Method for Analysis of Nonlinear Multiharmonic Vibrations of Mistuned Bladed Disks With Scatter of Contact Interface Characteristics

2005 ◽  
Vol 127 (1) ◽  
pp. 128-136 ◽  
Author(s):  
E. P. Petrov ◽  
D. J. Ewins
Keyword(s):  
Finite Element ◽  
Degrees Of Freedom ◽  
Large Scale ◽  
Forced Response ◽  
Finite Element Models ◽  
Linear Vibration ◽  
Bladed Disks ◽  
Bladed Disk ◽  
Interface Characteristics ◽  
Blade Frequency

An efficient method for analysis of nonlinear vibrations of mistuned bladed disk assemblies has been developed. This development has facilitated the use of large-scale finite element models for realistic bladed disks, used hitherto in analysis of linear vibration, to be extended for the analysis of nonlinear multiharmonic vibration. The new method is based on a technique for the exact condensation of nonlinear finite element models of mistuned bladed disks. The model condensation allows the size of the nonlinear equations to be reduced to the number of degrees of freedom where nonlinear interaction forces are applied. The analysis of nonlinear forced response for simplified and realistic models of mistuned bladed disks has been performed. For a practical high-pressure bladed turbine disk, several types of nonlinear forced response have been considered, including mistuning by (i) scatter of underplatform dampers, (ii) shroud gap scatter, and (iii) blade frequency scatter in the presence of nonlinear shroud interactions.

Method for Analysis of Nonlinear Multiharmonic Vibrations of Mistuned Bladed Discs With Scatter of Contact Interface Characteristics

2004 ◽  
Author(s):  
E. P. Petrov ◽  
D. J. Ewins
Keyword(s):  
Finite Element ◽  
Degrees Of Freedom ◽  
Large Scale ◽  
Nonlinear Vibrations ◽  
Forced Response ◽  
Finite Element Models ◽  
Contact Interface ◽  
Linear Vibration ◽  
Interface Characteristics ◽  
Blade Frequency

An efficient method for analysis of nonlinear vibrations of mistuned bladed disc assemblies has been developed. As a result, this development has facilitated the use of large-scale finite element models for realistic bladed discs, as used hitherto in analysis of linear vibration, to be extended for the analysis of nonlinear multiharmonic vibration. The new method is based on a technique for the exact condensation of nonlinear finite element models of mistuned bladed discs. The model condensation allows the size of the nonlinear equations to be reduced to the number of degrees of freedom where nonlinear interation forces are applied. The analysis of nonlinear forced response for simplified and realistic models of mistuned bladed discs has been performed. For a practical high-pressure bladed turbine disc, several types of nonlinear forced response have been considered including: (i) mistuning by scatter of underplatform dampers; (ii) mistuning by shroud gap scatter; (iii) mistuning by blade frequency scatter in the presence of nonlinear shroud interactions.

Analysis of the Worst Mistuning Patterns in Bladed Disk Assemblies

2003 ◽  
Vol 125 (4) ◽  
pp. 623-631 ◽  
Author(s):  
E. P. Petrov ◽  
D. J. Ewins
Keyword(s):  
Finite Element ◽  
Large Scale ◽  
Optimization Problem ◽  
Element Model ◽  
Design Parameters ◽  
Finite Element Models ◽  
Bladed Disks ◽  
Bladed Disk ◽  
The Many

The problem of determining the worst mistuning patterns is formulated and solved as an optimization problem. Maximum resonant amplitudes searched across the many nodes of a large-scale finite element model of a mistuned bladed disk and across all the excitation frequencies in a given range are combined into an objective function. Individual blade mistuning is controlled by varying design parameters, whose variation range is constrained by manufacture tolerances. Detailed realistic finite element models, which have so far only been used for analyzing tuned bladed disks, are used for calculation of the forced resonant response of mistuned assemblies and for determination of its sensitivity coefficients with respect to mistuning variation. Results of the optimum search of mistuning patterns for some practical bladed disks are analyzed and reveal higher worst cases than those found in previous studies.

Effects of Damping and Varying Contact Area at Blade-Disk Joints in Forced Response Analysis of Bladed Disk Assemblies

2005 ◽  
Vol 128 (2) ◽  
pp. 403-410 ◽  
Author(s):  
E. P. Petrov ◽  
D. J. Ewins
Keyword(s):  
Large Scale ◽  
Normal Load ◽  
Forced Response ◽  
Response Analysis ◽  
Finite Element Models ◽  
Bladed Disks ◽  
Contact Conditions ◽  
New Approach ◽  
Bladed Disk ◽  
Unilateral Contacts

