Dynamic Problems in Isotropic Plates

  • Victor Birman
Part of the Solid Mechanics and Its Applications book series (SMIA, volume 178)


Plates found in applications are often subject to dynamic loads. These loads can be directly applied to the plate (i.e., wave impact, wind gusts, blast overpressure, impact by birds or other objects, etc.). In numerous applications, dynamic loads are applied to the plate by unbalanced rotating machinery supported by the plate or through the kinematic excitation by beams that support both the plate and the engine. In all these problems, the structural integrity of the plate has to be analyzed to prevent immediate failure due to excessive dynamic stresses or fatigue damage as a result of continuous large-amplitude vibrations. The present chapter provides an insight into vibrations of isotropic plates, including free and forced vibrations, response to non-harmonic dynamic loads, large-amplitude vibrations and dynamic instability. Dynamic problems of composite plates that can be investigated using an extension of analytical and numerical tools employed for the analysis of their isotropic counterparts are outside the scope of this book. An exception applicable to the analysis of composite plates is vibration of plates reinforced with stringers whose constitutive equations and equations of motion resemble those of composite plates (Sect. 4.5).


Fundamental Frequency Free Vibration Fatigue Damage Composite Plate Dynamic Instability 
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  1. Birman, V. (1989). Problems of dynamic buckling of antisymmetric rectangular laminates. Composite Structures, 12, 1–15.CrossRefGoogle Scholar
  2. Birman, V., & Bert, C. W. (1987). Behavior of laminated plates subjected to conventional blast. International Journal of Impact Engineering, 6, 145–155.CrossRefGoogle Scholar
  3. Birman, V., & Byrd, L. W. (2007). Modeling and analysis of functionally graded materials and structures. Applied Mechanics Reviews, 60, 195–216.CrossRefGoogle Scholar
  4. Birman, V., & Byrd, L. W. (2008). Stability and natural frequencies of functionally graded stringer-reinforced plates. Composites: Part B, 39, 816–825.CrossRefGoogle Scholar
  5. Bolotin, V. V. (1954). Selected nonlinear problems of dynamic stability of plates, communications of the Academy of Science of the USSR. Department of Technical Sciences. (No. 10, pp. 47–59).Google Scholar
  6. Bolotin, V. V. (1956). Dynamic stability of elastic systems. Moscow: Gostechizdat (English translation: Holden Day, San Francisco, 1964).Google Scholar
  7. Chia, C. Y. (1980). Nonlinear analysis of plates. New York: McGraw-Hill.Google Scholar
  8. Genin, G. M., & Birman, V. (2009). Micromechanics and structural response of functionally graded particulate-matrix, fiber-reinforced composites. International Journal of Solids and Structures, 46, 2136–2150.CrossRefzbMATHGoogle Scholar
  9. Gupta, A. D., Gregory, F. H., Bitting, R. L., & Bhattacharya, S. (1987). Dynamic response of an explosively loaded hinged rectangular plate. Computers & Structures, 26, 339–344.CrossRefGoogle Scholar
  10. Houlston, R., Slater, J. E., Pegg, N., & DesRochers, C. G. (1985). On analysis of structural response of ship panels subject to air blast loading. Computers & Structures, 21, 273–289.CrossRefGoogle Scholar
  11. Houlton, R., & DesRochers, C. G. (1987). Nonlinear structural response of ship panels subjected to air blast loading. Computers & Structures, 26, 1–15.CrossRefGoogle Scholar
  12. Leissa, A. W. (1973). The free vibration of rectangular plates. Journal of Sound and Vibration, 31, 257–293.zbMATHCrossRefGoogle Scholar
  13. Librescu, L., & Nosier, A. (1990). Response of shear deformable elastic laminated composite flat panels to sonic boom and explosive blast loading. AIAA Journal, 28, 345–352.zbMATHCrossRefGoogle Scholar
  14. Nashif, A. D., Jones, D. I. G., & Henderson, J. P. (1985). Vibration damping. New York: Wiley.Google Scholar
  15. Nguyen, C. H., Butukuri, R. R., Chandrashekhara, K. & Birman, V. (2011). Dynamics and buckling of sandwich panels with stepped facings. International Journal of Structural Stability and Dynamics (in press).Google Scholar
  16. Vol’mir, A. C. (1972). Nonlinear dynamics of plates and shells. Moscow: Nauka Publishers.Google Scholar
  17. Xie, W.-C. (2006). Dynamic stability of structures. New York: Cambridge University Press.zbMATHGoogle Scholar

Copyright information

© Springer Science+Business Media B.V. 2010

Authors and Affiliations

  1. 1.Engineering Education CenterMissouri University of Science and TechnologySt. LouisUSA

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