Advertisement

Rotating Thin-Walled Anisotropic Beams

Part of the Solid Mechanics and Its Applications book series (SMIA, volume 131)

Keywords

Rotor Blade Rotating Beam Solid Beam Composite Rotor Blade Couple Natural Frequency 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Aboudi, J., Pindera, M. and Arnold, S. M. (1996) “Thermoelastic Theory for the Response of Materials Functionally Graded in Two Directions,” International Journal of Solids and Structures, Vol. 33, No. 7, pp. 931–966.CrossRefGoogle Scholar
  2. Aboudi, J., Pindera, M. J. and Arnold, S. M. (1999) “Higher-Order Theory for Functionally Graded Materials,” Composites: Part B, 30, pp. 777–832.CrossRefGoogle Scholar
  3. Ambartsumian, S. A., Bagdasarian, G. E. Durgarian, S. M. and Gnuny, V. T. (1966) “Some Problems of Vibration and Stability of Shells and Plates,” International Journal of Solids and Structures, Vol. 2, pp. 59–81.CrossRefGoogle Scholar
  4. Anderson, G. L. (1975) “On the Extensional and Flexural Vibrations of Rotating Bars,” International Journal of Nonlinear Mechanics, Vol. 10, pp. 223–236.zbMATHGoogle Scholar
  5. Balhaddad, A. S. and Onipede, D. Jr. (1998) “Three-Dimensional Free Vibration of Pretwisted Beams,” AIAA Journal, Vol. 36, No. 8, pp. 1524–1528.Google Scholar
  6. Banerjee, J. R. (2001), “Free Vibration Analysis of a Twisted Beam Using the Dynamic Stiffness Method,” International Journal of Solids and Structures, Vol. 38, pp. 6703–6722.zbMATHGoogle Scholar
  7. Bauchau, O. A. (1985) “A Beam Theory for Anisotropic Materials,” Journal of Applied Mechanics, Trans. ASME, Vol. 52, pp. 416–422.zbMATHGoogle Scholar
  8. Bauchau, O. A., Loewy, R. G. and Bryan, P. S. (1986) “Approach to Ideal Twist Distribution in Tilt Rotor VTOL Blade Designs,” RTC Report No. D-86-2, Rensselaer Polytechnic Institute, Troy, NY July.Google Scholar
  9. Bauchau, O. A. and Hong, C. H. (1987) “Large Displacement Analysis of Naturally Curved and Twisted Composite Beams,” AIAA Journal Vol. 25, No. 10, pp. 1469–1475.Google Scholar
  10. Bazoune, A., Khulief, Y. A. and Stephen, N. G. (1999) “Further Results for Modal Characteristics of Rotating Tapered Timoshenko Beams,” Journal of Sound and Vibration, Vol. 219, 1, pp. 157–174.CrossRefGoogle Scholar
  11. Berezovski, A., Engelbrecht, J. and Maugin, G. A. (2003) “Numerical Simulation of Two-Dimensional Ware Propagation in Functionally Graded Materials,European Journal of Mechanics A/Solids, 22, pp. 257–265.MathSciNetGoogle Scholar
  12. Bhat, R. B. (1986) “Transverse Vibrations of a Rotating Uniform Cantilever with Tip Mass as Predicted by Using Beam Characteristics Orthogonal Polynomials in the Rayleigh-Ritz Method,” Journal of Sound and Vibration, Vol. 105, No. 2, pp. 199–210.CrossRefMathSciNetGoogle Scholar
  13. Bhuta, P. G. and Jones, J. P. (1965) “On Axial Vibrations of a Whirling Bar,” Journal of the Acoustical Society of America, Vol. 35, No. 2, February, pp. 217–221.MathSciNetGoogle Scholar
  14. Bielawa, R. L. (1992) Rotary Wing Structural Dynamics and Aeroelasticity, AIAA Education Series, AIAA, Inc., Washington, D.C.Google Scholar
  15. Birman, V. (1995) “Buckling of Functionally Graded Hybrid Composite Plates,” Proceedings of the 10th Conference on Engineering Mechanics, Vol. 2, Boulder, CO, pp. 1199–1202.Google Scholar
  16. Boyce, W. E. (1956) “Effect of Hub Radius on the Vibration of a Uniform Bar,” Journal of Applied Mechanics, Trans. ASME, Vol. 23, pp. 287–290.zbMATHGoogle Scholar
  17. Boyce, W. E. and Handelman, G. H. (1961) “Vibration of Rotating Beams with Tip Mass,” Zeitschrift für Agew. Math. and Physik, XII, 5, 369–392.MathSciNetGoogle Scholar
  18. Büter, A. and Breitbach E. (2000) “Adaptive Blade Twist-Calculations and Numerical Results,” Aerospace Science and Technology, 4, pp. 309–319.Google Scholar
  19. Carnegie, W. (1959) “Vibrations of Pre-twisted Cantilever Blading,” Proc. Inst. Mech. Engrs. London, Vol. 173, pp. 343–362.Google Scholar
  20. Carnegie, W. and Thomas, J. (1972) “The Effects of Shear Deformation and Rotary Inertia on the Lateral Frequencies of Cantilever Beams in Bending,” Journal of Engineering for Industry, Trans. ASME, Vol. 94, pp. 267–278.Google Scholar
  21. Cesnik, C. E. S. and Shin, S. J. (2001a) “On the Twist Performance of a Multiple-Cell Active Helicopter Blade,” Smart Materials and Structures, Vol. 10, pp. 53–61.Google Scholar
  22. Cesnik, C. E. S. and Shin, S. J. (2001b) “On The Modeling of Integrally Activated Helicopter Blades,” International Journal of Solids and Structures, Vol. 38, pp. 1765–1789.CrossRefGoogle Scholar
