Free Vibration of Elastic Solids: Effect of Boundary Perturbation on Fundamental Frequencies

  • N. V. Movchan
Conference paper
Part of the Solid Mechanics and Its Applications book series (SMIA, volume 91)


The objective of the paper is to study the effect of imperfections (such as cracks, cavities or inclusions) on dynamic characteristics of elastic solids. As an illustrative example, we consider in-plane vibrations of a two-dimensional elastic domain with a small cavity. We present results that indicate the effect of the geometry and location of the cavity on fundamental frequencies, and show that the change in frequency is specified by an integral characteristic that may have the same value for a certain class of defects. The latter implies that the solution of the inverse problem is not unique; one can find a certain class of cavities which produce the same change in frequency.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    Maz’ya, V.G., Nazarov, S.A., and Plamenevskii, B.A. (1984) Asymptotic expansions of eigenvalues of elliptic boundary value problems for the Laplace operator in domains with small voids. Izv. Acad. Nauk SSSR. Ser. Mat. (Math. USSR-Izv.), 48(2), 347.MathSciNetGoogle Scholar
  2. [2]
    Movchan, A.B., and Movchan, N.V. (1995) Mathematical Modelling of Solids with Nonregular Boundaries. CRC Press.Google Scholar
  3. [3]
    Movchan, A.B. and Serkov, S.K. (1997) The Pólya-Szegö matrices in asymptotic models of dilute composites. Euro. J. Appl. Math., 8, 595.MathSciNetGoogle Scholar
  4. [4]
    Ward, M.J., and Keller, J.B. (1993) Strong localized perturbations of eigenvalue problems. SIAM J. Appl. Math., 53, 770.MathSciNetGoogle Scholar
  5. [5]
    Ward, M.J., Henshaw, W.D., and Keller, J.B. (1993) Summing logarithmic expansions for singularly perturbed eigenvalue problems. SIAM J. Appl. Math., 53, 799.MathSciNetGoogle Scholar

Copyright information

© Kluwer Academic Publishers 2001

Authors and Affiliations

  • N. V. Movchan
    • 1
  1. 1.Department of Mathematical SciencesUniversity of LiverpoolLiverpoolUK

Personalised recommendations