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An application of Floquet theory to prediction of mechanical instability
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In this paper, the problem of helicopter mechanical instability is considered for the case where one blade damper is inoperative, and it is shown that if the hub is considered to be nonisotropic, the equations of motion have periodic coefficients which cannot be eliminated.Abstract:
The problem of helicopter mechanical instability is considered for the case where one blade damper is inoperative, and it is shown that if the hub is considered to be nonisotropic, the equations of motion have periodic coefficients which cannot be eliminated. The Floquet transition matrix method is shown to be an effective way of dealing with the nonisotropic hub and nonisotropic rotor situation. Time history calculations are examined and shown to be inferior to the Floquet technique for determining system stability. It is shown that instabilities which occur when one blade damper is inoperative may consist of nearly pure blade motion or they may be similar to the classical mechanical instability.read more
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Efficient numerical treatment of periodic systems with application to stability problems
TL;DR: In this paper, two efficient numerical methods for dealing with the stability of linear periodic systems are presented, which combine the use of multivariable Floquet-Liapunov theory with an efficient numerical scheme for computing the transition matrix at the end of one period.
Book
Vibration of Axially-Loaded Structures
TL;DR: In this paper, a variety of structural components are analyzed with a view to predicting their response to various (primarily axial) loading conditions, and the authors present methods by which the combined effects of vibration and buckling on various structures can be assessed.
Journal ArticleDOI
Helicopter rotor dynamics by finite element time approximation
TL;DR: In this article, the authors exploit the finite element technique in the time domain in order to generate, by an automated procedure, a numerical approximation of the nonlinear periodic equations peculiar to the dynamics of helicopter rotors.
Journal ArticleDOI
Rotary wing aeroelasticity - A historical perspective
TL;DR: A historical perspective of the fundamental developments that have played a central role in rotarywing dynamics and aeroelasticity and have had a major impact on the design of rotary-wing aircraft is provided in this article.
Journal ArticleDOI
Numerical methods for determining the stability and response of periodic systems with applications to helicopter rotor dynamics and aeroelasticity
TL;DR: In this paper, the stability, linear response and nonlinear response of a rotor blade aeroelastic stability and response calculations in forward flight were analyzed using the Floquer theory.
References
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Theory of self-excited mechanical oscillations of helicopter rotors with hinged blades
TL;DR: In this article, a theoretical analysis of ground vibrations of a two-blade helicopter rotor on anisotropic flexible supports is presented, and the results of an investigation of the mechanical stability of a rotor having two vertically hinged blades mounted upon symmetrical supports, of equal stiffness and mass in all horizontal directions.
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