  23. Chandra, R. and Chopra, I. (1992) “Experimental-Theoretical Investigation of the Vibration Characteristics of Rotating Composite Box Beams,” Journal of Aircraft, Vol. 29, No. 4, pp. 657–664.Google Scholar
  24. Chandiramani, N. K., Librescu, L. and Shete, C. D. (2002) “On The Free-Vibration of Rotating Composite Beams Using a Higher-Order Transverse Shear Formulation,” Aerospace Science and Technology, Vol. 6, pp. 545–561.CrossRefGoogle Scholar
  25. Chandiramani, N. K. and Librescu, L. (2002) “Optimal Vibration Control of a Rotating Shearable Blade Using Distributed Piezoelectric Sensing and Actuation,” Smart Structures and Materials; Modeling Signal Processing and Control, (V. S. Rao Ed.) Proceedings of SPIE, Vol. 4693, SPIE, pp. 451–460.Google Scholar
  26. Chandiramani, N.K., Shete, C. D. and Librescu, L. (2003a) “Vibration of Higher-Order Shearable Pretwisted Rotating Composite Blades,” International Journal of Mechanical Sciences, Vol. 45, pp. 2017–2041.CrossRefGoogle Scholar
  27. Chandiramani, N. K., Shete, C. D. and Librescu, L. (2003b) “Optimal Control of Pretwisted Shearable Smart Composite Rotor Blades,” AIAA-2003-1540, 44th AIAA/ASME/ASCE/AHS Structures, Structural Dynamics and Materials Conference, Norfolk, VA, April 7–10.Google Scholar
  28. Chandiramani, N.K., Librescu, L., Saxena, V. and Kumar, A. (2004) “Optimal Vibration Control of a Rotating Composite Beam with Distributed Piezoelectric Sensing and Actuations,” Smart Materials and Structures, Vol. 13, pp. 433–442.CrossRefGoogle Scholar
  29. Chelu, P. and Librescu, L. (2005) “Dynamic Response of Spinning Thin-Walled Composite Booms Exposed to Solar Radiation Using Wavelet-Galerkin Method,” Proceedings of the Sixth International Congress on Thermal Stresses, TS 2005, Vienna University of Technology, F. Ziegler, R. Heuer and C. Adam (Eds), Vol. 2, pp. 459–462, TU Wien, May 2005.Google Scholar
  30. Cheng, Z.-W. and Batra, R. C. (2000) “Three-Dimensional Thermoelastic Deformation of a Functionally Graded Elliptic Plate,” Composites, Part B, Vol. 31, pp. 97–100.CrossRefGoogle Scholar
  31. Chopra, I. (2000) “Status of Application of Smart Structures Technology to Rotorcraft Systems,” Journal of the American Helicopter Society, Vol. 45, No. 4, pp. 228–252.Google Scholar
  32. Coyle, T. and Harris, W. R. (1960) “The Effects of Blast Against Rotor Blades,” (V) BRL, Technical Note No. 1342, Sept. 1960, AD 370885.Google Scholar
  33. Dawson, B. (1968), “Coupled Bending-Bending Vibrations of Pretwisted Cantilever Blading Treated by Rayleigh-Ritz Energy Method,” Journal of Mechanical Engineering Science, Vol. 10, No. 5, pp. 381–388.Google Scholar
  34. Dokumaci, E., Thomas, J. and Carnegie, W. (1967) “Matrix Displacement Analysis of Coupled Bending-Bending Vibration of Pretwisted Blading,” Journal of Mechanical Engineering Science, Vol. 9, No. 4, pp. 247–254.Google Scholar
  35. Du, H., Lim, M. K. and Liew, K.M. (1994) “A Power Series Solution for Vibration of a Rotating Timoshenko Beam,” Journal of Sound and Vibration, Vol. 175, No. 4, pp. 505–523.CrossRefGoogle Scholar
  36. Eick, C. D. and Mignolet, M. P. (1995, 1996) “Vibration and Buckling of Flexible Rotating Beams,” AIAA Journal, Vol. 33, No. 3, March. pp. 528–538, and AIAA Journal, Vol. 34, No. 3, pp. 641–643.Google Scholar
  37. Ewins, D. J. and Henry, R. (1992) “Structural Dynamic Characteristics of Individual Blades,” Vibration and Rotor Dynamics, von Kármán Institute for Fluid Dynamics, Lecture Series 1992-06, September, pp. 14.1–14.27.Google Scholar
  38. Fauconneau, G. and Marangoni, R. D. (1970) “Effect of a Thermal Gradient on the Natural Frequencies of a Rectangular Plate,” International Journal Mechanical Sciences, Vol. 12, pp. 113–122.Google Scholar
  39. Flax, A. H. (1996) “Comments on Vibration and Buckling of Flexible Rotating Beams,” AIAA Journal, Vol. 34, No. 3, March. pp. 640–641.Google Scholar
  40. Friedmann, P. (1977) “Recent Developments in Rotaway-Wing Aeroelasticity,” Journal of Aircraft, Vol. 14, No. 11, pp. 1027–1041.Google Scholar
  41. Friedmann, P. (1983) “Formulation and Solution of Rotary-Wing Aeroelastic Stability and Response Problems,” Vertica, Vol. 7, No. 2, pp. 101–141.Google Scholar
  42. Gern, F. H. and Librescu, L. (1998) “Effects of Externally Mounted Stores on Flutter Characteristics of Advanced Swept Cantilevered Aircraft Wings,” Aerospace Science and Technology, Vol. 2, No. 5, pp. 321–333.CrossRefGoogle Scholar
  43. Gern, F. H. and Librescu, L. (1999) “Aeroelatic Tailoring of Advanced Aircraft Wings Carrying External Stores,” Atti della Accademia delle Scienze di Torino, Classe di Scienze Fisiche, Mathematiche’s Naturali, Quaderni, 1, pp. 201–219, (Issue devoted to Placido Cicala).Google Scholar
