Analysis of Flutter-Induced Limit Cycle Oscillations in Gas-Turbine Structures With Friction, Gap, and Other Nonlinear Contact Interfaces

2012 ◽  
Vol 134 (6) ◽  
Author(s):  
E. P. Petrov
Keyword(s):  
Gas Turbine ◽  
Limit Cycle ◽  
Large Scale ◽  
Direct Calculation ◽  
Aerodynamic Characteristics ◽  
Frequency Domain Method ◽  
Nonlinear Contact ◽  
Limit Cycle Flutter ◽  
Interface Parameters ◽  
First Time

A frequency-domain method has been developed to predict and comprehensively analyze the limit-cycle flutter-induced vibrations in bladed disks and other structures with nonlinear contact interfaces. The method allows, for the first time, direct calculation of the limit-cycle amplitudes and frequencies as functions of contact interface parameters and aerodynamic characteristics using realistic large-scale finite element models of structures. The effects of the parameters of nonlinear contact interfaces on limit-cycle amplitudes and frequencies have been explored for major types of nonlinearities occurring in gas-turbine structures. New mechanisms of limiting the flutter-induced vibrations have been revealed and explained.

Analysis of Flutter-Induced Limit Cycle Oscillations in Gas-Turbine Structures With Friction, Gap and Other Nonlinear Contact Interfaces

2011 ◽  
Author(s):  
E. P. Petrov
Keyword(s):  
Limit Cycle ◽  
Large Scale ◽  
Direct Calculation ◽  
Aerodynamic Characteristics ◽  
Frequency Domain Method ◽  
Finite Element Models ◽  
Nonlinear Contact ◽  
Limit Cycle Flutter ◽  
Interface Parameters ◽  
First Time

A frequency-domain method has been developed to predict and comprehensively analyse the limit-cycle flutter-induced vibrations in bladed discs and other structures with nonlinear contact interfaces. The method allows, for the first time, direct calculation of the limit-cycle amplitudes and frequencies as functions of contact interface parameters and aerodynamic characteristics using realistic large-scale finite element models of structures. The effects of the parameters of nonlinear contact interfaces on limit-cycle amplitudes and frequencies have been explored for major types of nonlinearities occurring in gasturbine structures. New mechanisms of limiting the flutter-induced vibrations have been revealed and explained.

Sensitivity Analysis of Multiharmonic Self-Excited Limit-Cycle Vibrations in Gas-Turbine Engine Structures With Nonlinear Contact Interfaces

2014 ◽  
Author(s):  
E. P. Petrov
Keyword(s):  
Limit Cycle ◽  
Large Scale ◽  
Aerodynamic Characteristics ◽  
Frequency Domain Method ◽  
Contact Interface ◽  
Turbine Engine ◽  
Nonlinear Contact ◽  
Interface Parameters ◽  
Primary Frequency

An efficient frequency-domain method is developed to calculate the sensitivity of multiharmonic amplitudes of the limit-cycle oscillations and their primary frequency to variation of the nonlinear contact interface parameters and aerodynamic characteristics. The method allows highly accurate and fast determination of the sensitivity coefficients together with the calculation of the limit-cycle amplitudes and frequencies using realistic large-scale finite element models of structures. The nonlinear contact interactions analysed include: friction contacts, unilateral interaction along normal direction at a contact interface, closing and opening clearances and interferences, cubic spring nonlinearity. The capabilities of the method are demonstrated on a set of test cases.

Method for Direct Parametric Analysis of Nonlinear Forced Response of Bladed Discs With Friction Contact Interfaces

2004 ◽  
Author(s):  
E. P. Petrov
Keyword(s):  
Parametric Analysis ◽  
Large Scale ◽  
Normal Load ◽  
Forced Response ◽  
Finite Element Models ◽  
Contact Interface ◽  
Friction Contact ◽  
Interface Parameters ◽  
First Time ◽  
Contact Parameters

An effective method for direct parametric analysis of periodic nonlinear forced response of bladed discs with friction contact interfaces has been developed. The method allows, for the first time, forced response levels to be calculated directly as a function of contact interface parameters such as the friction coefficient, contact surface stiffness (normal and tangential coefficients), clearances, interferences, and the normal stresses at the contact interfaces. The method is based on exact expressions for sensitivities of the multiharmonic interaction forces with respect to variation of all parameters of the friction contact interfaces. These novel expressions are derived in the paper for a friction contact model, accounting for the normal load variation and the possibility of separation-contact transitions. Numerical analysis of effects of the contact parameters on forced response levels has been performed using large-scale finite element models of a practical bladed turbine disc with underplatform dampers and with shroud contacts.

