scholarly journals A Method for Parametric Analysis of Stability Boundaries for Nonlinear Periodic Vibrations of Structures With Contact Interfaces

2018 ◽  
Vol 141 (3) ◽  
Author(s):  
E. P. Petrov
Keyword(s):  
Parametric Analysis ◽  
Large Scale ◽  
Contact Stiffness ◽  
Stability Loss ◽  
Forced Response ◽  
Scale Model ◽  
Design Parameters ◽  
Stability Boundaries ◽  
Analysis Of Stability ◽  
The Stability

A method for parametric analysis of the stability loss boundary has been developed for periodic regimes of nonlinear forced vibrations for a first time. The method allows parametric frequency-domain calculations of the stability loss together with the vibration amplitudes and design parameter values corresponding to the stability boundaries. The tracing algorithm is applied to obtain the trajectories of stability loss points as functions of design parameters. The parametric stability loss is formulated for cases when (i) the design parameters characterize the properties of nonlinear contact interfaces (e.g., gap, contact stiffness, and friction coefficient); (ii) the design parameters describe linear components of the analyzed structure (e.g., parameters of geometric shape, material, natural frequencies, and modal damping); and (iii) these parameters describe the excitation loads (e.g., their level, distribution or frequency). An approach allowing the multiparametric analysis of stability boundaries is proposed. The method uses the multiharmonic representation of the periodic forced response and aimed at the analysis of realistic gas-turbine structures comprising thousands and millions degrees-of-freedom (DOF). The method can be used for the effective search of isolated branches of the nonlinear solutions and examples of detection and search of the isolated branches are given: for relatively small and for large-scale finite element (FE) models. The efficiency of the method for calculation of the stability boundaries and for the search of isolated branches is demonstrated on simple systems and on a large-scale model of a turbine blade.

scholarly journals A Method for Parametric Analysis of Stability Boundaries for Nonlinear Periodic Vibrations of Structures With Contact Interfaces

2018 ◽  
Author(s):  
E. P. Petrov
Keyword(s):  
Parametric Analysis ◽  
Large Scale ◽  
Contact Stiffness ◽  
Stability Loss ◽  
Forced Response ◽  
Scale Model ◽  
Design Parameters ◽  
Stability Boundaries ◽  
Analysis Of Stability ◽  
The Stability

A method for parametric analysis of the stability loss boundary has been developed for periodic regimes of nonlinear forced vibrations for a first time. The method allows parametric frequency-domain calculations of the stability loss together with the vibration amplitudes and design parameter values corresponding to the stability boundaries. The tracing algorithm is applied to obtain the trajectories of stability loss points as functions of design parameters. The parametric stability loss is formulated for cases when: (i) the design parameters characterise the properties of nonlinear contact interfaces (e.g. gap, contact stiffness, friction coefficient, etc.) and (ii) the design parameters describe linear components of the analysed structure (e.g. parameters of geometric shape, material, natural frequencies, modal damping etc.) and (iii) these parameters describe the excitation loads (e.g. their level, distribution or frequency). An approach allowing the multiparametric analysis of stability boundaries is proposed. The method uses the multiharmonic representation of the periodic forced response and aimed at the analysis of realistic gas-turbine structures comprising thousands and millions degrees of freedom. The method can be used for the effective search of isolated branches of the nonlinear solutions and examples of detection and search of the isolated branches are given: for relatively small and for large-scale finite element models. The efficiency of the method for calculation of the stability boundaries and for the search of isolated branches is demonstrated on simple systems and on a large-scale model of a turbine blade.

Frequency-Domain Sensitivity Analysis of Stability of Nonlinear Vibrations for High-Fidelity Models of Jointed Structures

2017 ◽  
Vol 140 (1) ◽  
Author(s):  
E. P. Petrov
Keyword(s):  
Sensitivity Analysis ◽  
Frequency Domain ◽  
Large Scale ◽  
Nonlinear Vibrations ◽  
Forced Response ◽  
Design Parameters ◽  
Analysis Of Stability ◽  
The Stability ◽  
Stability Regime ◽  
First Time

For the analysis of essentially nonlinear vibrations, it is very important not only to determine whether the considered vibration regime is stable or unstable but also which design parameters need to be changed to make the desired stability regime and how sensitive is the stability of a chosen design of a gas-turbine structure to variation of the design parameters. In the proposed paper, an efficient method is proposed for a first time for sensitivity analysis of stability for nonlinear periodic forced response vibrations using large-scale models structures with friction, gaps, and other types of nonlinear contact interfaces. The method allows using large-scale finite element (FE) models for structural components together with detailed description of nonlinear interactions at contact interfaces. The highly accurate reduced models are applied in the assessment of the sensitivity of stability of periodic regimes. The stability sensitivity analysis is performed in frequency domain with the multiharmonic representation of the nonlinear forced response amplitudes. Efficiency of the developed approach is demonstrated on a set of test cases including simple models and large-scale realistic blade model with different types of nonlinearities, including friction, gaps, and cubic elastic nonlinearity.