  44. Gern, F. H. and Librescu, L. (2000) “Aeroelastic Tailoring of Composite Wings Exhibiting Nonclassical Effects and Carrying External Stores,” Journal of Aircraft, Vol. 37, No. 6, pp. 1097–1004.Google Scholar
  45. Gern, F. H. and Librescu, L. (2001) “Static and Dynamic Aeroelasticity of Advanced Aircraft Wings Carrying Exernal Stores,” AIAA Journal, Vol. 36, No. 7, pp. 1121–1129.Google Scholar
  46. Giurgiutiu, V. and Stafford, R. O. (1977) “Semi-Analytic Methods for Frequencies and Mode Shapes of Rotor Blades,” Vertica, Vol. 1, pp. 291–306.Google Scholar
  47. Gong, S.W., Lam, K. Y. and Reddy, J. N. (1999) “The Elastic Response of Functionally Graded Cylindrical Shells to Low-Velocity Impact,” International Journal of Impact Engineering, Vol. 22, No. 4, pp. 397–417.CrossRefGoogle Scholar
  48. Hilton, H. H. (2005) “Optimum Linear and Nonlinear Viscoelastic Functionally Graded Materials-Characterizations and Analysis,” Composites Part A: Manufacturing and Applied Sciences, (in press).Google Scholar
  49. Hoa, S.V. (1979) “Vibration of a Rotating Beam with Tip Mass,” Journal of Sound and Vibration, Vol. 67, No. 2, pp. 369–381.zbMATHGoogle Scholar
  50. Hodges, D. H. (1977) “On the Extensional Vibrations of Rotating Bars,” International Journal of Nonlinear Mechanics, Vol. 12, pp. 293–296.zbMATHGoogle Scholar
  51. Hodges, D. H. (1980), “Torsion of Pretwisted Beams Due to Axial Loading,” ASME Journal of Applied Mechanics, Vol. 47, pp. 393–397.zbMATHGoogle Scholar
  52. Hodges, D. H. (1981) “An Approximate Formula for the Fundamental Frequency of a Uniform Rotating Beam Clamped off the Axis of Rotation,” Journal of Sound and Vibration, Vol. 77, No. 1, pp. 11–18.zbMATHGoogle Scholar
  53. Hodges, D. H. and Ormiston, R. A. (1976) “Stability of Elastic Bending and Torsion of Uniform Cantilever Rotor Blades in Hover with Variable Structural Coupling”, NASA TND-8192, April.Google Scholar
  54. Hodges, D. H., Rutkowski, M. J. (1981), “Free-Vibration Analysis of Rotating Beams by a Variable-Order Finite Element Method,” AIAA Journal, Vol. 19, No. 11, pp. 1459–1466.Google Scholar
  55. Hodges, D. H. (1990) “Review of Composite Rotor Blade Modeling,” AIAA Journal, Vol. 28, No. 3, pp. 561–565.Google Scholar
  56. Hong, C. H. and Chopra, I. (1985) “Aeroelastic Stability of a Composite Rotor Blade,” Journal of American Helicopter Society, Vol. 30, No. 2, pp. 57–67.Google Scholar
  57. Houbolt, J.C. and Brooks, G. W. (1958) “Differential Equations of Motion for Combined Flapwise Bending, Chordwise Bending, and Torsion of Twisted Nonuniform Rotor Blades,”NACA TR 1346.Google Scholar
  58. Isakson, G. and Eisley, J.G. (1960) “Natural Frequencies in Bending of Twisted Rotating Blades,” NASA TN D-371.Google Scholar
  59. Johnson, W. (1980) Helicopter Theory, Princeton University Press.Google Scholar
  60. Jung, S. N., Nagaraj, V. T. and Chopra, I. (1999) “Assessment of Composite Rotor Blade: Modeling Techniques,” Journal of the American Helicopter Society, Vol. 44, No. 3, pp. 188–205.Google Scholar
  61. Jung, S. N., Nagaraj, V. T. and Chopra, I. (2001) “Refined Structural Dynamics Model for Composite Rotor Blades,” AIAA Journal, Vol. 39, No. 2, pp. 339–348.Google Scholar
  62. Karpouzian G. and Librescu, L. (1994) “A Comprehensive Model of Anisotropic Composite Aircraft Wings and Its Use in Aeroelastic Analyses,” Journal of Aircraft, May–June, Vol. 31, No. 3, pp. 702–712.Google Scholar
  63. Karpouzian G. and Librescu, L. (1995) “Exact Flutter Solution of Advanced Composite Swept Wings in Various Flight Speed Regimes,” AIAA Paper 95-1382, Proceedings of the 36th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference, New Orleans, LA, April 10–12.Google Scholar
  64. Karpouzian, G. and Librescu, L. (1996) “Non-Classical Effects on Divergence and Flutter of Anisotropic Swept Aircraft Wings,” AIAA Journal, Vol. 34, No. 4, April, pp. 786–794.Google Scholar
  65. Kaza, K. B. and Kielb, R. E. (1984) “Effects of Warping and Pretwist on Torsional Vibration of Rotating Beams,” Journal of Applied Mechanics, Trans. ASME, Vol. 51, Dec., pp. 913–920.Google Scholar
  66. Khulief, Y. A. and Bazoune, A. (1992) “Frequencies of Rotating Tapered Timoshenko Beams with Different Boundary Conditions,” Computers & Structures, Vol. 42, No. 5, pp. 781–795.CrossRefGoogle Scholar
  67. Kosmatka, J. B. (1992) “Extension-Bend-Twist Coupling Behavior of Nonhomogeneous Anisotropic Beams with Initial Twist,” AIAA Journal, Vol. 30, No. 2, pp. 519–527.zbMATHGoogle Scholar
