Modeling and Analysis of Mistuned Bladed Disk Vibration: Status and Emerging Directions
01 Mar 2006-Journal of Propulsion and Power (American Institute of Aeronautics and Astronautics)-Vol. 22, Iss: 2, pp 384-396
TL;DR: The literature on reduced-order modeling, simulation, and analysis of the vibration of bladed disks found in gas-turbine engines is reviewed in this paper, where an emphasis is placed on key developments in the last decade that have enabled better prediction and understanding of the forced response of mistuned bladed disk, especially with respect to assessing and mitigating the harmful impact of mistuning on blade vibration, stress increases, and attendant high cycle fatigue.
Abstract: The literature on reduced-order modeling, simulation, and analysis of the vibration of bladed disks found in gas-turbine engines is reviewed. Applications to system identification and design are also considered. In selectively surveying the literature, an emphasis is placed on key developments in the last decade that have enabled better prediction and understanding of the forced response of mistuned bladed disks, especially with respect to assessing and mitigating the harmful impact of mistuning on blade vibration, stress increases, and attendant high cycle fatigue. Important developments and emerging directions in this research area are highlighted.
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TL;DR: The concept of nonlinear normal modes (NNMs) is discussed in the present paper and its companion, Part II as mentioned in this paper, and numerical methods for the continuation of periodic solutions pave the way for an effective and practical computation of NNMs, and timefrequency analysis is particularly suitable for the analysis of the resulting dynamics.
625 citations
TL;DR: In this article, a component-based modeling framework is developed by partitioning the system into a tuned bladed disk component and virtual blade mistuning components, defined by the differences between the mistuned and tuned blade mass and stiffness matrices.
Abstract: New techniques are presented for generating reduced-order models of the vibration of mistuned bladed disks from parent finite element models. A novel component-based modeling framework is developed by partitioning the system into a tuned bladed disk component and virtual blade mistuning components. The mistuning components are defined by the differences between the mistuned and tuned blade mass and stiffness matrices. The mistuned-system model is assembled with a component mode synthesis technique, using a basis of tuned-system normal modes and attachment modes. The formulation developed is general and can be applied to any mistuned bladed disk, including those with large geometric mistuning (e.g., severe blade damage). In the case of small (i.e., blade frequency) mistuning, a compact reduced-order model is derived by neglecting the attachment modes. For this component mode mistuning model, the blade mistuning is projected first onto the component modes of a tuned, cantilevered blade, and then projected again onto the tuned-system normal modes via modal participation factors. In this manner, several natural frequencies of each mistuned blade can be used to capture systematically the effects of the complex physical sources of mistuning. A numerical validation of the developed methods is performed for both large and small mistuning cases using a finite element model of an industrial rotor.
195 citations
TL;DR: In this article, the authors present a review of the state of the art in vibration prediction of rotating bladed disks with respect to aeroelastic effects, appropriate model order reduction techniques and the exploitation of the rotationally periodic nature of the problem.
Abstract: The present review article addresses the vibration behavior of bladed disks encountered e.g. in aircraft engines as well as industrial gas and steam turbines. The utilization of the dissipative effects of dry friction in mechanical joints is a common means of the passive mitigation of structural vibrations caused by aeroelastic excitation mechanisms. The prediction of the vibration behavior is a scientific challenge due to (a) the strongly nonlinear contact interactions involving local sticking, sliding and liftoff, (b) the model order required to accurately describe the dynamic behavior of the assembly, and (c) the multi-disciplinary character of the problem associated with the need to account for structural mechanical as well as fluid dynamical effects. The purpose of this article is the overview and discussion the current state of the art of vibration prediction approaches. The modeling approaches in this work embrace the description of the rotating bladed disk, the contact modeling, the consideration of aeroelastic effects, appropriate model order reduction techniques and the exploitation of the rotationally periodic nature of the problem. The simulation approaches cover the direct computation of periodic, steady-state externally forced and self-excited vibrations using the high-order harmonic balance method, the formulation of the contact problem in the frequency domain, methods for the solution of the governing algebraic equations and advanced simulation approaches, including the concept of nonlinear modes.
158 citations
TL;DR: The aim is to collect the most relevant results of the existing theory in a single paper, couch the mathematics in a form that is accessible to the vibrations analyst, and provide examples to highlight key concepts.
Abstract: This paper provides a tutorial and summary of the theory of circulant matrices and their application to the modeling and analysis of the free and forced vibration of mechanical structures with cyclic symmetry. Our presentation of the basic theory is distilled from the classic book of Davis (1979, Circulant Matrices, 2nd ed., Wiley, New York) with results, proofs, and examples geared specifically to vibration applications. Our aim is to collect the most relevant results of the existing theory in a single paper, couch the mathematics in a form that is accessible to the vibrations analyst, and provide examples to highlight key concepts. A nonexhaustive survey of the relevant literature is also included, which can be used for further examples and to point the reader to important extensions, applications, and generalizations of the theory. [DOI: 10.1115/1.4027722]
106 citations
Cites background from "Modeling and Analysis of Mistuned B..."
...The phenomenon of mode localization is also observed in the forced response and has practical implications for the fatigue life of bladed disks in turbomachinery [79,80]....
