scholarly journals Dynamic Analysis and Reduction of a Cyclic Symmetric System Subjected to Geometric Nonlinearities

2018 ◽  
Vol 141 (4) ◽  
Author(s):  
Adrien Martin ◽  
Fabrice Thouverez
Keyword(s):  
Symmetric System ◽  
Evaluation Procedure ◽  
Geometric Nonlinearities ◽  
Modeling Process ◽  
Nonlinear Solver ◽  
Step Procedure ◽  
Stator Vane ◽  
Cyclic Symmetric ◽  
Aeronautical Industry ◽  
Modal Derivatives

The search for ever lighter weight has become a major goal in the aeronautical industry as it has a direct impact on fuel consumption. It also implies the design of increasingly thin structures made of sophisticated and flexible materials. This may result in nonlinear behaviors due to large structural displacements. Stator vanes can be affected by such phenomena, and as they are a critical part of turbojets, it is crucial to predict these behaviors during the design process in order to eliminate them. This paper presents a reduced order modeling process suited for the study of geometric nonlinearities. The method is derived from a classical component mode synthesis (CMS) with fixed interfaces, in which the reduced nonlinear terms are obtained through a stiffness evaluation procedure (STEP) procedure using an adapted basis composed of linear modes completed by modal derivatives (MD). The whole system is solved using a harmonic balance procedure and a classic iterative nonlinear solver. The application is implemented on a schematic stator vane model composed of nonlinear Euler–Bernoulli beams under von Kàrmàn assumptions.

scholarly journals Dynamic Analysis and Reduction of a Cyclic Symmetric System Subjected to Geometric Nonlinearities

2018 ◽  
Author(s):  
Adrien Martin ◽  
Fabrice Thouverez
Keyword(s):  
Symmetric System ◽  
Geometric Nonlinearities ◽  
Reduced Order ◽  
Nonlinear Solver ◽  
Step Procedure ◽  
Stator Vane ◽  
Cyclic Symmetric ◽  
Aeronautical Industry ◽  
Modal Derivatives ◽  
Modelling Process

The search for ever lighter weight has become a major goal in the aeronautical industry as it has a direct impact on fuel consumption. It also implies the design of increasingly thin structures made of sophisticated and flexible materials. This may result in nonlinear behaviours due to large structural displacements. Stator vanes can be affected by such phenomena, and as they are a critical part of turbojets, it is crucial to predict these behaviours during the design process in order to eliminate them. This paper presents a reduced order modelling process suited for the study of geometric nonlinearities. The method is derived from a classical Component Mode Synthesis with fixed interfaces, in which the reduced nonlinear terms are obtained through a STEP procedure using an adapted basis composed of linear modes completed by modal derivatives. The whole system is solved using a harmonic balance procedure and a classic iterative nonlinear solver. The application is implemented on a schematic stator vane model composed of nonlinear Euler-Bernoulli beams under von Kàrmàn assumptions.

Assessment of Geometric Nonlinearities Influence on NASA Rotor 37 Response to Blade Tip/Casing Rubbing Events

2021 ◽  
Author(s):  
Elise Delhez ◽  
Florence Nyssen ◽  
Jean-Claude Golinval ◽  
Alain Batailly
Keyword(s):  
Dynamical Problem ◽  
Evaluation Procedure ◽  
Large Displacements ◽  
Geometric Nonlinearities ◽  
Abradable Coating ◽  
Stiffness Evaluation ◽  
Blade Tip ◽  
Modal Derivatives ◽  
Blade Model ◽  
Selection Of

Abstract This paper uses a recently derived reduction procedure to study the contact interactions of an industrial blade undergoing large displacements. The reduction technique consists in projecting the dynamical problem onto a reduction basis composed of Craig-Bampton modes and a selection of their modal derivatives. The internal nonlinear forces due to large displacements are evaluated with the stiffness evaluation procedure and contact is numerically handled using Lagrange multipliers. The numerical strategy is applied on an open industrial compressor blade model based on the NASA rotor 37 blade in order to promote re-producibility of results. Two contact scenarios are investigated: one with direct contact between the blade and the casing and one with an abradable material deposited on the casing. The influence of geometric nonlinearities is assessed in both cases. In particular, contact interaction maps and abradable coating wear pattern maps are used to identify the main interactions that can be detrimental for the engine integrity.

Assessment of Geometric Nonlinearities Influence On NASA Rotor 37 Response to Blade Tip/Casing Rubbing Events

2021 ◽  
Author(s):  
Elise Delhez ◽  
Florence Nyssen ◽  
Jean-Claude Golinval ◽  
Alain Batailly
Keyword(s):  
Dynamical Problem ◽  
Evaluation Procedure ◽  
Large Displacements ◽  
Geometric Nonlinearities ◽  
Abradable Coating ◽  
Stiffness Evaluation ◽  
Blade Tip ◽  
Modal Derivatives ◽  
Blade Model ◽  
Selection Of

Abstract This paper uses a recently derived reduction procedure to study the contact interactions of an industrial blade undergoing large displacements. The reduction technique consists in projecting the dynamical problem onto a reduction basis composed of Craig-Bampton modes and a selection of their modal derivatives. The internal nonlinear forces due to large displacements are evaluated with the stiffness evaluation procedure and contact is numerically handled using Lagrange multipliers. The numerical strategy is applied on an open industrial compressor blade model based on the NASA rotor 37 blade in order to promote reproducibility of results. Two contact scenarios are investigated: one with direct contact between the blade and the casing and one with an abradable material deposited on the casing. The influence of geometric nonlinearities is assessed in both cases. In particular, contact interaction maps and abradable coating wear pattern maps are used to identify the main interactions that can be detrimental for the engine integrity.