  68. Krenk, S. (1984) “A Linear Theory for Pretwisted Elastic Beams,” ASME Trans., Journal of Applied Mechanics, Vol. 50, pp. 137–142.Google Scholar
  69. Kumar R. (1974) “Vibration of Space Booms Under Centrifugal Force Field,” Canadian Aeronautics and Space Institute (CASI) Trans. Vol. 7, pp. 1–5.Google Scholar
  70. Kunz, D. L. (1994), “Survey and Comparison of Engineering Beam Theories for Helicopter Rotor Blades,” Journal of Aircraft, Vol. 31, No. 3, pp. 473–479.Google Scholar
  71. Kvaternik, R. G., White, W. F. Jr. and Kaza, K. R.V. (1978) “Nonlinear Flap-Lag-Axial Equations of a Rotating Beam with Arbitrary Precone Angle,” AIAA Paper No. 78-491.Google Scholar
  72. Lake, R. C., Nixon, M. W., Wilbur, M. L. Singleton, J. D. and Mirick, R. H. (1992) “A Demonstration of Passive Blade Twist Control Using Extension-Twist Coupling,” Paper AIAA-92-2468-CR, SDM Conference, Dallas, Texas.Google Scholar
  73. Lee, H. P. (1993) “Vibration of an Inclined Rotating Cantilever Beam With Tip Mass,” Journal of Vibration and Acoustics, Trans. ASME, 115, July, pp. 241–245.Google Scholar
  74. Lee, S. Y. and Kuo, Y. H., (1992) “Bending Vibrations of a Rotating Non-Uniform Beam with an Elastically Restrained Root,” Journal of Sound and Vibration, Vol. 154, No. 3, pp.441–451.CrossRefGoogle Scholar
  75. Lee, S.Y. and Lin, S. M. (1994) “Bending Vibration of Rotating Nonuniform Timoshenko Beams with an Elastically Restrained Root,” Journal of Applied Mechanics, Trans. ASME, Paper No. 94-WA/APM-8.Google Scholar
  76. Leissa, A. and Co, C.M. (1984) “Coriolis Effects on the Vibration of Rotating Beams and Plates,” Proceedings of the 12th Southeastern Conference on Theoretical and Applied Mechanics, Callaway Gardens, Pine Mountain, GA, May 10–11, pp. 508–513.Google Scholar
  77. Librescu, L. (1975) Elastostatics and Kinetics of Anisotropic and Heterogeneous Shell-Type Structures, Noordhoff International Publishing, Leyden, Netherlands, pp. 560–598.Google Scholar
  78. Librescu, L. and Song, O. (1991) “Behavior of Thin-Walled Beams Made of Advanced Composite Materials and Incorporating Non-Classical Effects,” Applied Mechanics Reviews, Vol. 44, No. 11, Part 2, November, pp. 174–180.Google Scholar
  79. Librescu, L. and Thangjiham, S. (1991) “Analytical Studies on Static Aeroelastic Characteristics for Composite Forward-Swept Wing Aircraft,” Journal of Aircraft, Vol. 28, No. 2, pp. 151–157.Google Scholar
  80. Librescu, L. and Song, O. (1992) “On the Static Aeroelastic Tailoring of Composite Aircraft Swept Wings Modelled as Thin-Walled Beam Structures,” Composites Engineering, Vol. 2, No. 5–7, pp. 497–512.Google Scholar
  81. Librescu, L., Song, O. and Rogers, C. A. (1993) “On Adaptive Vibration Behavior of Cantilevered Structures Modelled as Composite Thin-Walled Beams,” International Journal of Engineering Science, Vol. 31, No. 5, pp. 775–792.CrossRefGoogle Scholar
  82. Librescu, L., Meirovitch, L. and Song, O. (1996a) “Refined Structural Modeling for Enhancing Vibrational and Aeroelastic Characteristics of Composite Aircraft Wings,” La Recherche Aerospatiale, 1, pp. 23–35.Google Scholar
  83. Librescu, L., Meirovitch, L. and Song, O. (1996b) “Integrated Structural Tailoring and Control Using Adaptive Materials for Advanced Aircraft Wings,” Journal of Aircraft, Vol. 22, No. 1, Jan.–Feb., pp. 203–213.Google Scholar
  84. Librescu, L., Lin, W., Nemeth, M. P. and Starnes, Jr., J. H., (1996c) “Vibration of Geometrically Imperfect Panels Subjected to Thermal and Mechanical Loads,” Journal of Spacecraft and Rockets, Vol. 33, No. 2, March–April, pp. 285–291.Google Scholar
  85. Librescu, L., Lin, W., Nemeth, M. P. and Starnes, Jr., J. H., (1996d) “Frequency-Load Interaction of Geometrically Imperfect Curved Panels Subjected to Heating,” AIAA Journal, Vol. 34, No. 1, pp. 166–177.Google Scholar
  86. Librescu, L., Meirovitch, L. and Na, S. S. (1997) “Control of Cantilevers Vibration via Structural Tailoring and Adaptive Materials,” AIAA Journal, Vol. 35, No. 8, August pp. 1309–1315.Google Scholar
  87. Librescu, L., Song, O. and Kwon, H. D. (1999) “Vibration and Stability Control of Gyroelastic Thin-Walled Beams via Smart Materials Technology,” in Smart Structures, J. Holnicki-Szulk and J. Rodellar, (Eds.), Kluwer Academic Publication, pp. 163–172.Google Scholar
  88. Librescu, L. and Na, S. S. (2001) “Active Vibration of Thin-Walled Tapered Beams Using Piezoelectric Strain Actuation,” Journal of Thin-Walled Structures, Vol. 39, No. 1, pp. 65–68.Google Scholar
  89. Librescu, L., Oh, S-Y. and Song, O. (2003) “Spinning Thin-Walled Beams Made of Functionally Graded Materials: Modeling, Vibration and Instability,” European Journal of Mechanics A/Solids, Vol. 23, No. 3, pp. 499–515.Google Scholar
