Summary
This work considers a group of problems associated with rotating Timoshenko beams. The beam is not assumed to be hubclamped, i.e. the axis of rotation does not necessarily pass through the beam's clamped end. Cases of physical interest involving off-clamped beams include wobbling rotors, impellor blades, and turbine blades.
For clamped-free boundary conditions, we seek solutions of the governing equations which correspond to transverse buckling. For the rotor, it is known that Euler-Bernoulli beams do not have buckled modes. By contrast, the Timoshenko beam will have an infinite number of buckled modes. In the impellor blade case, both Euler-Bernoulli and Timoshenko beams will have an infinite number of buckled modes. However, the Timoshenko beam will buckle at a lower eigenrotation speed. This is also true for the case of a rotating Timoshenko beam with clamped-clamped boundary conditions, e.g. a turbine blade clamped at both the rim and hub of a rotating platform.
Analytic results for both the clamped-free and clamped-clamped cases are augmented by results obtained from numerical solution of the corresponding boundary value problems.
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References
S. Timoshenko, D. H. Young and W. Weaver, Vibration problems in engineering, 4th ed., John Wiley & Sons, 433.
W. D. Lakin and A. Nachman, Unstable vibrations and buckling of rotating flexible rods, Quart. Appl. Math. 35 (1978) 479–493.
W. D. Lakin, Vibrations of a rotating flexible rod clamped off the axis of rotation, J. Eng. Math. 10 (1976) 313–321.
W. D. Lakin, R. Mathon and A. Nachman, Buckling and vibration of a rotating spoke, J. Eng. Math. 12 (1978) 193–206.
W. D. Lakin and A. Nachman, Vibration and buckling of rotating flexible rods at transitional parameter values, J. Eng. Math. 13 (1979) 339–346.
S. S. Antman and A. Nachman, Large buckled states of rotating rods, Nonlinear Analysis, Theory, Methods and Appl. 4 (1980) 303–327.
H. F. Weinberger, A first course in partial differential equations with complex variables and transform methods, Blaisdell Publ., 1965.
M. Abramowitz and I. A. Stegun, Handbook of mathematical functions, Dover Publ., New York, 1965.
U. Ascher, J. Christiansen, and R. D. Russell, COLSYS—A collocation code for boundary-value problems, in Notes on Computer Science eds. G. Goos and J. Hartmanis, no. 76, Codes for Boundary-Value Problems in Ordinary Differential Equations, Springer-Verlag, (1978) 164–185.
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Nachman, A., Lakin, W.D. Transverse buckling of a rotating Timoshenko beam. J Eng Math 16, 181–195 (1982). https://doi.org/10.1007/BF00042553
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DOI: https://doi.org/10.1007/BF00042553