System Mode Shapes in the Flutter of Compressor Blade Rows
01 Jan 1956-Journal of the Aeronautical Sciences (American Institute of Aeronautics and Astronautics (AIAA))-Vol. 23, Iss: 1, pp 54-66
TL;DR: In this article, the existence and uniqueness of extremely simple system flutter modes are proved for blade rows consisting of identical blades equally spaced about a common rotor, with no loss of generality whatsoever, in terms of a single "equivalent blade."
Abstract: The problems associated with the prohibitive number of possible system modes for a fluttering compressor or turbine blade row are eliminated by the development that comprises the present report. The existence and uniqueness of extremely simple system flutter modes are proved for blade rows consisting of identical blades equally spaced about a common rotor. These simple system modes, if properly interpreted, have the effect of reducing by a factor of n the number of degrees of freedom necessary to analyze an w-bladed configuration. Stated differently, the system of n blades may be considered, with no loss of generality whatsoever, in terms of a single "equivalent blade." The proof holds under any type of flow and any and all types of interblade coupling, so long as a linear analysis is permissible. Moreover, since it is the flutter-inception point that is of interest in predicting critical velocity or rotational speed, it may well be that the conclusions developed apply even to the onset of stall flutter. Practical application of the method to stall-flutter calculations would, of course, require the availability of aerodynamic stallflutter coefficients. The development is carried out first under the assumption of infinite rotor inertia or, in other words, constant rotor velocity. This restriction is then relaxed, and the treatment is expanded to permit torsional oscillations of the rotor itself. I t is proved that under certain conditions the assumption of infinite rotor inertia introduces no error whatsoever.
Citations
More filters
TL;DR: In this paper, the effects of blade mistiming on the aeroelastic stability and response of a cascade in incompressible flow were investigated, and it was shown that the mistuning has a beneficial effect on the coupled bending-torsion and uncoupled torsion flutter.
Abstract: This paper presents an investigation of the effects of blade mistiming on the aeroelastic stability and response of a cascade in incompressible flow. The aerodynamic, inertial, and structural coupling between the bending and torsional motions of each blade and the aerodynamic coupling between the blades are included in the formulation. A digital computer program was developed to conduct parametric studies. Results indicate that the mistuning has a beneficial effect on the coupled bending-torsion and uncoupled torsion flutter. The effect of mistuning on forced response, however, may be either beneficial or adverse, depending on the engine order of the forcing function. Additionally, the results illustrate that it may be feasible to utilize mistuning as a passive control to increase flutter speed while maintaining forced response at an acceptable level. [A ] [Ar] {AD } { ADr } a b c [D], [Ds [E] E(s,r) [G],[G S
131 citations
TL;DR: A survey of vibration localization in the context of structural dynamics and vibrations is presented in this paper, where the authors show how the problem of mode localization and vibration confinement can be formulated as a problem in the theory of stability of differential equations with ap coefficients using stability theory.
Abstract: A survey of vibration localization phenomena in the context of structural dynamics and vibrations is presented The review covers the more common and relevant cases where mode localization and vibration confinement are likely to occur in engineering structures Examples considered include periodic or nearly periodic multi-span beams and multi-bay trusses, large space structures, space antennas, and almost periodic (ap) structures with circular symmetry, eg, bladed disks in turbomachines Both analytical and numerical methods for analyzing and predicting localization in finite and infinite systems are discussed In this paper, we show how the problem of mode localization and vibration confinement can be formulated as a problem in the theory of stability of differential equations with ap coefficients Using stability theory, new definitions of mode localization can be established for both linear and nonlinear structures The possibility of stabilizing certain nonconservative fluid-structure systems using structural disorder is demonstrated, and stability theorems are given for aeroelastic systems governed by normal operators We also illustrate how the results from localization theory and the associated stability theory can be applied to the vibration control problem, by triggering vibration confinement by active or passive means
109 citations
TL;DR: In this article, a survey of methods for modeling and analyzing bladed disk assemblies common to gas turbine aircraft is presented, followed by a literature review of studies modeling bladed disks, blade mistuning, and the effect of forced response.