  90. Librescu, L., Oh, S-Y. and Song, O. (2005) “Thin-Walled Beams Made of Functionally Graded Materials and Operating in a High Temperature Environment: Vibration and Stability,” Journal of Thermal Stresses, Vol. 28, Nos. 6–7, pp. 649–712.Google Scholar
  91. Lin, S. M. (1997) “Vibration of Elastically Restrained Nonuniform Beams with Arbitrary Pretwist,” AIAA Journal, Vol. 35, No. 11, pp. 1681–1687.zbMATHGoogle Scholar
  92. Lo, H. and Renbarger, J. L. (1952) “Bending Vibrations of a Rotating Beam,” Proceedings of the First U. S. National Congress of Applied Mechanics, New York, N.Y., pp. 75–79.Google Scholar
  93. Lo, H., Goldberg, J. E. and Bogdanoff, J. L. (1960) “Effect of Small Hub-Radius Change on Bending Frequencies of a Rotating Beam,” Journal of Applied Mechanics, Trans. ASME, Vol. 27, September, pp. 548–550.Google Scholar
  94. Loy, C. T., Lam, K. Y. and Reddy, J. N. (1999) “Vibration of Functionally Graded Cylindrical Shells,” International Journal of Mechanical Sciences, Vol. 41, No. 3, pp. 309–324.CrossRefGoogle Scholar
  95. Mansfield, E. H. and Sobey, A. J. (1979) “The Fibre Composite Helicopter Blade — Part I: Stiffness Properties: Part II: Prospects for Aeroelastic Tailoring,” Aeronautical Quarterly, Vol. 30, No. 2, pp. 413–449.Google Scholar
  96. McGee, O. G. (1992) “Influence of Warping-Pretwist Coupling on the Torsional Vibration of Centrifugally-Stressed Cantilevers with Thin-Walled Open Profiles,” Computers & Structures, Vol, 42, No. 2, pp. 175–195.zbMATHGoogle Scholar
  97. Na, S. S. and Librescu (2000) “Modeling and Vibration Feedback Control of Rotating Tapered Beams Incorporating Adaptive Capabilities,” Recent Advanced in Solids and Structures-2000, PVP-Vol. 415, H. H. Chung and Y. W. Kwon (Eds.), ASME, New York, pp. 35–43.Google Scholar
  98. Na, S. S., Librescu, L. and Shim J-K. (2003a) “Modeling and Bending Vibration Control of Nonuniform Thin-Walled Rotating Beams Incorporating Adaptive Capabilities,” International Journal of Mechanical Sciences, Vol. 45, No. 8, pp. 1347–1367.CrossRefGoogle Scholar
  99. Na, S. S., Librescu, L. and Jung, H. (2003b) “Vibration Control of Rotating Composite Thin-Walled Beams in a Temperature Environment,” in Proceedings of the 5th International Congress on Thermal Stresses and Related Topics, Blacksburg, VA, June 8–11, L. Librescu and P. Marzocca (Eds.), Vol. 2, WA-6-4-(1-4).Google Scholar
  100. Na, S. S. and Librescu, L. and Jung, H. (2004) “Dynamics and Active Bending Vibration Control of Turbomachinery Rotating Blades Featuring Temperature-Dependent Material Properties,” Journal of Thermal Stresses, Vol. 24, pp. 625–644.Google Scholar
  101. Na, S. S., Librescu, L., Rim, S. and Jeong, I-J., (2004) “Free Vibration and Control of Composite Non-Uniform Thin-Walled Beams Featuring Bending-Bending Elastic Coupling,” Proceeding of the IMECE 2004, ASME International Mechanical Engineering Congress, November 13–19, 2004, Anaheim, Califormia.Google Scholar
  102. Nagaraj, V. T. and Sahu, N. (1982) “Torsional Vibration of Non-Uniform Rotating Blades with Attachment Flexibility,” Journal of Sound and Vibration, Vol. 80, No. 3, pp. 401–411.CrossRefGoogle Scholar
  103. Nixon, M.W. (1987) “Extension-Twist Coupling of Composite Circular Tubes with Application to Tilt Rotor Blade Design,” 28th Structure, Structural Dynamics and Materials Conference, April 6–8, Monterey, CA, AIAA Paper No. 87-0772, pp. 295–303.Google Scholar
  104. Nixon, M. W. (1989) “Analytical and Experimental Investigations of Extension-Twist-Coupled Structures,” George Washington University Masters Thesis, Hampton, VA.Google Scholar
  105. Nixon, M.W. (1992) “Parameter Studies for Tiltrotor Aeroelastic Stability in High-Speed Flight,” AIAA-92-5568-CR.Google Scholar
  106. Noda, N. and Jin, Z. H. (1993) “Thermal Stress Intensity Factors for a Crack in a Strip of a Functionally Gradient Material,” International Journal of Solids and Structures, Vol. 30, pp. 1039–1056.CrossRefGoogle Scholar
  107. Noor, A. K. and Burton, W. S. (1992) “Computational Models for High-Temperature Multilayered Composite Plates and Shells,” Applied Mechanics Reviews, Vol. 45, No. 10, pp. 414–446.Google Scholar
  108. Oh, S-Y., Song, O. and Librescu, L. (2003a) “Effects of Pretwist and Presetting on Coupled Bending Vibrations of Rotating Composite Beams,” International Journal of Solids and Structures, Vol. 40, pp. 1203–1224.CrossRefGoogle Scholar
