Vibration of higher-order-shearable pretwisted rotating composite blades

Abstract The free and forced vibration of a rotating, pretwisted blade modeled as a laminated composite, hollow (single celled), uniform box-beam is studied. The structural model includes transverse shear flexibility, restrained warping, and centrifugal and Coriolis effects. A key element of this model is its ability to satisfy the zero shear–traction requirement on the external bounding surfaces. The governing system possesses complicated and eigenvalue-dependent natural boundary conditions. Hence an extended Galerkin method using admissible functions is employed. Free-vibration results obtained for the present higher-order shearable model are compared with those of the existing first-order shearable and the non-shearable models. For the data considered, the present theory provides conservative predictions. This suggests that through-the-thickness variations of transverse shear strains are significant and should be considered when pursuing non-resonant designs. The effect of pretwist, while marginal for the lowest eigenfrequency, is substantial for the higher ones especially for lower rotation speeds and larger ply angles. A combination of softening and stiffening effects are also possible for the same eigenfrequency when pretwist is varied. Tailoring studies using the present model show an enhancement of eigenfrequency characteristics and also reveal the potential for passive mitigation of forced response.

[1]  Inderjit Chopra,et al.  Structural behavior of two-cell composite rotor blades with elastic couplings , 1991 .

[2]  Hejun Du,et al.  A Power Series Solution For Vibration Of A Rotating Timoshenko Beam , 1994 .

[3]  Aviv Rosen,et al.  Structural and Dynamic Behavior of Pretwisted Rods and Beams , 1991 .

[4]  Hong Hee Yoo,et al.  Vibration Analysis of Rotating Pre-Twisted Blades with a Concentrated Mass , 2001 .

[5]  K. Rohwer,et al.  Application of higher order theories to the bending analysis of layered composite plates , 1992 .

[6]  E. Smith,et al.  Formulation and evaluation of an analytical model for composite box-beams , 1991 .

[7]  Takashi Yokoyama,et al.  Free vibration characteristics of rotating Timoshenko beams , 1988 .

[8]  Ohseop Song,et al.  Modeling, vibration, and stability of elastically tailored composite thin-walled beams carrying a spinning tip rotor , 2001 .

[9]  Donald L. Kunz,et al.  Survey and comparison of engineering beam theories for helicopter rotor blades , 1994 .

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

[11]  Dewey H. Hodges,et al.  Nonclassical Behavior of Thin-Walled Composite Beams with Closed Cross Sections , 1990 .

[12]  Ohseop Song,et al.  BENDING VIBRATION OF CANTILEVERED THIN-WALLED BEAMS SUBJECTED TO TIME-DEPENDENT EXTERNAL EXCITATIONS , 1995 .

[13]  Donald L. Kunz.  Multimode control of a rotating, uniform, cantilever beam , 2001 .

[14]  D. J. Ewins,et al.  Structural dynamic characteristics of individual blades , 1992 .

[15]  J. R. Banerjee,et al.  Free vibration analysis of a twisted beam using the dynamic stiffness method , 2001 .

[16]  N. K. Chandiramani,et al.  On the free-vibration of rotating composite beams using a higher-order shear formulation , 2002 .

[17]  K. B. Subrahmanyam,et al.  Vibration and Buckling of Rotating, Pretwisted, Preconed Beams Including Coriolis Effects , 1986 .

[18]  L. Librescu,et al.  Structural Modeling and Free Vibration Analysis of Rotating Composite Thin-Walled Beams , 1997 .

[19]  I. Chopra,et al.  Thin-walled composite beams under bending, torsional, and extensional loads , 1990 .

[20]  Scott R. White,et al.  Analysis of thick hollow composite beams under general loadings , 1996 .

[21]  Ohseop Song,et al.  Vibration of pretwisted adaptive rotating blades modeled as anisotropic thin-walled beams , 2001 .

[22]  V. T. Nagaraj,et al.  Higher-order shear deformation theory for thin-walled composite beams , 1996 .

[23]  Inderjit Chopra,et al.  Refined Structural Dynamics Model for Composite Rotor Blades , 2001 .

[24]  Inderjit Chopra,et al.  Assessment of Composite Rotor Blade Modeling Techniques , 1999 .

[25]  Dewey H. Hodges,et al.  An Approximate Formula for the Fundamental Frequency of a Uniform Rotating Beam Clamped Off the Axis of Rotation , 1981 .

[26]  Scott R. White,et al.  Thick-walled composite beam theory including 3-d elastic effects and torsional warping , 1997 .

[27]  Liviu Librescu,et al.  Effects of pretwist and presetting on coupled bending vibrations of rotating thin-walled composite beams , 2003 .

[28]  Raimund Rolfes,et al.  Higher-order theories for thermal stresses in layered plates , 2001 .