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TL;DR: In this paper, the Asymptotic Mistuning Model (AMM) was applied to determine the key ingredients of the amplification process and to evaluate the maximum mistuning amplification factor of a given modal family with a particular distribution of tuned frequencies.
Abstract: The problem of determining the maximum forced response vibration amplification that can be produced just by the addition of a small mistuning to a perfectly cyclical bladed disk still remains not completely clear. In this paper we apply a recently introduced perturbation methodology, the Asymptotic Mistuning Model (AMM), to determine which are the key ingredients of this amplification process, and to evaluate the maximum mistuning amplification factor that a given modal family with a particular distribution of tuned frequencies can exhibit. A more accurate upper bound for the maximum forced response amplification of a mistuned bladed disk is obtained from this description, and the results of the AMM are validated numerically using a simple mass-spring model.Copyright © 2008 by ASME
76 citations
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TL;DR: In this article, a simple model for spin diffusion or conduction in the "impurity band" is presented, which involves transport in a lattice which is in some sense random, and in them diffusion is expected to take place via quantum jumps between localized sites.
Abstract: This paper presents a simple model for such processes as spin diffusion or conduction in the "impurity band." These processes involve transport in a lattice which is in some sense random, and in them diffusion is expected to take place via quantum jumps between localized sites. In this simple model the essential randomness is introduced by requiring the energy to vary randomly from site to site. It is shown that at low enough densities no diffusion at all can take place, and the criteria for transport to occur are given.
9,647 citations
TL;DR: In this article, a method for treating a complex structure as an assemblage of distinct regions, or substructures, is presented using basic mass and stiffness matrices, together with conditions of geometrical compatibility along substructure boundaries.
Abstract: A method for treating a complex structure as an assemblage of distinct regions, or substructures, is presented. Using basic mass and stiffness matrices for the substructures, together with conditions of geometrical compatibility along substructure boundaries, the method employs two forms of generalized coordinates. Boundary generalized coordinates give displacements and rotations of points along substructure boundaries and are related to the displacement modes of the substructures known as "constraint modes." All constraint modes are generated by matrix operations from substructure input data. Substructure normal-mode generalized coordinates are related to free vibration modes of the substructures relative to completely restrained boundaries. The definition of substructure modes and the requirement of compatibility along substructure boundaries lead to coordinate transformation matrices that are employed in obtaining system mass and stiffness matrices from the mass and stiffness matrices of the substructures. Provision is made, through a RayleighRitz procedure, for reducing the total number of degrees of freedom of a structure while retaining accurate description of its dynamic behavior. Substructure boundaries may have any degree of redundancy. An example is presented giving a free vibration analysis of a structure having a highly indeterminate substructure boundary.
3,035 citations
TL;DR: In this article, a method is developed for analyzing complex structural systems that can be divided into interconnected components, where displacement of the separate components are expressed in generalized coordinates that are defined by displacement modes.
Abstract: A method is developed for analyzing complex structural systems that can be divided into interconnected components. Displacements of the separate components are expressed in generalized coordinates that are defined by displacement modes. These are generated in three categories: rigid-body, "constraint," and "normal" modes. Rigid-body modes are convenient where displacements are denned in inertial space for dynamic analysis. "Constraint" modes are included to treat redundancies in the interconnection system. "Normal" modes define displacements relative to the connections. Generalized mass, stiffness, and damping matrices are determined for each component, as are generalized forces. The requirement of system continuity gives rise to equations of displacement compatibility at the connections. These serve as equations of constraint among the component coordinates and are used to construct a transformation relating component coordinates to system coordinates. This transformation is used to derive system properties and forces from component properties and forces. System equations of motion are formulated and solved to determine system response. Component responses are found using the transformation. Connection forces are computed from the component equations. Each component can then be isolated and treated separately.
1,166 citations
Book•
19 Aug 1981TL;DR: The Science and Art of Structural Dynamics as discussed by the authors is a popular topic in the field of structural engineering, especially in the area of dynamic response of multidimensional dynamical systems.
Abstract: The Science and Art of Structural Dynamics. SINGLE-DEGREE-OF-FREEDOM SYSTEMS. Mathematical Models of SDOF Systems. Free Vibration of SDOF Systems. Response of SDOF Systems to Harmonic Excitation. Response of SDOF Systems to Special Forms of Excitation. Response of SDOF Systems to General Dynamic Excitation. Numerical Evaluation of Dynamic Response of SDOF Systems. Response of SDOF Systems to Periodic Excitation Frequency Domain Analysis. CONTINUOUS SYSTEMS. Mathematical Models of Continuous Systems. Free Vibration of Continuous Systems. MULTIPLE-DEGREE-OF-FREEDOM SYSTEMS. Mathematical Models of MDOF Systems. Vibration of Undamped 2-DOF Systems. Free Vibration of MDOF Systems. Numerical Evaluation of Modes and Frequencies of MDOF Systems. Dynamic Response of MDOF Systems: Mode-Superposition Method. Finite Element Modelling of Structures. Vibration Analysis Employing Finite Element Models. Direct Integration Methods for Dynamic Response. Component Mode Synthesis. Introduction to Earthquake Response of Structures.
826 citations