  109. Oh, S-Y., Librescu, L. and Song, O. (2003b) “Thin-Walled Rotating Blades Made of Functionally Graded Materials: Modeling and Vibration Analysis,” AIAA 2003-1541, 44th AIAA/ASME/ASCE/AHS Structures, Structural Dynamics, and Materials Conference, Norfolk, VA April 7–10.Google Scholar
  110. Oh, S-Y., Librescu, L. and Song, O. (2003c) “Thin-Walled Rotating Blades Made of Functionally Graded Materials: Thermoelastic Modeling and Vibration Analysis,” in Thermal Stresses 03, Vol. 1, MA-2-5-1-MA-2-5-4, L. Librescu and P. Marzocca (Eds.), Virginia Tech, Blacksburg, VA, USA.Google Scholar
  111. Oh, S-Y., Librescu, L. and Song, O. (2003d) “Thermoelastic Modeling and Vibration of Functionally Graded Thin-Walled Rotating Blades,” AIAA Journal, Vol. 41, No. 10, pp. 2051–2060.Google Scholar
  112. Oh, S-Y., Librescu, L. and Song, O. (2003e) “Vibration of Turbomachinery Rotating Blades Made-Up of Functionally Graded Materials and Operating in a High Temperature Field,” Acta Mechanica, Vol. 166, pp. 69–87.CrossRefGoogle Scholar
  113. Oh, S-Y., Librescu, L. and Song, O. (2004) “Thin-Walled Rotating Composite Blades Featuring Extension-Twist Elastic Coupling,” AIAA-2004-2049, 45th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics & Materials Conference, Palm Springs, CA April 19–22.Google Scholar
  114. Oh, S-Y., Librescu, L. and Song, O. (2005) “Modeling and Vibration of Thin-Walled Rotating Composite Blades Featuring Extension-Twist Elastic Coupling,” The Aeronautical Journal, Vol. 109, May, No. 1095, pp. 233–246.Google Scholar
  115. Oh, S-Y. (2004) Personal Communication.Google Scholar
  116. Palazotto, A.N. and Linnemann, P.E. (1991) “Vibration and Buckling Characteristics of Composite Cylindrical Panels Incorporating the Effects of a Higher Order Shear Theory,” International Journal of Solids and Structures, Vol. 28, No. 3, pp. 341–361.CrossRefGoogle Scholar
  117. Peters, D. A. (1973) “An Approximate Solution for the Free Vibrations of Rotating Uniform Cantilever Beams,” NASA TM X-62, 299, September.Google Scholar
  118. Peters, D. A. (1995) “Aeroelastic Response of Rotorcraft,” in a Modern Course in Aeroelasticity, (Third Edition), Edited by E. H. Dowell, Kluwer Academic Publishers, Dordrecht, The Netherlands.Google Scholar
  119. Pindera, M-J. and Aboudi, J. (2000) “A Coupled Higher-Order Theory for Cylindrical Structural Components with Bi-Directionally Graded Microstructures,” NASA CR 210350, NASA-Glenn Research Center, Cleveland, OH.Google Scholar
  120. Pradhan, S. C., Loy, C. T., Lam, K. Y. and Reddy, J. N. (2000) “Vibration Characteristics of Functionally Graded Cylindrical Shells Under Various Boundary Conditions,” Journal of Applied Acoustics, Vol. 61, No. 1, pp. 119–129.Google Scholar
  121. Praveen, G. N. and Reddy, J. N. (1998) “Nonlinear Transient Thermoelastic Analysis of Functionally Graded Ceramic-Metal Plates,” International Journal of Solids Structures, Vol. 35, No. 33, pp. 4457–4476.Google Scholar
  122. Putter, S. and Manor, H. (1978), “Natural Frequencies of Radial Rotating Beams,” Journal of Sound and Vibrations, Vol. 56, No. 2, pp. 175–185.Google Scholar
  123. Qin, Z. and Librescu, L. (2001) “Static and Dynamic Validations of a Refined Thin-Walled Composite Beam Model,” AIAA Journal, Vol. 39, No. 12, pp. 2422–2424.Google Scholar
  124. Qin, Z. and Librescu, L. (2002) “On a Shear-Deformable Theory of Anisotropic Thin-Walled Beams: Further Contribution and Validations,” Composite Structures, Vol. 56, No. 4, pp. 345–358.CrossRefGoogle Scholar
  125. Rand, O. (1991) “Periodic Response of Thin-Walled Composite Helicopter Rotor Blades,” Journal of the American Helicopter Society, Vol. 36, No. 4, pp. 3–11.Google Scholar
  126. Rand, O. (1996) “Analysis of Composite Rotor Blades,” in Numerical Analysis and Modelling of Composite Materials, J. W. Bull, Editor, Blackie Academic and Professional, Chapman and Hall, pp. 1–26.Google Scholar
  127. Rao, J. S. (1971) “Flexural Vibration of Pre-Twisted Beams of Rectangular Cross-Section,” Journal of the Aeronautical Society of India, Vol. 23, No. 1, pp. 62–64.Google Scholar
  128. Rao, J. S. (1977), “Coupled Vibrations of Turbomachine Blades,” The Shock Vibration Bulletin, Vol. 47, pp. 107–125.Google Scholar
  129. Rao, J. S. (1991) Turbomachine Blade Vibration, John Wiley & Sons, New York, Chickester, Brisbane, Toronto, Singapore.Google Scholar
  130. Reddy, J. N. and Chin, C. D. (1998) “Thermomechanical Analysis of Functionally Graded Cylinders and Plates,” Journal of Thermal Stresses, Vol. 21, pp. 593–626.Google Scholar
  131. Reddy, J.N. (2000) “Analysis of Functionally Graded Plates,” International Journal of Numerical Meth. Engr., No. 47, pp. 663–684.zbMATHGoogle Scholar