Abstract: This work surveys methods for modeling and analyzing bladed disk assemblies common to gas turbine aircraft. An introduction to symmetric (tuned) bladed disk dynamics is presented, followed by a literature review of studies modeling bladed disks, blade mistuning. and the effect of mistuning forced response. A summary of results is given, and suggestions for future work are made.
96 citations
TL;DR: In this article, a closed-form analytical solution is obtained by using a double application of the Wiener-Hopf technique for predicting the unsteady flow in a supersonic cascade with subsonic axial flow velocity.
Abstract: Linearized theory is used to predict the unsteady flow in a supersonic cascade with subsonic axial flow velocity. A closed-form analytical solution is obtained by using a double application of the Wiener-Hopf technique. Although numerical and semianalytical solutions of this problem have already appeared in the literature, this paper contains the first completely analytical solution. It has been stated in the literature that the blade source should vanish at the infinite duct resonance condition. The present analysis shows that this does not occur. This apparent discrepancy is explained in the paper.
85 citations
TL;DR: In this article, an investigation of the effects of mistuning on flutter and forced response of a cascade in subsonic and supersonic flows is presented, where the aerodynamic and structural coupling between the bending and torsional motions and the turbine blades are included.
Abstract: An investigation of the effects of mistuning on flutter and forced response of a cascade in subsonic and supersonic flows is presented. The aerodynamic and structural coupling between the bending and torsional motions and the aerodynamic coupling between the blades are included. It is shown that frequency mistuning always has a beneficial effect on flutter. Additionally, the results indicate that frequency mistuning may have either a beneficial or an adverse effect on forced response, depending on the engine order of the excitation and Mach number.
72 citations
References
More filters
02 May 1934
TL;DR: In this paper, the Kutta condition was used to analyze the aerodynamic forces on an oscillating airfoil or an air-foil-aileron combination of three independent degrees of freedom.
Abstract: The aerodynamic forces on an oscillating airfoil or airfoil-aileron combination of three independent degrees of freedom were determined. The problem resolves itself into the solution of certain definite integrals, which were identified as Bessel functions of the first and second kind, and of zero and first order. The theory, based on potential flow and the Kutta condition, is fundamentally equivalent to the conventional wing section theory relating to the steady case. The air forces being known, the mechanism of aerodynamic instability was analyzed. An exact solution, involving potential flow and the adoption of the Kutta condition, was derived. The solution is of a simple form and is expressed by means of an auxiliary parameter k. The flutter velocity, treated as the unknown quantity, was determined as a function of a certain ratio of the frequencies in the separate degrees of freedom for any magnitudes and combinations of the airfoil-aileron parameters.
2,153 citations
Book•
01 Jan 1951
TL;DR: This book, although having the same title as the 1938 edition, is an entirely new text, in which the whole subject matter is brought up to date and the theoretical foundations of chain reactions are well set out.
Abstract: This book, although having the same title as the 1938 edition, is an entirely new text, in which the whole subject matter is brought up to date. It is divided into four parts. Part I describes the chemistry and kinetics of the reactions of fuel gases with oxygen, and in detail with hydrogen, carbon monoxide and various hydrocarbon gases. The theoretical foundations of chain reactions are well set out in an initial chapter and the authors have not been shy of using mathematics to give precision to the subject. The hydrocarbon chapter ends with an account of recent work on engine knock.
205 citations
33 citations
TL;DR: In this article, the interaction of a plane shock wave with a thermal boundary layer has been studied experimentally in the shock tube and a theory developed for those cases in which the shock is sufficiently strong and the heating small enough for the shock to extend clear to the surface.
Abstract: The interaction of a plane shock wave with a thermal boundary layer has been studied experimentally in the shock tube and a theory developed for those cases in which the shock is sufficiently strong and the heating small enough for the shock to extend clear to the surface. The experiment involves a technique of sliding a hot plate into the shock tube just before the shock arrives. The time required for establishment of steady conditions has been determined and the theory tested with experiments using shocks up to a pressure ratio of 1.36 and surface temperatures up to 80°C. The observed shape of the shock and pressure distribution along the surface agree well with predictions. When the speed of sound a t the surface exceeds the shock velocity, pressure disturbances propagate ahead of the main wave and the total pressure rise extends over about two heated thicknesses. Finally, the possibility of extending the experimental results to more extreme conditions by an analogy with diffusion of gases is discussed.
21 citations