Finite element model updating for repeated eigenvalue structures via the reduced-order model using incomplete measured modes

Abstract It is widely known that the vibration characteristics of blade integrated discs can dramatically change in the presence of manufacturing tolerances and wear. In this context, an increasing number of publications discuss the influence of the geometrical variability of blades on phenomena like frequency splitting and mode localization. This contribution is investigating the validity of a stiffness modified reduced order model for predicting the modal parameters of a geometrically mistuned compressor stage. In detail, the natural frequencies and mode shapes, as well as the corresponding mistuning patterns, are experimentally determined for an exemplary rotor. Furthermore, a blue light fringe projector is used to identify the geometrical differences between the actual rotor and the nominal blisk design. With the help of these digitization results, a realistic finite element model of the whole compressor stage is generated. Beyond that, a reduced order model is implemented based on the nominal design intention. Finally, the numerical predictions of the geometrically updated finite element model and the stiffness modified reduced order model are compared to the vibration measurement results. The investigation is completed by pointing out the benefits and limitations of the SNM-approach in the context of geometrically induced mistuning effects.

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Inverse Determination of Moving Heat Flux Distributions Using Reduced Order Models

Volume 1A: 34th Computers and Information in Engineering Conference ◽

10.1115/detc2014-35274 ◽

2014 ◽

Cited By ~ 1

Author(s):

Brian H. Dennis ◽

Ashkan Akbariyeh ◽

John Michopoulos ◽

Foteini Komninelli ◽

Athanasios Iliopoulos

Keyword(s):

Heat Flux ◽

Finite Element ◽

Finite Element Model ◽

Target Surface ◽

Element Model ◽

Basis Functions ◽

Reduced Order Model ◽

Analysis Model ◽

Order Model ◽

Reduced Order

Optimization-based solutions to inverse problems involve the coupling of an analysis model, such as a finite element model, with a numerical optimization method. The goal is to determine a set of parameters that minimize an objective function that is determined by solving the analysis model. In this paper, we present an approach that dramatically reduces the computational cost for solving this inverse problems in this way by replacing the original full order finite element model (FOM) with a reduced order model (ROM) that is both accurate and quick to compute. The reduced order model is constructed with basis functions generated using proper orthogonal decomposition of set of solutions from the FOM. A discrete Galerkin method is used to project the differential equation on the basis functions. This approach allows us to transform the linear full order finite element model into an equivalent discrete ROM with far fewer unknowns. The method is applied to a parameter estimation problem in heat transfer. Specifically, we determine the parameters governing the magnitude and distribution of an unknown surface heat flux moving at a constant velocity across the surface of a solid bar of material. A finite element model was implemented in the commercial package COMSOL and a corresponding ROM was constructed. The ROM was coupled with an optimization algorithm to determine the parameter values that minimized the distance between the computed surface temperatures and the target surface temperature. The target surface temperature was generated using simulated measurements produced from the full order finite element model. Several optimization methods were used. The results show the approach can recover the parameters with high accuracy with twenty seven FOM runs.

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A Nonlinear Finite Element Model for Leaf Springs

Volume 5: 19th Biennial Conference on Mechanical Vibration and Noise, Parts A, B, and C ◽

10.1115/detc2003/vib-48360 ◽

2003 ◽

Author(s):

Mohamed A. Omar ◽

Hiroyuki Sugiyama ◽

Ahmed A. Shabana ◽

Wei-Yi Loh ◽

Rena Basch

Keyword(s):

Finite Element ◽

Finite Element Model ◽

Element Model ◽

Nonlinear Finite Element ◽

Reduced Order Model ◽

Body Motion ◽

Leaf Spring ◽

Order Model ◽

Reduced Order ◽

Nonlinear Finite Element Model

This paper presents a nonlinear finite element model for the leaf spring that can be used in multibody applications and vehicle dynamic simulations. The floating frame of reference formulation is used in this investigation to model leaf spring nonlinear dynamics. This formulation accounts for the coupling between different modes of deformation as well as the nonlinear coupling between the rigid body motion and the elastic deformation. By employing component mode synthesis techniques, a reduced order model is obtained for the leaf spring while maintaining a good degree of accuracy. The inertia shape integrals can be calculated once in advance using a preprocessor and then stored to be used to automatically generate the nonlinear equations of motion of the leaf spring. The use of a preprocessor to evaluate the inertia shape integrals before the dynamic simulation leads to considerable saving in CPU time and allows the utilization of existing finite element computer codes to obtain the data required for the flexible body simulation. This reduced order model is implemented in a general multibody algorithm in order to examine the effectiveness and robustness of the proposed techniques. As an application, the wind-up deformation of the front suspension system of a typical sport utility vehicle under severe braking condition is investigated.

