Dynamic variational-asymptotic procedure for laminated composite shells-part I: Low-frequency vibration analysis

Journal of Applied Mechanics, Transactions ASME

Volumn 76, Issue 1, 2009, Pages 1-7

  Lee, Chang Yong ^a   Hodges, Dewey H ^a  

^a Georgia Institute of Technology   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ASYMPTOTIC PROCEDURES; COMPLEX GEOMETRIES; DIMENSIONAL REDUCTION; ENERGY FUNCTIONALS; HIGH FREQUENCY HF; HIGH-FREQUENCY VIBRATIONS; LAMINATED COMPOSITE SHELL; LAYERED SHELL; LONG WAVELENGTH; LOW FREQUENCY; LOW-FREQUENCY VIBRATION; NUMERICAL MODELING; POSITIVE DEFINITE; SHELL THEORY; SHORT-WAVELENGTH; THEORETICAL FOUNDATIONS; THREE DIMENSIONAL STRESS STATE; THREE-DIMENSIONAL ELASTICITY; VARIATIONAL ASYMPTOTIC METHODS; ASYMPTOTIC METHOD; HIGH-FREQUENCY EFFECTS; ISOTROPIC SHELLS; MONOCLINIC MATERIALS; NORMAL DISPLACEMENT; SHORT WAVES; TIME-SCALES; TWO-DIMENSIONAL THEORY;

LAMINATED COMPOSITES; SHELLS (STRUCTURES); VIBRATION ANALYSIS; APPROXIMATION THEORY;

ASYMPTOTIC ANALYSIS;

EID: 70949098198     PISSN: 00218936     EISSN: 15289036     Source Type: Journal    
DOI: 10.1115/1.3002761     Document Type: Article

References (30)