  132. Rehfield, L. W. (1985) “Design Analysis Methodology for Composite Rotor Blades,” AFWALTR-85-3094, June, pp. (V(a)-1)–(V(a)-15).Google Scholar
  133. Rehfield, L.W. and Atilgan, A. R. (1989) “Toward Understanding the Tailoring Mechanisms for Thin-Walled Composite Tubular Beams,” in Proceeding of the First USSR-USA Symposium on Mechanics of Composite Materials, Riga, Latvia, USSR, May 23–26, 1989, S. W. Tsai, J. M. Whitney, T. W. Choi and R. M. Jones (Eds.), ASME, pp. 187–196.Google Scholar
  134. Rosen, A. and Friedmann, P. (1978) “Nonlinear Equations of Equilibrium for Elastic Helicopter or Wind Turbine Blades Undergoing Moderate Deformation,” University of California at Los Angeles, School of Engineering and Applied Science Report, UCLA-ENG-7718, DOE/NASA/3082-78/1, NASA CR-159478.Google Scholar
  135. Rosen, A. (1978, 1980) “The Effect of Initial Twist on the Torsional Rigidity of Beams-Another Point of View,” Technion, Department of Aeronautical Engineering, TAE Report No. 360, published also in 1980, Journal of Applied Mechanics, ASME Vol. 47, pp. 389—393.Google Scholar
  136. Rosen, A., Loewy, R. G., Mathew, M. B. (1987), “Use of Twisted Principal Coordinates and Non-Physical Coordinates in Blade Analysis, Vertica, Vol. 11, 541–572.Google Scholar
  137. Rosen, A. (1991) “Structural and Dynamic Behavior of Pretwisted Rods and Beams,” Applied Mechanics Reviews, Vol. 44, No. 12, art 1, pp. 483–515.Google Scholar
  138. Sabuncu, M. (1985) “Coupled Vibration Analysis of Blades with Angular Pretwist of Cubic Distribution,” AIAA Journal, Vol. 23, No. 9, pp. 1424–1430.Google Scholar
  139. Sankar, B. V. (2001) “An Elasticity Solution for Functionally Graded Beams,” Composites Science and Technology, Vol. 61, pp. 689–696.CrossRefGoogle Scholar
  140. Sankar, B. V. and Tzeng, T. J. (2002) “Thermal Stresses in Functionally Graded Beams,” AIAA Journal, Vol. 40, No. 6, pp. 1228–1232.Google Scholar
  141. Shen, H.-S. (2002) “Postbuckling Analysis of Axially-Loaded Functionally Graded Cylindrical Shells in Thermal Environments,” Composites Science and Technology, Vol. 62, pp. 977–987.Google Scholar
  142. Slyper, H. A. (1962) “Coupled Bending Vibration of Pretwisted Cantilever Beams,” Journal of Mechanical Engineering Sciences, Vol. 4, No. 4, pp. 365–379.Google Scholar
  143. Song, O. and Librescu, L. (1993) “Free Vibration of Anisotropic Composite Thin-Walled Beams of Closed Cross-Section Contour,” Journal of Sound and Vibration, Vol. 167, No. 1, pp. 129–147.CrossRefGoogle Scholar
  144. Song, O., Librescu, L. and Rogers, C. A. (1994) “Adaptive Response Control of Cantilevered Thin-Walled Beams Carrying Heavy Concentrated Masses,” Journal of Intelligent Materials Systems and Structures, Vol. 5, No. 1, January, pp. 42–48.Google Scholar
  145. Song, O. and Librescu, L. (1995) “Bending Vibration of Cantilevered Thin-Walled Beams Subjected to Time-Dependent External Excitations,” Journal of the Acoustical Society of America, Vol. 98, No. 1, pp. 313–319.CrossRefGoogle Scholar
  146. Song, O. and Librescu, L. (1996) “Bending Vibrations of Adaptive Cantilevers with External Stores,” International Journal of Mechanical Sciences, Vol. 28, No. 5, pp. 483–498.Google Scholar
  147. Song, O. and Librescu, L. (1997) “Structural Modeling and Free Vibration Analysis of Rotating Composite Thin-Walled Beams,” Journal of the American Helicopter Society, Vol. 42, No. 4, pp. 358–369.Google Scholar
  148. Song, O. and Librescu, L. (1999) “Modeling and Dynamic Behavior of Rotating Blades Carrying a Tip Mass and Incorporating Adaptive Capabilities,” Acta Mechanica,Vol. 134, pp. 169–197.CrossRefGoogle Scholar
  149. Song, O., Librescu, L. and Oh, S-Y. (2001a) “Vibration of Pretwisted Adaptive Rotating Blades Modeled as Anisotropic Thin-Walled Beams,” AIAA Journal, Vol. 39, No. 2, February, pp. 285–295.Google Scholar
  150. Song, O., Librescu, L. and Oh, S.-Y (2001b) “Dynamic of Pretwisted Rotating Thin-Walled Beams Operating in a Temperature Environment,” Journal of Thermal Stresses, Vol. 24, No. 3, pp. 255–279.Google Scholar
  151. Song, O, Oh, S-Y. and Librescu, L. (2002) “Dynamic Behavior of Elastically Tailored Rotating Blades Modeled as Pretwist Thin-Walled Beams and Incorporating Adaptive Capabilities,” International Journal of Rotating Machinery, Vol. 8, No. 1.Google Scholar
  152. Stafford, R. O. and Giurgiutiu, V. (1975) “Semi-Analytic Methods for Rotating Timoshenko Beams,” International Journal of Mechanical Sciences, Vol. 17, pp. 719–727.CrossRefGoogle Scholar