An approach is developed to analyze the multiharmonic forced response of large-scale finite element models of bladed disks taking account of the nonlinear forces acting at the contact interfaces of blade roots. Area contact interaction is modeled by area friction contact elements which allow for friction stresses under variable normal load, unilateral contacts, clearances, and interferences. Examples of application of the new approach to the analysis of root damping and forced response levels are given and numerical investigations of effects of contact conditions at root joints and excitation levels are explored for practical bladed disks.

scholarly journals High-Fidelity Sensitivity Analysis of Modal Properties of Mistuned Bladed Disks Regarding Material Anisotropy

2018 ◽  
Author(s):  
Adam Koscso ◽  
Guido Dhondt ◽  
E. P. Petrov
Keyword(s):  
Sensitivity Analysis ◽  
Finite Element ◽  
Natural Frequencies ◽  
Mode Shapes ◽  
Finite Element Models ◽  
Coordinate Systems ◽  
Bladed Disks ◽  
Bladed Disk ◽  
Material Orientation

A new method has been developed for sensitivity calculations of modal characteristics of bladed disks made of anisotropic materials. The method allows the determination of the sensitivity of the natural frequencies and mode shapes of mistuned bladed disks with respect to anisotropy angles that define the crystal orientation of the monocrystalline blades using full-scale finite element models. An enhanced method is proposed to provide high accuracy for the sensitivity analysis of mode shapes. An approach has also been developed for transforming the modal sensitivities to coordinate systems used in industry for description of the blade anisotropy orientations. The capabilities of the developed methods are demonstrated on examples of a single blade and a mistuned realistic bladed disk finite element models. The modal sensitivity of mistuned bladed disks to anisotropic material orientation is thoroughly studied.

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.

scholarly journals How to compute invariant manifolds and their reduced dynamics in high-dimensional finite element models

2021 ◽  
Author(s):  
Shobhit Jain ◽  
George Haller
Keyword(s):  
Finite Element ◽  
Degrees Of Freedom ◽  
Invariant Manifolds ◽  
Mechanical Systems ◽  
Forced Response ◽  
High Dimensional ◽  
Nonlinear Phenomena ◽  
Finite Element Models ◽  
Engineering Structures ◽  
Backbone Curves

AbstractInvariant manifolds are important constructs for the quantitative and qualitative understanding of nonlinear phenomena in dynamical systems. In nonlinear damped mechanical systems, for instance, spectral submanifolds have emerged as useful tools for the computation of forced response curves, backbone curves, detached resonance curves (isolas) via exact reduced-order models. For conservative nonlinear mechanical systems, Lyapunov subcenter manifolds and their reduced dynamics provide a way to identify nonlinear amplitude–frequency relationships in the form of conservative backbone curves. Despite these powerful predictions offered by invariant manifolds, their use has largely been limited to low-dimensional academic examples. This is because several challenges render their computation unfeasible for realistic engineering structures described by finite element models. In this work, we address these computational challenges and develop methods for computing invariant manifolds and their reduced dynamics in very high-dimensional nonlinear systems arising from spatial discretization of the governing partial differential equations. We illustrate our computational algorithms on finite element models of mechanical structures that range from a simple beam containing tens of degrees of freedom to an aircraft wing containing more than a hundred–thousand degrees of freedom.

Explicit Finite Element Models of Friction Dampers in Forced Response Analysis of Bladed Disks

2008 ◽  
Vol 130 (2) ◽  
Author(s):  
E. P. Petrov
Keyword(s):  
Finite Element ◽  
Large Scale ◽  
Dynamic Properties ◽  
Forced Response ◽  
Response Analysis ◽  
Contact Interactions ◽  
Contact Interface ◽  
Bladed Disks ◽  
Explicit Finite Element ◽  
Friction Dampers

A generic method for analysis of nonlinear forced response for bladed disks with friction dampers of different designs has been developed. The method uses explicit finite element modeling of dampers, which allows accurate description of flexibility and, for the first time, dynamic properties of dampers of different designs in multiharmonic analysis of bladed disks. Large-scale finite element damper and bladed disk models containing 104−106 degrees of freedom can be used. These models, together with detailed description of contact interactions over contact interface areas, allow for any level of refinement required for modeling of elastic damper bodies and for modeling of friction contact interactions. Numerical studies of realistic bladed disks have been performed with three different types of underplatform dampers: (i) a “cottage-roof” (also called “wedge”) damper, (ii) seal wire damper, and (iii) a strip damper. Effects of contact interface parameters and excitation levels on damping properties of the dampers and forced response are extensively explored.