Frequency-Domain Sensitivity Analysis of Stability of Nonlinear Vibrations for High-Fidelity Models of Jointed Structures

2017 ◽  
Author(s):  
E. P. Petrov
Keyword(s):  
Sensitivity Analysis ◽  
Frequency Domain ◽  
Large Scale ◽  
Nonlinear Vibrations ◽  
Forced Response ◽  
Design Parameters ◽  
Analysis Of Stability ◽  
The Stability ◽  
Stability Regime ◽  
First Time

For the analysis of essentially nonlinear vibrations it is very important not only to determine whether the considered vibration regime is stable or unstable but also which design parameters need to be changed to make the desired stability regime and how sensitive is the stability of a chosen design of a gas-turbine structure to variation of the design parameters. In the proposed paper, an efficient method is proposed for a first time for sensitivity analysis of stability for nonlinear periodic forced response vibrations using large-scale models structures with friction, gaps and other types of nonlinear contact interfaces. The method allows using large-scale finite element models for structural components together with detailed description of nonlinear interactions at contact interfaces. The highly accurate reduced models are applied in the assessment of the sensitivity of stability of periodic regimes. The stability sensitivity analysis is performed in frequency domain with the multiharmonic representation of the nonlinear forced response amplitudes. Efficiency of the developed approach is demonstrated on a set of test cases including simple models and large-scale realistic blade model with different types of nonlinearities, including: friction, gaps, and cubic elastic nonlinearity.

scholarly journals Stability Analysis of Multiharmonic Nonlinear Vibrations for Large Models of Gas-Turbine Engine Structures With Friction and Gaps

2016 ◽  
Author(s):  
E. P. Petrov
Keyword(s):  
Gas Turbine ◽  
Large Scale ◽  
Frequency Domain Analysis ◽  
Gas Turbine Engine ◽  
Forced Response ◽  
Scale Model ◽  
Turbine Engine ◽  
Nonlinear Springs ◽  
Large Scale Model ◽  
The Stability

An efficient method is proposed for the multiharmonic frequency domain analysis of the stability for nonlinear periodic forced vibrations in gas-turbine engine structures and turbomachines with friction, gaps and other types of nonlinear contact interfaces. The method allows using large-scale finite element models for structural components together with detailed description of nonlinear interactions at contact interfaces between these components. The highly accurate reduced models are applied in the assessment of stability of periodic regimes for large-scale model of gas-turbine structures. An approach is proposed for the highly-accurate calculation of motion of a structure after it is perturbed from the periodic nonlinear forced response. Efficiency of the developed approach is demonstrated on a set of test cases including simple models and large-scale realistic bladed disc models with different types of nonlinearities: friction, gaps and cubic nonlinear springs.

scholarly journals Stability Analysis of Multiharmonic Nonlinear Vibrations for Large Models of Gas Turbine Engine Structures With Friction and Gaps

2016 ◽  
Vol 139 (2) ◽  
Author(s):  
E. P. Petrov
Keyword(s):  
Gas Turbine ◽  
Large Scale ◽  
Frequency Domain Analysis ◽  
Gas Turbine Engine ◽  
Forced Response ◽  
Scale Model ◽  
Turbine Engine ◽  
Nonlinear Springs ◽  
Large Scale Model ◽  
The Stability

An efficient method is proposed for the multiharmonic frequency-domain analysis of the stability for nonlinear periodic forced vibrations in gas turbine engine structures and turbomachines with friction, gaps, and other types of nonlinear contact interfaces. The method allows using large-scale finite element models for structural components together with detailed description of nonlinear interactions at contact interfaces between these components. The highly accurate reduced models are applied in the assessment of stability of periodic regimes for large-scale model of gas turbine structures. An approach is proposed for the highly accurate calculation of motion of a structure after it is perturbed from the periodic nonlinear forced response. Efficiency of the developed approach is demonstrated on a set of test cases including simple models and large-scale realistic bladed disk models with different types of nonlinearities: friction, gaps, and cubic nonlinear springs.

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.

Analysis of Stability for Generalized Discrete Large-Scale Systems

2013 ◽  
Vol 467 ◽  
pp. 627-632
Author(s):  
Chen Fang ◽  
Jiang Hong Shi ◽  
Shuang Yu ◽  
Jian Fang Mao
Keyword(s):  
Lyapunov Function ◽  
Large Scale ◽  
Lyapunov Equation ◽  
Large Scale Systems ◽  
Stability And Instability ◽  
Analysis Of Stability ◽  
The Stability

Based on the condition that all independent subsystems of the generalized large-scale systems are regular and causal, this thesis studied both stability and instability of discrete linear generalized large-scale systems through Lyapunov equation and Lyapunov function, and proposed the criterion theorem for the stability or instability of discrete linear generalized large-scale systems.

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

2004 ◽  
Vol 126 (4) ◽  
pp. 654-662 ◽  
Author(s):  
E. P. Petrov
Keyword(s):  
Parametric Analysis ◽  
Large Scale ◽  
Normal Load ◽  
Forced Response ◽  
Finite Element Models ◽  
Contact Interface ◽  
Friction Contact ◽  
Bladed Disks ◽  
Interface Parameters ◽  
Contact Parameters

An effective method for direct parametric analysis of periodic nonlinear forced response of bladed disks with friction contact interfaces has been developed. The method allows, 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 disk with underplatform dampers and with shroud contacts.

Automated Stability Analysis of a Vehicle in Combined Pitch and Roll

2002 ◽  
Author(s):  
James K. Sprague ◽  
Shyi-Ping Liu
Keyword(s):  
Stability Analysis ◽  
Rigid Body ◽  
Contact Forces ◽  
Design Parameters ◽  
Spherical Coordinates ◽  
Stability Boundaries ◽  
Overturning Stability ◽  
Heading Angle ◽  
The Stability ◽  
Six Degree Of Freedom

This paper presents a rigid body modeling approach using ADAMS™ for an overturning stability analysis of a vehicle stopped at an arbitrary heading angle on a steep grade. The vehicle is modeled as a six-degree-of-freedom rigid body with multiple contact forces acting on the ground. A gravity vector bounded by sets of spherical coordinates is applied to the vehicle to represent the physics of a vehicle stopped on a grade with any arbitrary combination of pitch and roll angles. A design of experiments study is performed to locate the overturning stability boundaries within given levels of design parameters. Results are output using two effective graphical means of depicting the stability regions and magnitude of contact forces.

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.

Sign in / Sign up

Export Citation Format

Share Document