Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Ambartsumian, S. A. (1964) Theory of Anisotropic Shells, NASA Report, TTF-118.
Armanios E. A. and Badir, A. M. (1995) “Free Vibration Analysis of Anisotropic Thin-Walled Closed-Section Beams,” AIAA Journal, Vol. 33, No. 10, pp. 1905–1910.
Atilgan, A. R. and Rehfield, L. W. (1990) “Vibrations of Composite Thin-Walled Beams with Design in Elastic Couplings,” in Achievements in Composites in Japan and United States, Proceedings of the Fifth Japan-U.S. Conference on Composite Materials, June 24–27, Tokyo, Japan, pp. 687–694.
Bailey, T. and Hubbard, J. E., Jr. (1985) “Distributed Piezoelectric-Polymer Active Vibration Control of a Cantilever Beam,” Journal of Guidance, Control and Dynamics, Vol. 8, No. 5, Sept.–Oct., pp. 605–611.
Bank, L. C. and Kao, C. K. (1989) “The Influence of Geometric and Material Design Variables on the Free Vibration of Thin-Walled Composite Material Beams,” Journal of Vibration, Acoustics, Stress and Reliability in Design, Vol. 111, pp. 290–297.
Banerjee, J. R. (1989) “Coupled Bending-Torsional Dynamic Stiffness Matrix for Beam Elements,” International Journal of Numer. Meth. Eng., Vol. 28, pp. 1283–1298.
Baz, A. (1997) “Dynamic Boundary Control Beams Using Active Constrained Layer Damping,” Journal of Vibration and Acoustics, Trans. ASME, Vol. 119, April, pp. 266–272.
Belinskiy, B. P. and Dauer, J. P. (1998) “Eigenoscillations of Mechanical Systems with Boundary Conditions Containing the Frequency,” Quarterly of Applied Mathematics, Vol. LVI, No. 3, pp. 521–541.
Berlincourt, D. A., Curran, Dr. R. and Jaffe, H. (1964) “Piezoelectric and Piezomagnetic Materials and Their Function in Transducers,” in Physical Acoustics — Principles and Methods, E. P. Mason (Ed.), Vol. 1, Part A, Academic Press, New York, pp. 202–204.
Bishop, R. E. D., Price, W.G. and Chang, Z.X. (1983) “On The Structural Dynamics of a Vlasov Beam,” Proceedings of the Royal Society London, Vol. A388, pp. 49–83.
Budiansky, B. and Kruszewski, T. (1952) “Transverse Vibrations of Hollow Thin-Walled Cylindrical Beams,” NACA TN 2682.
Chopra, I. (2002) “Review of State of Art of Smart Structures and Integrated Systems,” AIAA Journal, Vol. 40, No. 11, pp. 2145–2187.
Crawley, E. F. (1994) “Intelligent Structures for Aerospace; A Technology Overview and Assessment,” AIAA Journal, Vol. 31, No. 8, pp. 1689–1699.
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.
Chandra, R. and Chopra, I. (1992a) “Experimental-Theoretical Investigation of the Vibration Characteristics of Rotating Composite Box Beams,” Journal of Aircraft, Vol. 29, No. 4, pp. 657–664.
Chandra, R. and Chopra, I. (1992b) “Structural Response of Composite Beams and Blades with Elastic Couplings,” Composites Engineering, Vol. 2, No. 5–7, pp. 437–374.
Downs, B. (1977) “Transverse Vibrations of Cantilever Beams Having Unequal Breadth and Depth,” Journal of Applied Mechanics, Trans. ASME, Vol. 44, pp. 737–742.
Gay, D. and Boudet, R. (1980) “A Technical Theory of Dynamical Torsion for Beams of Any Cross-Section Shapes,” ASME Paper No. 79-DET-59, pp. 1–6.
Gern, F. H. and Librescu, L. (1998a) “Static and Dynamic Aeroelasticity of Advanced Aircraft Wings Carrying External Stores,” AIAA Journal, Vol. 36, No. 7, July, pp. 1121–1129.
Gern, F.H. and Librescu (1998b) “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.
Hallauer, W. L., Liu, R. Y. L. (1982) “Beam Bending-Torsion Dynamic Stiffness Method for Calculation of Exact Vibration Modes,” Journal of Sound and Vibration, Vol. 85, pp. 105–113.
Hashemi, S. M. and Richard, J. M. (2000) “A Dynamic Finite Element (DFE) Method for Free Vibrations of Bending-Torsion Coupled Beams,” Aerospace Science and Technology, Vol. 4, No. 1, pp. 41–55.
