Dynamic stability of rotating blades with transverse cracks

In this paper, the main objective is to examine the effects of transverse cracks on the dynamic instability regions of an axially loaded rotating blade. The blade is modeled as an Euler-Bernoulli beam. To reduce the governing equations to a set of ordinary differential equations in matrix form, Hamilton's principle is used in conjunction with the assumed-mode method. The crack is accounted for by considering the energy release rate and the parametric instability regions are obtained using Bolotin's first approximation. Benchmark results are presented for cracked rotating blades at different rotating speeds, crack lengths and crack positions.

[1]  M. L. Renard,et al.  | EQUATORIAL VIBRATIONS OF A LONG FLEXIBLE BOOM ON A SPIN-STABILIZED SATELLITE OF NON-ZERO RADIUS , 1972 .

[2]  Dewey H. Hodges,et al.  Free-Vibration Analysis of Rotating Beams by a Variable-Order Finite-Element Method , 1981 .

[3]  Andrew D. Dimarogonas,et al.  VIBRATION OF CRACKED SHAFTS IN BENDING , 1983 .

[4]  F. D. Ju,et al.  Experimental Diagnosis of Fracture Damage in Structures by the Modal Frequency Method , 1988 .

[5]  V. V. Bolotin,et al.  The Dynamic Stability of Elastic Systems , 1966 .

[6]  T. Chondros,et al.  Analytical Methods in Rotor Dynamics , 1983 .

[7]  W. T. Springer,et al.  A General Beam Element for Use in Damage Assessment of Complex Structures , 1988 .

[8]  Robert D. Adams,et al.  A Vibration Technique for Non-Destructively Assessing the Integrity of Structures: , 1978 .

[9]  J. S. Rao,et al.  Application of the Reissner method to derive the coupled bending-torsion equations of dynamic motion of rotating pretwisted cantilever blading with allowance for shear deflection, rotary inertia, warping and thermal effects , 1982 .

[10]  P. Gudmundson.  The dynamic behaviour of slender structures with cross-sectional cracks , 1983 .

[11]  T. R. Kane,et al.  Dynamics of a cantilever beam attached to a moving base , 1987 .

[12]  Shyh-Chin Huang,et al.  On the vibration of a cracked rotating blade , 1998 .

[13]  Andrew D. Dimarogonas,et al.  Stability of Cracked Rotors in the Coupled Vibration Mode , 1988 .

[14]  Nikos A. Aspragathos,et al.  Identification of crack location and magnitude in a cantilever beam from the vibration modes , 1990 .

[15]  Andrew D. Dimarogonas,et al.  Dynamic Sensitivity of Structures to Cracks , 1989 .

[16]  C. Pierre,et al.  Natural modes of Bernoulli-Euler beams with symmetric cracks , 1990 .

[17]  G. L. Anderson,et al.  On the extensional and flexural vibrations of rotating bars , 1975 .

[18]  J. S. Rao,et al.  Vibrations of rotating, pretwisted and tapered blades , 1977 .

[19]  P. Gudmundson.  Eigenfrequency changes of structures due to cracks, notches or other geometrical changes , 1982 .

[20]  C. E. Hammond.  An application of Floquet theory to prediction of mechanical instability. [in helicopter rotor blades] , 1974 .

[21]  J.-S. Jiang,et al.  The dynamic behaviour and crack detection of a beam with a crack , 1990 .

[22]  Andrew D. Dimarogonas,et al.  Coupled Longitudinal and Bending Vibrations of a Cracked Shaft , 1988 .

[23]  P. Likins,et al.  Mathematical modeling of spinning elastic bodies for modal analysis. , 1973 .