Direct Parametric Analysis of Resonance Regimes for Nonlinear Vibrations of Bladed Discs

2006 ◽  
Author(s):  
E. P. Petrov
Keyword(s):  
Large Scale ◽  
Contact Stiffness ◽  
Design Parameters ◽  
Strongly Nonlinear ◽  
Resonance Frequencies ◽  
Interface Parameters ◽  
First Time ◽  
Analytical Expressions ◽  
Contact Stiffness Coefficients

A method has been developed to calculate directly resonance frequencies and resonance amplitudes as functions of design parameters or as a function of excitation levels. The method provides, for a first time, this capability for analysis of strongly nonlinear periodic vibrations of bladed discs and other structures with nonlinear interaction at contact interfaces. A criterion for determination of major, sub- and superharmonic resonance peaks has been formulated. Analytical expressions have been derived for accurate evaluation of the criterion and for tracing resonance regimes as function of such contact interface parameters as gap and interference values, friction and contact stiffness coefficients, normal stresses. High accuracy and efficiency of the new method have been demonstrated on numerical examples including large-scale nonlinear bladed disc model and major types of contact interfaces including friction contact interfaces, gaps and cubic nonlinearities.

Analysis of Friction-Saturated Flutter Vibrations With a Fully Coupled Frequency Domain Method

2020 ◽  
Vol 142 (11) ◽  
Author(s):  
Christian Berthold ◽  
Johann Gross ◽  
Christian Frey ◽  
Malte Krack
Keyword(s):  
Limit Cycle ◽  
Energy Method ◽  
Structural Deformation ◽  
Contact Boundary ◽  
Frequency Domain Method ◽  
Elastic Model ◽  
Contact Interactions ◽  
Design Constraint ◽  
Nonlinear Contact ◽  
Fully Coupled

Abstract Flutter stability is a dominant design constraint of modern turbines. Thus, flutter-tolerant designs are currently explored, where the resulting vibrations remain within acceptable bounds. In particular, friction damping has the potential to yield limit cycle oscillations (LCOs) in the presence of a flutter instability. To predict such LCOs, it is the current practice to model the aerodynamic forces in terms of aerodynamic influence coefficients for a linearized structural model with fixed oscillation frequency. This approach neglects that both the nonlinear contact interactions and the aerodynamic stiffness cause a change in the deflection shape and the frequency of the LCO. This, in turn, may have a substantial effect on the aerodynamic damping. The goal of this paper is to assess the importance of these neglected interactions. To this end, a state-of-the-art aero-elastic model of a low pressure turbine blade row is considered, undergoing nonlinear frictional contact interactions in the tip shroud interfaces. The LCOs are computed with a fully coupled harmonic balance method, which iteratively computes the Fourier coefficients of structural deformation and conservative flow variables, as well as the a priori unknown frequency. The coupled algorithm was found to provide excellent computational robustness and efficiency. Moreover, a refinement of the conventional energy method is developed and assessed, which accounts for both the nonlinear contact boundary conditions and the linearized aerodynamic influence. It is found that the conventional energy method may not predict a limit cycle oscillation at all while the novel approach presented here can.

scholarly journals Analysis of Bifurcations in Multiharmonic Analysis of Nonlinear Forced Vibrations of Gas Turbine Engine Structures With Friction and Gaps

2016 ◽  
Vol 138 (10) ◽  
Author(s):  
E. P. Petrov
Keyword(s):  
Gas Turbine ◽  
Large Scale ◽  
Parameter Variation ◽  
Forced Vibrations ◽  
Forced Response ◽  
Operating Conditions ◽  
Frequency Domain Method ◽  
Cubic Nonlinearity ◽  
Turbine Engine ◽  
Detection And Localization

An efficient frequency-domain method has been developed to analyze the forced response of large-scale nonlinear gas turbine structures with bifurcations. The method allows detection and localization of the design and operating conditions sets where bifurcations occur, calculation of tangents to the solution trajectory, and continuation of solutions under parameter variation for structures with bifurcations. The method is aimed at calculation of steady-state periodic solution, and multiharmonic representation of the variation of displacements in time is used. The possibility of bifurcations in realistic gas-turbine structures with friction contacts and with cubic nonlinearity has been shown.

Direct Parametric Analysis of Resonance Regimes for Nonlinear Vibrations of Bladed Disks

2006 ◽  
Vol 129 (3) ◽  
pp. 495-502 ◽  
Author(s):  
E. P. Petrov
Keyword(s):  
Large Scale ◽  
Contact Stiffness ◽  
Design Parameters ◽  
Bladed Disks ◽  
Disk Model ◽  
Strongly Nonlinear ◽  
Resonance Frequencies ◽  
Interface Parameters ◽  
First Time ◽  
Analytical Expressions

A method has been developed to calculate directly resonance frequencies and resonance amplitudes as functions of design parameters or as a function of excitation levels. The method provides, for the first time, this capability for analysis of strongly nonlinear periodic vibrations of bladed disks and other structures with nonlinear interaction at contact interfaces. A criterion for determination of major, sub-, and superharmonic resonance peaks has been formulated. Analytical expressions have been derived for accurate evaluation of the criterion and for tracing resonance regimes as function of such contact interface parameters as gap and interference values, friction and contact stiffness coefficients, and normal stresses. High accuracy and efficiency of the new method have been demonstrated on numerical examples including a large-scale nonlinear bladed disk model and major types of contact interfaces including friction contact interfaces, gaps, and cubic nonlinearities.

