Homogenization of eigenvalue problems of elasticity in perforated domains

Article type: Research Article

Authors: Nandakumar, A.K.

Affiliations: TIFR Centre, Post Box No. 1234, Indian Institute of Science, Bangalore 560 012, India

Note: [] Correspondence to: A.K. Nandakumar, TIFR Centre, Post Box No. 1234, Indian Institute of Science, Bangalote 560 012, India.

Abstract: In this paper, we study the homogenization of eigenvalue problem associated with the elasticity system in a periodically (with period ε>0, a small parameter) perforated domain with tiny holes. The critical size of the holes aε is given by aε=C0εN/N−2 if N≥3 and aε=exp (−C0/ε2) if N=2, where C0 is a constant and N is the dimension. We will study the above eigenvalue problem as ε→0 and eigenvalues and eigenvectors.

DOI: 10.3233/ASY-1994-9403

Journal: Asymptotic Analysis, vol. 9, no. 4, pp. 337-358, 1994