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ANALYTICAL DETERMINATION OF COUPLED BENDING VIBRATIONS OF ROTATING TWISTED CANTILEVER BEAMS BY MEANS OF STATION FUNCTIONS
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Abstract
The work by Mendelson and Gendler on the application of station functions to the treatment of coupled bending vibrations of cantilever beams is extended to include centrifugal effects. The effect of centrifugal forces is obtained by the introduction of additional terms into the loading functions of the governing integral equations. The use of station functions is made possible by integrations by parts of the centrifugal terms.
The analysis was applied to several rectangular beams of variable geometry, representative of the automotive type turbine and compressor blading. The increase in the natural frequencies due to shaft rotation was found to be very pronounced in the fundamental mode, diminishing rapidly in significance with the increasing order of frequencies. Furthermore, it is shown that this effect is considerably influenced by the geometry of the beam.
Experimental work with several stationary beams was initiated to check the accuracy of the method of analysis. The degree of correlation obtained was well within the engineering accuracy.
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PALUSZNY, A. and BLECH, J., "ANALYTICAL DETERMINATION OF COUPLED BENDING VIBRATIONS OF ROTATING TWISTED CANTILEVER BEAMS BY MEANS OF STATION FUNCTIONS," SAE Technical Paper 630114, 1963, https://doi.org/10.4271/630114.Also In
References
- Mykelstad, N. O. Vibration Analysis McGraw-Hill Book Co. 1944
- Rosard, D. D. “Natural Frequencies of Twisted Cantilever Beams,” Journal of Apl. Mech. June 1953
- Duncan, W. J. Collar, A. R. “A Method for the Solution of Oscillation Problems by Matrices,” Phil. Mag. and Journal Sci., Ser. 7 17 115 865 909 May 1934
- White, W. T. “Integral Equations for Rotating Beams,” Journal of Franklin Inst. 245 25 36 117 133 Jan. and Feb. 1948
- Mendelson, A. Gendler, S. Analytical and Experimental Investigation of Effect of Twist on Vibrations of Cantilever Beams 1951
- Mendelson, A. Gendler, S. Analytical Determination of Coupled Bending-Torsion Vibrations of Cantilever Beams by Means of Station Functions 1950
- Rauscher, M. “Station Functions and Air Density Variations in Flutter Analysis,” Journal Aero. Sci. 16 6 345 354 June 1949
- Schilhansl, M. J. “Bending Frequency of a Rotating Cantilever Beam,” Journal of Appl. Mech., Paper No. 57-F-6 1957
- Huang, T. C. “The Effect of Rotary Inertia and of Shear Deformation on the Frequency and Normal Mode Equations of Uniform Beams with Simple End Conditions,” Journal of Apl. Mech., ASME Transactions 579 584 Dec. 1961
- Shanley, F. R. Strength of Materials McGraw-Hill Book Company 1957