Analysis of Friction-Saturated Flutter Vibrations With a Fully-Coupled Frequency Domain Method

2020 ◽  
Author(s):  
Christian Berthold ◽  
Johann Gross ◽  
Christian Frey ◽  
Malte Krack
Keyword(s):  
Limit Cycle ◽  
Energy Method ◽  
Structural Deformation ◽  
Contact Boundary ◽  
Frequency Domain Method ◽  
Elastic Model ◽  
Contact Interactions ◽  
Design Constraint ◽  
Nonlinear Contact ◽  
Fully Coupled

Abstract Flutter stability is a dominant design constraint of modern gas and steam turbines. Thus, flutter-tolerant designs are currently explored, where the resulting vibrations remain within acceptable bounds. In particular, friction damping has the potential to yield Limit Cycle Oscillations (LCOs) in the presence of a flutter instability. To predict such LCOs, it is the current practice to model the aerodynamic forces in terms of aerodynamic influence coefficients, derived for some normal modes of the linearized structural model and fixed oscillation frequency. However, this approach neglects that both the nonlinear contact interactions and the aerodynamic stiffness cause a change in the deflection shape and the frequency of the LCO. This, in turn, may have a substantial effect on the aerodynamic damping. The goal of this paper is to assess the technical importance of these neglected interactions. To this end, a state-of-the-art aero-elastic model of a low pressure turbine blade row is considered, undergoing nonlinear frictional contact interactions in the tip shroud interfaces. The LCOs are computed with a fully-coupled harmonic balance method, which iteratively computes the Fourier coefficients of structural deformation and conservative flow variables, as well as the a priori unknown frequency. The coupled algorithm was tested for various combinations of harmonics in both domains and found to provide excellent computational robustness and efficiency. Moreover, a refinement of the conventional energy method is developed and assessed, which accounts for both the nonlinear contact boundary conditions and the linearized aerodynamic influence. It is found that the conventional energy method may not predict a limit cycle oscillation at all while the novel approach presented here can. Furthermore the refined energy method provides deep understanding of the nonlinear aero-elastic interactions.

scholarly journals Analysis of Bifurcations in Multiharmonic Analysis of Nonlinear Forced Vibrations of Gas-Turbine Engine Structures With Friction and Gaps

2015 ◽  
Author(s):  
E. P. Petrov
Keyword(s):  
Gas Turbine ◽  
Large Scale ◽  
Parameter Variation ◽  
Forced Vibrations ◽  
Forced Response ◽  
Operating Conditions ◽  
Frequency Domain Method ◽  
Cubic Nonlinearity ◽  
Turbine Engine ◽  
Detection And Localization

An efficient frequency-domain method has been developed to analyse the forced response of large-scale nonlinear gas-turbine structures with bifurcations. The method allows: detection and localization of the design and operating conditions sets where bifurcations occur; calculation of tangents to the solution trajectory and continuation of solutions under parameter variation for structures with bifurcations. The method is aimed at calculation of steady-state periodic solution and multiharmonic representation of the variation of displacements in time is used. The possibility of bifurcations in realistic gas-turbine structures with friction contacts and with cubic nonlinearity has been shown.

Scheming

2018 ◽  
Author(s):  
Seán Damer
Keyword(s):  
Social Class ◽  
Housing Policy ◽  
Large Scale ◽  
Class Structure ◽  
Local Council ◽  
Housing Scheme ◽  
Post War ◽  
First Time ◽  
The Voice ◽  
House Building

This book seeks to explain how the Corporation of Glasgow, in its large-scale council house-building programme in the inter- and post-war years, came to reproduce a hierarchical Victorian class structure. The three tiers of housing scheme which it constructed – Ordinary, Intermediate, and Slum-Clearance – effectively signified First, Second and Third Class. This came about because the Corporation uncritically reproduced the offensive and patriarchal attitudes of the Victorian bourgeoisie towards the working-class. The book shows how this worked out on the ground in Glasgow, and describes the attitudes of both authoritarian housing officials, and council tenants. This is the first time the voice of Glasgow’s council tenants has been heard. The conclusion is that local council housing policy was driven by unapologetic considerations of social class.

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