  153. Stemple, A. D. and Lee, S.W. (1989) “Finite Element Modeling for Composite Beams Undergoing Large Deflections with Arbitrary Cross Sectional Warping,” Int. of J. Numerical Methods in Engineering, Vol. 28, No. 9, pp. 2143–2160.Google Scholar
  154. Subrahmanyam, K. B., Kulkarni, S. V. and Rao, J. S. (1981) “Coupled Bending-Bending Vibrations of Pretwisted Cantilever Blading Allowing for Shear Deformation and Rotary Inertia by Reissner Method,” International Journal of Mechanical Sciences, Vol. 23, pp. 517–530.CrossRefGoogle Scholar
  155. Subrahmanyam, K. B. and Kaza, K. R. V. (1985) “Finite Difference Analysis of Torsional Vibrations of Pretwisted, Rotating, Cantilever Beams with Effects of Warping,” Journal of Sound and Vibration, Vol. 99, No. 2, pp. 213–224.CrossRefGoogle Scholar
  156. Subrahmanyam, K. B. and Kaza, K. R.V. (1986) “Vibration and Buckling of Rotating Pretwisted, Preconed Beams Including Coriolis Effects,” Journal of Vibration, Acoustics, Stress and Reliability in Design, Trans. ASME, Vol. 108, April, pp. 140–149.Google Scholar
  157. Subrahmanyam, K. B., Kaza, K. R. V., Brown, G. V. and Lawrence, C. (1987) “Nonlinear Vibration and Stability of Rotating Pretwisted, Preconed Blades Including Coriolis Effects,” Journal of Aircraft, Vol. 24, No. 5, pp. 342–352.Google Scholar
  158. Tang, S. (1969) “Natural Vibration of Isotropic Plates with Temperature-Dependent Properties,” AIAA Journal, Vol. 7, No. 4, pp. 725–727.zbMATHGoogle Scholar
  159. Tanigawa, Y. (1992) “Theoretical Approach of Optimum Design for a Plate of Functionally Gradient Materials Under Thermal Loading,” Thermal Shock and Thermal Fatigue Behavior of Advanced Ceramics, NATO ASI Series E, Vol. 241, pp. 171–180.Google Scholar
  160. Tomar, J. A. and Jain, R. (1985) “Thermal Effect on Frequencies of Coupled Vibrations of Pretwisted Rotating Beams,” AIAA Journal, Vol. 23, No. 8, pp. 1293–1296.Google Scholar
  161. Touloukian, Y. S. (1967) Thermophysical Properties of High Temperature Solid Materials, Macmillan, New York.Google Scholar
  162. Tsuiji, T. (1976) “Torsion of Pretwisted Thin-Walled Beams,” Theoretical and Applied Mechanics, Vol. 26, University of Tokyo Press, pp. 75–80.Google Scholar
  163. Tzou, H. S. and Zhong, J. R. (1991) “Adaptive Piezoelectric Shell Structures: Theory and Experiments,” 32nd AIAA SDM Conference, Baltimore, Maryland, April 8–12, Paper No. AIAA-91-1238.Google Scholar
  164. Tzou, H. S. (1993) Piezoelectric Shells, Distributed Sensing and Control of Continua, Kluwer Academic Publ., Dordrecht/Boston/London.Google Scholar
  165. Vel, S. S. and Batra, R. C., (2002) “Exact Solution for Thermoelastic Deformations of Functionally Graded Thick Rectangular Plates,” AIAA Journal, Vol. 40, No. 7, pp. 1421–1433.Google Scholar
  166. Venkatesan, C. and Nagaraj, C. T., (1981) “On the Axial Vibrations of Rotating Bars,” Journal of Sound and Vibration, Vol. 74, No. 1, pp. 143–147.CrossRefGoogle Scholar
  167. Volovoi, V. V., Hodges, D. H., Cesnik, C. E. S. and Popescu, B., (2001) “Assessment of Beam Modeling Methods for Rotor Blades Applications,” Mathematical and Computer Modelling, Vol. 33, Nos. 10–11, pp. 1099–1112.Google Scholar
  168. Vorob’ev, I. S. (1988) Vibrations of Turbomachinery Blades (In Russian),” Kiev, Naukova, Dumka.Google Scholar
  169. Wang, J. T. S., Mahrenholtz, O., Böhm, J. (1976), “Extended Galerkin’s Method for Rotating Beam Vibrations Using Legendre Polynomials, Solid Mechanics Archives, Vol. 1, pp. 341–356.Google Scholar
  170. Washizu, K. (1964) “Some Considerations on a Naturally Curved and Twisted Slender Beams,” Journal of Mathematics and Physics, Vol. 43, No. 2, pp. 111–116.zbMATHMathSciNetGoogle Scholar
  171. Wright, A. D., Smith, C. E., Thresher, R. W. and Wang, J. L. C., (1982) “Vibration Modes of Centrifugally Stiffened Beams,” Journal of Applied Mechanics, Trans. ASME, Vol. 49, March, pp. 197–202.Google Scholar
  172. Yokoyama, T. (1988), “Free Vibration Characteristics of Rotating Timoshenko Beams,” International Journal of Mechanical Sciences, Vol. 30, No. 10, pp. 743–755.CrossRefzbMATHGoogle Scholar
  173. Yokoyama, T. and Markiewicz, M. (1993) “Flexural Vibrations of Rotating Timoshenko Beam with Tip Mass,” Asia-Pacific Vibration Conference, Kitakyushu, Japan, Nov. pp. 382–387.Google Scholar
  174. Yoo, H. H., Kwak, J.Y. and Chung, J. (2001) “Vibration Analysis of Rotating Pre-Twisted Blades with a Concentrated Mass,” Journal of Sound and Vibration, Vol. 240, No. 5, pp. 891–908.CrossRefGoogle Scholar
  175. Young, M. I. (1973) “The Influence of Pitch and Twist on Blade Vibration,” Journal of Aircraft, Vol. 10, No. 6, pp. 383–384.Google Scholar

Copyright information

© Springer 2006

Personalised recommendations