, different types of excitation can occur in a turbine, from stationary to transient, synchronous to asynchronous as well as deterministic to random excitation. Random excitation in combination with the presence of nonlinearities makes the calculation of the vibrational behavior even more complex. So far, this 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 fundamental idea of the method is to linearize a nonlinear system in such a way that the most suitable equivalent linear system is found taking into account the approximated distribution of the response amplitude. To apply this method to a system with a friction nonlinearity, the linear part of the system is considered in state space and extended with additional nonlinear equations. The nonlinear contact is modelled with a Bouc-Wen formulation to reproduce the hysteretic character of a nonlinearity occurring in the presence of a friction damper. The classical Bouc-Wen formulation is standardized in such a way that the usual parameters can be replaced by physical ones such as the normal force or contact stiffness. The nonlinear force of the friction nonlinearity is linearized regarding the stochastic distribution of the system response. 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. However, the spectrum of the excitation is not limited to being constant, as it is the case with Gaussian white noise. The equivalent linearization method could also deal with a narrowband or broadband excitation spectrum. Unlike previous papers on this topic, the calculations are performed on a full bladed disk assembly in which each sector is represented by a reduced order model with several degrees of freedom.

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