Hodges, D. H., Atilgan, A. R., Fulton, M.V. and Rehfield, L. W., (1991) “Free Vibration Analysis of Composite Beams,” Journal of the American Helicopter Society, Vol. 36, No. 3, pp. 36–47.
Housner, G. W. and Keightley, W. O. (1962) “Vibration of Linearly Tapered Cantilever Beams,” Journal of the Engineering Mechanics Division, Trans. ASME, April EM2, pp. 95–122.
Inman, D. J. (2000) “Active Modal Control for Smart Structures,” Phil. Trans. R. Soc. London, A, 359, pp. 205–219.
Karpouzian, G. and Librescu, L. (1994a) “Comprehensive Model of Anisotropic Composite Aircraft Wings Suitable for Aeroelastic Analyses,” Journal of Aircraft, Vol. 31, No. 3, May–June, pp. 703–712.
Karpouzian, G. and Librescu, L. (1994b) “Three-Dimensional Flutter Solution of Aircraft Wings Composed of Advanced Composite Materials,” in Proceedings of the AIAA/ASME/ASCE/AHS/ASC 35th Structures, Structural Dynamics and Materials Conference, Washington, DC, AIAA Paper 94-1490, pp. 2851–2856.
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.
Ko, K-E and Kim, J-H. (2003) “Thermally Induced Vibrations of Spinning Thin-Walled Composite Beams,” AIAA Journal, Vol. 41, No. 2, pp. 296–303.
Kosmatka, J. B. and Lakes, R. C. (1996) “Extension-Twist Behavior of Initially Twisted Composite Spars for Till-Rotor Applications,” AIAA-96-1565-CP.
Lagnese, J. E. and Lions, J. L. (1988) Boundary Stabilization of Thin Plates, Collection RMA, Masson, Paris.
Lagnese, J.E. (1989) Boundary Stabilization of Thin Plates, SIAM Studies in Applied Mechanics, SIAM, Philadelphia, PA.
Lake, R. C. (1990) “Investigation of the Use of Extension-Twist Coupling in Composite Rotor Blades for Application to Tiltrotor Aircraft,” The Third Workshop on Dynamic and Aeroelastic Stability Modeling of Rotorcraft Systems, Duke University, Durham, North Carolina, March 12–14.
Lake, R.C., Nixon, M.W., Wilbur, M. L., Singleton, J.D. and Mirick, P.H. (1992) “A Demonstration of Passive Blade Twist Control Using Extension Twisting Coupling,” NASA TM-107642 AVSCOMTR-92-B-010.
Lake, R. C., Izadpanah, A. P. and Bancom, R. B. (1993) “Experimental and Analytical Investigation of Dynamic Characteristics of Extension-Twist-Coupled Composite Tubular Spars,” NASA TP-3225, ARL-TR-30.
Laudiero, F. and Savoia, M. (1991) “The Shear Strain Influence on the Dynamic of Thin-Walled Beams,” Thin-Walled Structures, Vol. 11, pp. 375–407.
Librescu, L. (1975) Elastostatics and Kinetics of Anisotropic and Heterogeneous Shell-Type Structures, Noordhoff, Leyden, The Netherlands.
Librescu, L. and Thangjitham, S. (1991) “Analytical Studies on Static Aeroelastic Behavior of Forward Swept Composite Wings Structures,” Journal of Aircraft, Vol. 28, No. 2, pp. 151–157.
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, Nos. 5–7 (special issue: Use of Composites in Rotorcraft and Smart Structures), pp. 497–512.
Librescu, L., Meirovitch, L. and Song, O. (1993a) “A Refined Structural Model of Composite Aircraft Wings for the Enhancement of Vibrational and Aeroelastic Response Characteristics,” in Proceedings of the 34th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference, LaJolla, CA, April 19–22, AIAA Paper 93-1536CP.
Librescu, L., Song, O. and Rogers, C. A. (1993b) “Adaptive Vibrational Behavior of Cantilevered Structures Modelled as Composite Thin-Walled Beams,” International Journal of Engineering Science, Vol. 31, No. 5, pp. 775–792.
Librescu, L., Meirovitch, L. and Song, O. (1996a) “Integrated Structural Tailoring and Control Using Adaptive Materials for Advanced Aircraft Wings,” Journal of Aircraft, Vol. 33, No. 1, Jan.–Feb., pp. 203–213.
Librescu, L., Meirovitch, L. and Song, O. (1996b) “Refined Structural Modeling for Enhancing Vibrational and Aeroelastic Characteristics of Composite Aircraft Wings,” La Recherche Aerospatiale, Vol. 1, pp. 23–35.