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A Reduced Order Approach for the Vibration of Mistuned Bladed Disk Assemblies

Journal of Engineering for Gas Turbines and Power ◽

10.1115/1.2815542 ◽

1997 ◽

Vol 119 (1) ◽

pp. 161-167 ◽

Cited By ~ 60

Author(s):

M.-T. Yang ◽

J. H. Griffin

Keyword(s):

Finite Element ◽

Finite Element Model ◽

Degrees Of Freedom ◽

Element Model ◽

Reduced Order Model ◽

Order Model ◽

Disk System ◽

Element Analysis ◽

Reduced Order ◽

Bladed Disk

A reduced order approach is introduced in this paper that can be used to predict the steady-state response of mistuned bladed disks. This approach takes results directly from a finite element analysis of a tuned system and, based on the assumption of rigid blade base motion, constructs a computationally efficient mistuned model with a reduced number of degrees of freedom. Based on a comparison of results predicted by different approaches, it is concluded that: The reduced order model displays structural fidelity comparable to that of a finite element model of the entire bladed disk system with significantly improved computational efficiency; and under certain circumstances both the finite element model and the reduced order model predict quite different response from simple spring-mass models.

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A Reduced Order Approach for the Vibration of Mistuned Bladed Disk Assemblies

Volume 5: Manufacturing Materials and Metallurgy; Ceramics; Structures and Dynamics; Controls, Diagnostics and Instrumentation; Education; IGTI Scholar Award ◽

10.1115/95-gt-454 ◽

1995 ◽

Cited By ~ 1

Author(s):

M.-T. Yang ◽

J. H. Griffin

Keyword(s):

Finite Element ◽

Finite Element Model ◽

Degrees Of Freedom ◽

Element Model ◽

Reduced Order Model ◽

Order Model ◽

Disk System ◽

Element Analysis ◽

Reduced Order ◽

Bladed Disk

A reduced order approach is introduced in this paper that can be used to predict the steady-state response of mistuned bladed disks. This approach takes results directly from a finite element analysis of a tuned system and, based on the assumption of rigid blade base motion, constructs a computationally efficient mistuned model with a reduced number of degrees of freedom. Based on a comparison of results predicted by different approaches it is concluded that: the reduced order model displays structural fidelity comparable to that of a finite element model of the entire bladed disk system with significantly improved computational efficiency; and under certain circumstances both the finite element model and the reduced order model predict quite different response from simple spring-mass models.

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Finite-Element-Based Nonlinear Modal Reduction of a Rotating Beam with Large-Amplitude Motion

Journal of Vibration and Control ◽

10.1177/107754603030751 ◽

2003 ◽

Vol 9 (3-4) ◽

pp. 235-263 ◽

Cited By ~ 20

Author(s):

Polarit Apiwattanalunggarn ◽

Steven W. Shaw ◽

Christophe Pierre ◽

Dongying Jiang

Keyword(s):

Finite Element ◽

Finite Element Model ◽

Degrees Of Freedom ◽

Element Model ◽

Reduced Order Model ◽

Rotating Beam ◽

Order Model ◽

Reduced Order ◽

Modal Reduction ◽

The Finite Element Model

A nonlinear one-dimensional finite-element model representing the axial and transverse motions of a cantilevered rotating beam is reduced to a single nonlinear normal mode using invariant manifold techniques. This system is an idealized representation for large-amplitude vibrations of a rotorcraft blade. Although this model is relatively simple, it possesses the essential nonlinear coupling effects between the axial and transverse degrees of freedom. The nature of this coupling leads to the fact that we must use many degrees of freedom, whether based on finite elements or modal expansions, in order to accurately represent the beam vibrations. In this work, the slow modal convergence problem is overcome by nonlinear modal reduction that makes use of invariant manifold based nonlinear modes. This reduction procedure generates a single-degree-of-freedom reduced-order model that systematically accounts for the dynamics of all the linear modes, or finite elements, considered in the original model. The approach is used to study the dynamic characteristics of the finite-element model over a wide range of vibration amplitudes. Using extensive simulations, it is shown that the response of the reduced-order model is nearly identical to a reference system which is based on a large-scale representation of the finite-element model, and to a reduced-order Rayleigh-Ritz model. All of the procedures presented here have been computationally automated. Hence, in this study we demonstrate that it is feasible and practical to interface nonlinear finite-element methods with nonlinear modal reduction.

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