Fundamentals Concepts in Elasticity, Mechanics and Wave Propagation

  • Srinivasan Gopalakrishnan
  • Massimo Ruzzene
  • Sathyanarayana Hanagud
Part of the Springer Series in Reliability Engineering book series (RELIABILITY)


This chapter provides an overview of fundamental concepts in elasticity and structural mechanics which will support the understanding of the material presented in the later chapters. The topics covered include basics of elasticity, mechanics of composites, beam and plate theories, and wave propagation.


Discrete Fourier Transform Traction Vector First Order Shear Deformation Theory Evanescent Mode Governing Differential Equation 


  1. 1.
    Caviglia G, Morro A (1992) Inhomogeneous waves in solids and fluids. World Scientific, SingaporeMATHGoogle Scholar
  2. 2.
    Clough RW, Penzin J (1975) Dynamics of structures. Printice-Hall, New YorkGoogle Scholar
  3. 3.
    Doyle JF (1997) Wave propagation in structures. Springer, New YorkMATHCrossRefGoogle Scholar
  4. 4.
    Golub G, Van Loan C (1989) Matrix computations. Johns Hopkins University Press, BaltimoreGoogle Scholar
  5. 5.
    Gopalakrishnan S, Chakraborty A, Roy Mahapatra D (2008) Spectral finite element method. Springer, LondonMATHGoogle Scholar
  6. 6.
    Jones RM (1975) Mechanics of composites material. McGraw Hill, New YorkGoogle Scholar
  7. 7.
    Krezig E (1992) Advanced engineering mathematics, 9th edn. McGraw Hill, New YorkGoogle Scholar
  8. 8.
    Lancaster P (1966) Lambda matrices and vibrating systems. Pergamon Press, OxfordMATHGoogle Scholar
  9. 9.
    Lancaster P (1969) Theory of matrices. Acaxdemic Press, New YorkMATHGoogle Scholar
  10. 10.
    Mindlin RD, Herrmann G (1950) A one dimensional theory of compressional waves in an elastic rod. In: Proceedings of first U.S. national congress of applied mechanics, pp 187–191Google Scholar
  11. 11.
    Nayfeh AH (1995) Wave propagation in layered anisotropic media. North Holland, AmsterdamMATHGoogle Scholar
  12. 12.
    Reddy JN (1997) Mechanics of laminated composite plates. CRC Press, Boca RatonMATHGoogle Scholar
  13. 13.
    Roy Mahapatra D, Gopalakrishnan S, Sankar TS (2000) Spectral-element-based solutions for wave propagation analysis of multiply connected laminated composite beams. J Sound Vib 237(5):819–836CrossRefGoogle Scholar
  14. 14.
    Roy Mahapatra D, Gopalakrishnan S (2002) A spectral finite element model for analysis of axial–flexural–shear coupled wave propagation in laminated composite beams. Compos Struct 59(1):57–88Google Scholar
  15. 15.
    Timoshenko SP (1921) On the correction factor for shear of the differential equation for transverse vibrations of bars of uniform cross-section. Philosophical Magazine, p 744Google Scholar
  16. 16.
    Tisseur F, Meerbergen K (2001) The quadratic eigenvalue problem. SIAM Rev 43(2):235–286MathSciNetMATHCrossRefGoogle Scholar
  17. 17.
    Tsai SW, Hahn HT (1980) Introduction to composite materials. Technomic, WestportGoogle Scholar
  18. 18.
    Varadan VK, Vinoy KJ, Gopalakrishnan S (2006) Smart material systems and MEMS. Wiley, ChichesterCrossRefGoogle Scholar

Copyright information

© Springer-Verlag London Limited 2011

Authors and Affiliations

  • Srinivasan Gopalakrishnan
    • 1
  • Massimo Ruzzene
    • 2
  • Sathyanarayana Hanagud
    • 3
  1. 1.Department of Aerospace EngineeringIndian Institute of ScienceBangaloreIndia
  2. 2.School of Aerospace Engineering, School of Mechanical EngineeringGeorgia Institute of TechnologyAtlantaUSA
  3. 3.School of Aerospace EngineeringGeorgia Institute of TechnologyAtlantaUSA

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