The purpose of the present paper is to investigate the modal characteristics of rotating cantilever plates (e.g. helicopter rotor blades) that are attached to a rigid hub with a setting angle (angle of attack). A dynamic modeling method for plates undergoing overall motions is employed to derive the modal equations of the rotating cantilever plate. The plate is characterized by its lengths, widths, thickness, Young's modulus, shear modulus, mass per unit area and Poisson's ratio. The transverse shear and the rotary inertia effects are not considered. Based on the Kirchhoff hypothesis, any straight line segments perpendicular to the midplane of the plate remain perpendicular to the midplane during the deformation. The modal equations are transformed into dimensionless forms. Three dimensionless parameters are identified through a dimensional analysis: the aspect ratio of the plate, the ratio of hub radius to plate length, and the dimensionless angular speed. The Rayleigh-Ritz method using a set of admissible functions that satisfies the geometric boundary conditions as mode functions is employed to obtain numerical results. It is shown that the rotating plate's natural frequencies increase with the angular speed, that their increasing rates grow as the hub radius increases, and that the natural frequency loci are lowered by increasing the setting angle. It is also found that some natural frequencies increase faster than others as the aspect ratio or the angular speed increases. This results in the phenomena of eigenvalue loci crossing and veering. When two loci cross, the corresponding two mode shapes are simply switched and remain nearly unchanged. When two loci veer, however, mode shape variations occur continuously in the veering region. It is observed that fixed common nodal points exist for the two continuously changing mode shapes.
Free vibration analysis of rotating cantilever plates
Analyse der freien Schwingungen rotierender einseitig eingespannter Platten
AIAA Journal ; 40 , 11 ; 2188-2196
2002
9 Seiten, 12 Bilder, 3 Tabellen, 18 Quellen
Article (Journal)
English
Anstellwinkel (Tragflügel) , Bewegungsgleichung , dimensionslose Kennzahl , Eigenfrequenz , Eigenwertproblem , freie Schwingung , frei tragender Träger , Modalanalyse , Modenkonversion , Platte (Theorie) , Rotor (Drehflügel) , Schwingungsmode , Variationsrechnung , Verformungsenergie , elastische Schwingung
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