Librescu, L., Meirovitch, L. and Na, S. S. (1997) “Control of Cantilever Vibration Via Structural Tailoring and Adaptive Materials,” AIAA Journal, Vol. 35, No. 8, August, pp. 1309–1315.
Librescu, L. and Na, S. S. (1997) “Vibration and Dynamic Response Control of Cantilevers Carrying Externally Mounted Stores,” Journal of the Acoustical Society of America, Vol. 102, No. 6, December, pp. 3516–3522.
Librescu, L. and Na, S. S. (1998a) “Bending Vibration Control of Cantilevers Via Boundary Moment and Combined Feedback Control Law,” Journal of Vibration and Controls, Vol. 4, No. 6, pp. 733–746.
Librescu, L. and Na, S. S. (1998b) “Boundary Control of Free and Forced Oscillation of Shearable Thin-Walled Beam Cantilevers,” European Journal of Mechanics/A Solids, Vol. 17,4, pp. 687–700.
Librescu, L., Na, S. S. and Park, S. (2000) “Dynamics and Active Feedback Control of Wing-Type Structures Modeled as Thin-Walled Beams: Implications of Beam Cross-Section Nonuniformity,” Journal of the Chinese Society of Mechanical Engineers, Vol. 21, No. 1, pp. 87–96.
Librescu, L. and Na, S. S. (2001) “Active Vibration Control of Doubly Tapered Thin-Walled Beams Using Piezoelectric Actuation,” Thin-Walled Structures, Vol. 39, No. 1, pp. 65–82.
Librescu, L., Qin, Z. and Ambur, D. R. (2003) “Implications of Warping Restraint on Statics and Dynamics of Elastically Tailored Thin-Walled Composite Beams,” International Journal of Mechanical Sciences, Vol. 45, No. 8, pp. 1247–1267.
Loewy, R. G. (1997) “Recent Developments in Smart Structures with Aeronautical Applications,” Smart Materials and Structures, Vol. 5, Oct. pp. 11–42.
Meirovitch, L. (1997) Principles and Techniques of Vibrations, Prentice Hall, Englewood Cliffs, NJ.
Mindlin, R. D. (1951) “Influence of Rotatory Inertia and Shear Flexural Motions of Isotropic, Elastic Plates,” Journal of Applied Mechanics, Trans. ASME, Vol. 18, No. 1, pp. 31–38.
Na, S. S. and Librescu, L. (1998) “Oscillation Control of Cantilevers via Smart Materials Technology and Optimal Feedback Control: Actuator Location and Power Consumption Issues,” Smart Materials and Structures, Vol. 7, No. 6, pp. 833–842.
Na, S. S. and Librescu, L. (1999) “Dynamic Behavior of Aircraft Wings Modeled as Doubly-Tapered Composite Thin-Walled Beams,” PVP, Vol. 398, Recent Advances in Solids and Structures, 1999, Y.W. Kwon and H. H. Chung (Eds.), 1999 ASME International Mechanical Engineering Congress Exposition, Nashville, TN, November 14–19, pp. 59–68.
Na, S. S. and Librescu, L. (2000a) “Dynamic Response of Adaptive Cantilevers Carrying External Stores and Subjected to Blast Loading,” Journal of Sound and Vibration, Vol. 231, No. 4, pp. 1039–1055.
Na, S. S. and Librescu, L. (2000b) “Optimal Vibration Control of Thin-Walled Anisotropic Cantilevers Exposed to Blast Loading,” Journal of Guidance, Control, and Dynamics, Vol. 23, No. 3, pp. 491–500.
Na, S. S. and Librescu, L. (2001a) “Dynamic Response of Elastically Tailored Adaptive Cantilevers of Nonuniform Cross Section Exposed to Blast Pressure Pulses,” International Journal of Impact Engineering, Vol. 25, No. 9, pp. 847–867.
Na, S. S. (2001b) Personal Communication.
Oh, S-Y., Song, O. and Librescu, L. (2003) “Effects of Pretwist and Presetting on Coupled Bending Vibrations of Rotating Composite Beams,” International Journal of Solids and Structures, Vol. 40, pp. 1203–1224.
Park, C. and Chopra, I. (1996) “Modeling Piezoceramic Actuation of Beams in Torsion,” AIAA Journal, Vol. 34, No. 12, pp. 2582–2589.
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.
Qin, Z. and Librescu, L. (2002a) “Static/Dynamic Solutions and Validation of a Refined Anisotropic Thin-Walled Beam Model,” AIAA-2002-1394, in Proceedings of 43rd AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference, 10th AIAA/ASME/AHS Adaptive Structures Conference, April 22–25, Denver, Co.