1. Langley, R. S., and Bardell, N. S., 1998, "A Review of Current Analysis Capabilities Applicable to the High Frequency Vibration Prediction of Aerospace Structures," Aeronaut. J., 102, pp. 287-297.
2. Kaplunov, J. D., Kossovich, L. Y., and Nolde, E. V., 1998, Dynamics of Thin Walled Elastic Bodies, Academic, New York.
3. Leissa, A. W., 1973, "Vibration of Shells," NASA, Report No. SP 288.
4. Noor, A. K., and Burton, W. S., 1989, "Assessment of Shear Deformation Theories for Multilayered Composite Plates," Appl. Mech. Rev., 42(1), pp. 1-13.
5. Qatu, M. S., 2002, "Recent Research Advances in the Dynamic Behavior of Shells, 1989-1999, Part 1: Laminated Shells," Appl. Mech. Rev., 55(7), pp. 1989-2000.
6. Qatu, M. S., 2002, "Recent Research Advances in the Dynamic Behavior of Shells, 1989-1999, Part 2: Homogeneous Shells," Appl. Mech. Rev., 55(5), pp. 415-434.
7. Reddy, J. N., 2003, Mechanics of Laminated Composite Plates and Shells: Theory and Analysis, 2nd ed., CRC, Boca Raton, FL.
8. Amabili, M., and Païdoussis, M. P., 2003, "Review of Studies on Geometrically Nonlinear Vibrations and Dynamics of Circular Cylindrical Shells and Panels, With and Without Fluid-Structure Interaction," Appl. Mech. Rev., 56(4), pp. 349-381.
9. Le, K. C., 1997, "High Frequency Vibrations and Wave Propagation in Elastic Shells: Variational-Asymptotic Approach," Int. J. Solids Struct., 34(30), pp. 3923-3939.
10. Kienzler, R., Altenbach, H., and Ott, I., 2004, Theories of Plates and Shells: Critical Review and New Applications, Springer, New York.
11. Braga, A. M. B., and Rivas A, C. E., 2005, "High-Frequency Response of Isotropic-Laminated Cylindrical Shells Modeled by a Layer-Wise Theory," Int. J. Solids Struct., 42, pp. 4278-4294.
12. Yang, S., and Yuan, F. G., 2005, "Transient Wave Propagation of Isotropic Plates Using a Higher-Order Plate Theory," Int. J. Solids Struct., 42, pp. 4115-4153.
13. Andrianov, I. V., Awrejcewicz, J., and Barantsev, R. G., 2003, "Asymptotic Approaches in Mechanics: New Parameters and Procedures," Appl. Mech. Rev., 56(1), pp. 87-110.
14. Berdichevsky, V. L., 1983, Variational Principles of Continuum Mechanics, Nauka, Moscow.
15. Losin, N. A., 1997, "Asymptotics of Flexural Waves in Isotropic Elastic Plates," ASME J. Appl. Mech., 64, pp. 336-342.
16. Losin, N. A., 1998, "Asymptotics of Extensional Waves in Isotropic Elastic Plates," ASME J. Appl. Mech., 65, pp. 1042-1047.
17. Berdichevsky, V. L., 1979, "Variational-Asymptotic Method of Constructing a Theory of Shells," Prikl. Mat. Mekh., 43(3), pp. 664-687.
18. Berdichevsky, V. L., 1980, "Variational-Asymptotic Method of Constructing the Nonlinear Shell Theory," Theory of Shells, W. T. Koiter and G. K. Mikhailov, eds., North-Holland, Amsterdam, pp. 137-161.
19. Yu, W., Hodges, D. H., Volovoi, V. V., and Cesnik, C. E. S., 2002, "On Timoshenko-Like Modeling of Initially Curved and Twisted Composite Beams," Int. J. Solids Struct., 39(19), pp. 5101-5121.
20. Hodges, D. H., 2006, Nonlinear Composite Beam Theory, AIAA, Reston, VA.
21. Yu, W., Hodges, D. H., and Volovoi, V. V., 2002, "Asymptotic Generalization of Reissner-Like Composite Plate Theory With Accurate Strain Recovery," Int. J. Solids Struct., 39(20), pp. 5185-5203.
22. Yu, W., Hodges, D. H., and Volovoi, V. V., 2002, "Asymptotic Generalization of Reissner-Mindlin Theory: Accurate Three-Dimensional Recovery for Composite Shells," Comput. Methods Appl. Mech. Eng., 191(44), pp. 5087-5109.
23. Le, K. C., 1999, Vibrations of Shells and Rods, 1st ed., Springer, Germany.
24. Danielson, D. A., 1997, Vectors and Tensors in Engineering and Physics, 2nd ed., Pereus Books, Cambridge, MA.
25. Hodges, D. H., Ati{dotless}lgan, A. R., and Danielson, D. A., 1993, "A Geometrically Nonlinear Theory of Elastic Plates," ASME J. Appl. Mech., 60, pp. 109-116.
26. Hodges, D. H., Yu, W., and Patil, M. J., 2006. "Geometrically-Exact, Intrinsic Theory for Dynamics of Moving Composite Plates and Shells," Proceedings of the 47th Structures, Structural Dynamics, and Materials Conference.
27. Danielson, D. A., and Hodges, D. H., 1987, "Nonlinear Beam Kinematics by Decomposition of the Rotation Tensor," ASME J. Appl. Mech., 54(2), pp. 258-262.
28. Libai, A., and Simmonds, J. G., 1998, The Nonlinear Theory of Elastic Shells, 2nd ed., Cambridge University Press, Cambridge, New York.
29. Yu, W., and Hodges, D. H., 2004, "Geometrically Nonlinear Shear Deformation Theory for Composite Shells," ASME J. Appl. Mech., 71(1), pp. 1-9.
30. Lee, B. W., 1993. "Application of Variational-Asymptotic Method to Laminated Composite Plates," Ph.D. thesis, Aerospace Engineering, Georgia Institute of Technology, Atlanta, GA.