A Logical Procedure for the Construction of Bond Graphs in Systems Modeling

1972 ◽  
Vol 94 (3) ◽  
pp. 183-188 ◽  
Author(s):  
H. R. Martens ◽  
A. C. Bell
Keyword(s):  
Complex Model ◽  
Bond Graphs ◽  
State Equations ◽  
Final Model ◽  
Resonance Behavior ◽  
Modeling Process ◽  
Step Procedure ◽  
Internal Dissipation ◽  
Linear State ◽  
Experimental Values

The problem of deriving a suitable mathematical model for complex devices is discussed. A small vibratory air pump is used as the medium of presentation. The modeling process begins with the basic coupling structure of the device. In a logical step-by-step procedure the initial model is built up to satisfy a number of functional considerations inherent to the device, such as the resonance behavior, input impedance, output impedance, and internal dissipation. At each step in the modeling process the completeness and suitability of the model is examined. Bond graphs drawn for the successively larger and more complex model clearly predict the shortcomings of the partial model and point the way to the next step. It is evident that the principle of causal relations forms a most important guiding element in the modeling process. The final model is in the form of a set of linear state equations, and scaling of the A-matrix indicates the relative importance of parameters when experimental values are substituted for literals.

A Procedure for Comparative Evaluation of Design for Assembly Methodologies

1987 ◽  
Author(s):  
M. S. Darlow ◽  
D. M. Avidar ◽  
M. W. Steiner
Keyword(s):  
Product Design ◽  
Comparative Evaluation ◽  
Evaluation Method ◽  
Cost Effective ◽  
Evaluation Procedure ◽  
Design For Assembly ◽  
Step Procedure ◽  
Individual Needs ◽  
Effective Design

Abstract It has been generally agreed that it is necessary to include assembly considerations during product design in order to produce a cost-effective design. To this end, a number of design for assembly (DFA) methodologies have been proposed. This presents the designer with a choice of methodology and little or no criteria on which to base a decision. This paper presents a comparative evaluation procedure which has been developed as a tool to help the designer select the DFA methodology which is most appropriate for a particular situation. This tool is a step-by-step procedure for evaluating and selecting a DFA method from a group of alternatives by bringing together factors and criteria used to measure their characteristics and capabilities. This paper presents the details of this evaluation procedure and applies it to three DFA methodologies, to illustrate its use. The results of the evaluation presented herein are interesting, although the subjective nature of the criteria and the ratings limits their usefulness. Rather, the point of this paper is that the evaluation method described, modified for individual needs and tastes, can be used to provide useful results for that individual.

scholarly journals Effects of Bearings and Housing on Mode Localization of a Nearly Cyclic Symmetric System

2016 ◽  
Vol 138 (5) ◽  
Author(s):  
Y. F. Chen ◽  
I. Y. Shen
Keyword(s):  
Finite Element ◽  
Reference System ◽  
Deductive Reasoning ◽  
Mode Shapes ◽  
Symmetric System ◽  
Finite Element Analyses ◽  
Localized Modes ◽  
Mode Localization ◽  
Bladed Disk ◽  
Cyclic Symmetric

This technical brief is to study how flexible bearings and housing affect mode localization of a nearly cyclic symmetric system with mistuning. This study is conducted via finite-element analyses and deductive reasoning. A reference system studied is a bladed disk with two groups of 24 localized modes. When bearings and housing are introduced into the reference system, their presence changes natural frequencies, mode shapes, and the number of the localized modes. Moreover, the mistuning causes bearing forces to surge for all the localized modes. A deductive reasoning based on the existing literature supports the observation from the finite-element analyses.

Product Life-Cycle Modeling and Evaluation at the Conceptual Design Stage: A Digraph and Matrix Approach

2010 ◽  
Vol 132 (9) ◽  
Author(s):  
A. Anand ◽  
M. F. Wani
Keyword(s):  
Life Cycle ◽  
Product Life Cycle ◽  
Design Stage ◽  
Evaluation Procedure ◽  
Matrix Approach ◽  
Product Life ◽  
Life Cycle Design ◽  
Design Attributes ◽  
Step Procedure ◽  
Digraph And Matrix Approach

An evaluation procedure for product life-cycle design at the conceptual stage is presented using a digraph and matrix approach. Life-cycle design attributes are identified and used to evaluate a life-cycle design index. The ideal value of this index is also obtained, which is useful in assessing the relative life-cycle design value of product design alternatives. A step-by-step procedure for the evaluation of the life-cycle design index is presented and illustrated by means of two examples.