A Reduced-Order Meshless Energy Model for the Vibrations of Mistuned Bladed Disks—Part II: Finite Element Benchmark Comparisons

2013 ◽  
Vol 135 (6) ◽  
Author(s):  
C. Fang ◽  
O. G. McGee ◽  
Y. El Aini
Keyword(s):  
Finite Element ◽  
Theoretical Basis ◽  
Energy Model ◽  
Forced Response ◽  
Particle Methods ◽  
Test Model ◽  
Bladed Disks ◽  
Reduced Order ◽  
Bladed Disk ◽  
Flexible Disk

This paper draws upon the theoretical basis and applicability of the three-dimensional (3-D) reduced-order spectral-based “meshless” energy technology presented in a companion paper (McGee et al., 2013, “A Reduced-Order Meshless Energy Model for the Vibrations of Mistuned Bladed Disks—Part I: Theoretical Basis,” ASME J. Turbomach., to be published) to predict free and forced responses of bladed disks comprised of randomly mistuned blades integrally attached to a flexible disk. The 3-D reduced-order spectral-based model employed is an alternative choice in the computational modeling landscape of bladed disks, such as conventionally-used finite element methods and component mode synthesis techniques, and even emerging element-free Hamiltonian–Galerkin, Petrov–Galerkin, boundary integral, and kernel-particle methods. This is because continuum-based modeling of a full disk annulus of mistuned blades is, at present, a steep task using these latter approaches for modal-type mistuning and/or rogue blade failure analysis. Hence, a considerably simplified and idealized bladed disk of 20 randomly mistuned blades mounted to a flexible disk was created and modeled not only to analyze its free and forced 3-D responses, but also to compare the predictive capability of the present reduced-order spectral-based “meshless” technology to general-purpose finite element procedures widely-used in industry practice. To benchmark future development of reduced-order technologies of turbomachinery mechanics analysts may use the present 3-D findings of the idealized 20-bladed disk as a new standard test model. Application of the 3-D reduced-order spectral-based “meshless” technology to an industry integrally-bladed rotor, having all of its blades modally mistuned, is also offered, where reasonably sufficient upper-bounds on the exact free and forced 3-D responses are predicted. These predictions expound new solutions of 3-D vibration effects of modal mistuning strength and pattern, interblade mechanical coupling, and localized modes on the free and forced response amplitudes.

Analysis of Forced Response for Bladed Disks Mistuned by Material Anisotropy Orientation Scatters

2017 ◽  
Vol 140 (2) ◽  
Author(s):  
Chaoping Zang ◽  
Yuanqiu Tan ◽  
E. P. Petrov
Keyword(s):  
Finite Element ◽  
Monte Carlo ◽  
High Accuracy ◽  
Forced Response ◽  
Response Analysis ◽  
High Fidelity ◽  
Fe Model ◽  
Material Anisotropy ◽  
Bladed Disks ◽  
Bladed Disk

A new method is developed for the forced response analysis of mistuned bladed disks manufactured from anisotropic materials and mistuned by different orientations of material anisotropy axes. The method uses (i) sector finite element (FE) models of anisotropic bladed disks and (ii) FE models of single blades and allows the calculation of displacements and stresses in a mistuned assembly. A high-fidelity reduction approach is proposed which ensures high-accuracy modeling by introducing an enhanced reduction basis. The reduction basis includes the modal properties of specially selected blades and bladed disks. The technique for the choice of the reduction basis has been developed, which provides the required accuracy while keeping the computation expense acceptable. An approach for effective modeling of anisotropy-mistuned bladed disk without a need to create a FE model for each mistuning pattern is developed. The approach is aimed at fast statistical analysis based on Monte Carlo simulations. All components of the methodology for anisotropy-mistuned bladed disks are demonstrated on the analysis of models of practical bladed disks. Effects of anisotropy mistuning on forced response levels are explored.

scholarly journals High-Fidelity Sensitivity Analysis of Modal Properties of Mistuned Bladed Disks Regarding Material Anisotropy

2018 ◽  
Vol 141 (2) ◽  
Author(s):  
Adam Koscso ◽  
Guido Dhondt ◽  
E. P. Petrov
Keyword(s):  
Sensitivity Analysis ◽  
Finite Element ◽  
Natural Frequencies ◽  
Mode Shapes ◽  
Finite Element Models ◽  
Coordinate Systems ◽  
Bladed Disks ◽  
Bladed Disk ◽  
Material Orientation

A new method has been developed for sensitivity calculations of modal characteristics of bladed disks made of anisotropic materials. The method allows the determination of the sensitivity of the natural frequencies and mode shapes of mistuned bladed disks with respect to anisotropy angles that define the crystal orientation of the monocrystalline blades using full-scale finite element models. An enhanced method is proposed to provide high accuracy for the sensitivity analysis of mode shapes. An approach has also been developed for transforming the modal sensitivities to coordinate systems (CS) used in industry for description of the blade anisotropy orientations. The capabilities of the developed methods are demonstrated on examples of a single blade and a mistuned realistic bladed disk finite element models. The modal sensitivity of mistuned bladed disks to anisotropic material orientation is thoroughly studied.

Sign in / Sign up

Export Citation Format

Share Document