Parametric instability of spinning pretwisted beams subjected to spin speed perturbation

The equations of motion of a spinning pretwisted beam under compressive loads and subjected to spin speed perturbations are formulated using Euler beam theory and the assumed mode method. Unstable regions of flutter instability are found to exist for beams with non-zero pretwist angles, within the stable critical speed zones. The narrower regions of flutter instability separate the stable critical speed zones into smaller stable sub-regions. The spin speed consists of a steady state value and a time-dependent portion. The resulting dimensionless equations of motion are reduced to matrix differential equations with time-dependent coefficients. A modal analysis method is employed to uncouple the equations followed by application of the multiple scale method to determine the regions of instability due to parametric excitations. Parameters investigated include pretwisted angles, aspect ratio of the beam cross-sections, steady-state spin speed and axial loads. Dynamic instability due to both the summed and difference-type resonance were studied.

[1]  V. V. Bolotin,et al.  Nonconservative problems of the theory of elastic stability , 1963 .

[2]  J. S. Rao,et al.  Coupled bending-bending vibrations of pre-twisted cantilever blading allowing for shear deflection and rotary inertia by the Reissner method , 1981 .

[3]  B.-W. Huang,et al.  Parametric resonance of a spinning pretwisted beam with time-dependent spinning rate , 1995 .

[4]  Dynamic Response of a Rotating Blade with Time-Dependent Rotating Speed , 1993 .

[5]  Yoshihiko Sugiyama,et al.  Parametric instability of clamped-clamped and clamped-simply supported columns under periodic axial load , 1973 .

[6]  T. H. Young,et al.  Coriolis Effect on the Vibration of a Cantilever Plate With Time-Varying Rotating Speed , 1992 .

[7]  C.-L. Liao,et al.  Structural characteristics of spinning pretwisted orthotropic beams , 1992 .

[8]  Marta B. Rosales,et al.  Free vibrations of a spinning uniform beam with ends elastically restrained against rotation , 1987 .

[9]  H. Bauer.  Vibration of a rotating uniform beam, part I: Orientation in the axis of rotation , 1980 .

[10]  H. P. Lee.  Buckling and dynamic stability of spinning pre-twisted beams under compressive axial loads , 1994 .

[11]  R. Laurenson.  Modal Analysis of Rotating Flexible Structures , 1976 .

[12]  Leonard Meirovitch,et al.  A New Method of Solution of the Eigenvalue Problem for Gyroscopic Systems , 1974 .

[13]  W. Carnegie,et al.  The Coupled Bending—Bending Vibration of Pre-Twisted Tapered Blading , 1972 .

[14]  R. S. Gupta,et al.  Finite element eigenvalue analysis of tapered and twisted Timoshenko beams , 1978 .

[15]  Leonard Meirovitch,et al.  Computational Methods in Structural Dynamics , 1980 .

[16]  T. H. Young,et al.  Dynamic resppnse of a pretwisted, tapered beam with non-constant rotating speed , 1991 .