Qin, Z. and Librescu, L. (2002b) “On a Shear-Deformable Theory of Anisotropic Thin-Walled Beams: Further Contribution and Validations,” Composite Structures, Vol. 56, No. 4, June, pp. 435–358.
Rao, J. S. (1991) Turbomachine Blade Vibration, John Wiley & Sons, New York, Chester, Toronto.
Rehfield, L.W., Atilgan, A. R. and Hodges, D. H. (1990) “Nonclassical Behavior of Thin-Walled Composite Beams with Closed Cross Sections,” Journal of the American Helicopter Society, Vol. 35, pp. 42–50.
Song, O. and Librescu, L. (1991) “Free Vibration and Aeroelastic Divergence of Aircraft Wings Modelled as Composite Thin-Walled Beams,” in Proceedings of the 32nd Structures, Structural Dynamics and Material Conference, Baltimore, Maryland, Paper AIAA 91-1187-CP.
Song, O., Librescu, L. and Rogers, C. A. (1992) “Application of Adaptive Technology to Static Aeroelastic Control of Wing Structures,” AIAA Journal, Vol. 30, No. 12, pp. 2882–2889, December.
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.
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, June, pp. 313–319.
Song, O. and Librescu, L. (1996) “Bending Vibrations of Adaptive Cantilevers with External Stores,” International Journal of Mechanical Sciences, Vol. 38, No. 5, pp. 483–498.
Song, O. and Librescu, L. (1997a) “Structural Modeling and Free Vibration Analysis of Rotating Composite Thin-Walled Beams,” Journal of the American Helicopter Society, Vol. 42, No. 4, October, pp. 358–369.
Song, O. and Librescu, L. (1997b) “Anisotropy and Structural Coupling on Vibration and Instability of Spinning Thin-Walled Beams,” Journal of Sound and Vibration, Vol. 204, No. 3, pp. 477–494.
Song, O., Ju, J. S. and Librescu L. (1998) “Dynamic Response of Anisotropic Thin-Walled Beams to Blast and Harmonically Oscillating Loads,” International Journal of Impact Engineering, Vol. 21, No. 8, pp. 663–682.
Song, O., Kim, J-B. and Librescu, L. (2001) “Synergistic Implications of Tailoring and Adaptive Materials Technology on Vibration Control of Anisotropic Thin-Walled Beams,” International Journal of Engineering Science, Vol. 39, No. 1, December, pp. 71–94.
Song, O., Oh, S-Y. and Librescu, L. (2002) “Dynamic Behavior of Elastically Tailored Rotating Blades Modeled as Pretwisted Thin-Walled Beams and Incorporating Adaptive Capabilities,” International Journal of Rotating Machinery, Vol. 8, No. 1, pp. 13–25.
Sunar, M. and Rao, S. S. (1999) “Recent Advances in Sensing and Control of Flexible Structures via Piezoelectric Materials Technology,” Applied Mechanics Reviews, Vol. 52, No. 1, pp. 1–16.
Thangjitham, S. and Librescu, L. (1991) “Free Vibration Characteristics of Anisotropic Composite Wing Structures,” in Proceedings of the 32nd SDM Structures, Structural Dynamics and Material Conference, Paper AIAA-01-1185, Baltimore, Maryland, April.
Tzou, H. S. and Zhong, J. P. (1992) “Adaptive Piezoelectric Structures: Theory and Experiment,” Active Materials and Adaptive Structures, Materials and Structures Series, G. J. Knowles (Ed.), Institute of Physics Publ., pp. 219–224.
Tzou, H. S. (1993) Piezoelectric Shells, Distributed Sensing and Control of Continua, Kluwer Academic Publication, Dordrecht.
Tzou, H. S., Johnson, D. D. and Liu, K. J. (1999) “Damping Behavior of Cantilevered Structronic Systems with Boundary Control,” Journal of Vibration and Acoustics, Trans. ASME, Vol. 126, July, pp. 402–407.
Weisshaar, T. A. and Foist, B. L. (1985) “Vibration Tailoring of Advanced Composite Lifting Surfaces,” Journal of Aircraft, Vol. 25, No. 4, pp. 364–371.
Rights and permissions
Copyright information
© 2006 Springer
About this chapter
Cite this chapter
(2006). Free Vibration. In: Thin-Walled Composite Beams. Solid Mechanics and Its Applications, vol 131. Springer, Dordrecht. https://doi.org/10.1007/1-4020-4203-5_6
Download citation
DOI: https://doi.org/10.1007/1-4020-4203-5_6
Publisher Name: Springer, Dordrecht
Print ISBN: 978-1-4020-3457-2
Online ISBN: 978-1-4020-4203-4
eBook Packages: EngineeringEngineering (R0)