Effects of Bearings and Housing on Mode Localization of a Nearly Cyclic Symmetric System

2014 ◽  
Author(s):  
Y. F. Chen ◽  
I. Y. Shen
Keyword(s):  
Boundary Condition ◽  
Reference System ◽  
Mode Shapes ◽  
Symmetric System ◽  
Localized Modes ◽  
Disk System ◽  
Element Analysis ◽  
Mode Localization ◽  
Bladed Disk ◽  
Cyclic Symmetric

This paper is to study how flexible bearings and housing affect mode localization of a nearly cyclic symmetric system with mistune. A finite element analysis is first conducted on a reference system that consists of a circular disk and 24 blades with mistune. The disk is annular with an inner rim and an outer rim. A fixed boundary condition is imposed at the inner rim, while the 24 blades with mistune are evenly attached to the outer rim and subjected to a free boundary condition. As a result of the mistune, the reference system presents 26 localized torsional modes as well as 24 localized in-plane modes in its blade vibration. When the fixed inner rim is replaced by a bearing support (i.e., an elastic boundary condition), not only the localized torsional modes can change their natural frequencies and mode shapes but also the number of the localized torsional modes may be increased to 28 in some range of bearing stiffness. Similarly, when the bladed-disk reference system is mounted on a stationary housing via a bearing support, the number of the localized in-plane modes can change from 24 to 33 modes. Moreover, localized mode shapes change significantly, and some of them involve significant housing deformation. To understand this phenomenon theoretically, we first demonstrate that the presence of bearing and housing provides additional degrees of freedom, which, in turn, allow the bladed-disk system to have additional disk modes. When the bearing and housing stiffness is properly tuned, some of these additional disk modes may possess significant torsional or in-plane displacement components in the blades. If these additional modes happen to have a natural frequency that is close to those of the localized modes of the reference system, these additional modes will join the localized modes to form new localized modes. As a result, the number of localized modes increases and the mode shapes change significantly.

Scanning Tunneling Microscopy of Amorphous Carbon Films

1990 ◽  
Vol 48 (1) ◽  
pp. 318-319
Author(s):  
Mircea Fotino ◽  
D.C. Parks
Keyword(s):  
Scanning Tunneling Microscopy ◽  
Amorphous Carbon ◽  
Carbon Films ◽  
Atomic Scale ◽  
Scanning Tunneling ◽  
Tunneling Microscopy ◽  
Amorphous Carbon Films ◽  
Image Optimization ◽  
Step Procedure ◽  
Stm Images

In the last few years scanning tunneling microscopy (STM) has made it possible and easily accessible to visualize surfaces of conducting specimens at the atomic scale. Such performance allows the detailed characterization of surface morphology in an increasing spectrum of applications in a wide variety of fields. Because the basic imaging process in STM differs fundamentally from its equivalent in other well-established microscopies, good understanding of the imaging mechanism in STM enables one to grasp the correct information content in STM images. It thus appears appropriate to explore by STM the structure of amorphous carbon films because they are used in many applications, in particular in the investigation of delicate biological specimens that may be altered through the preparation procedures.All STM images in the present study were obtained with the commercial instrument Nanoscope II (Digital Instruments, Inc., Santa Barbara, California). Since the importance of the scanning tip for image optimization and artifact reduction cannot be sufficiently emphasized, as stressed by early analyses of STM image formation, great attention has been directed toward adopting the most satisfactory tip geometry. The tips used here consisted either of mechanically sheared Pt/Ir wire (90:10, 0.010" diameter) or of etched W wire (0.030" diameter). The latter were eventually preferred after a two-step procedure for etching in NaOH was found to produce routinely tips with one or more short whiskers that are essentially rigid, uniform and sharp (Fig. 1) . Under these circumstances, atomic-resolution images of cleaved highly-ordered pyro-lytic graphite (HOPG) were reproducibly and readily attained as a standard criterion for easily recognizable and satisfactory performance (Fig. 2).

Procedure for Maximizing Phonological Information from Single-Word Responses

1984 ◽  
Vol 15 (4) ◽  
pp. 267-274 ◽  
Author(s):  
Harriet B. Klein
Keyword(s):  
Phonological Information ◽  
Single Word ◽  
Preliminary Assessment ◽  
Target Attainment ◽  
Phonological Processes ◽  
Step Procedure ◽  
Yield Information ◽  
Assessment Measure ◽  
Busy Clinician ◽  
Planning Intervention

Formal articulation test responses are often used by the busy clinician as a basis for planning intervention goals. This article describes a 6-step procedure for using efficiently the single-word responses elicited with an articulation test. This procedure involves the assessment of all consonants within a word rather than only test-target consonants. Responses are organized within a Model and Replica chart to yield information about an individual's (a) articulation ability, (b) frequency of target attainment, substitutions, and deletions, (c) variability in production, and (d) phonological processes. This procedure is recommended as a preliminary assessment measure. It is advised that more detailed analysis of continuous speech be undertaken in conjunction with early treatment sessions.

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