ASYMPTOTIC BEHAVIOR OF THE SPECTRAL MATRIX OF THE OPERATOR OF ELASTICITY

Abstract

Let D be a bounded , open , and connected domain in R3 with boundary D'; set Lv = b2grad div v - a2 rot rot v with a , b constant. The object of this paper is to find the asymptotic representation of the spectral matrix of the problem Lv + v = 0 , x D , v = 0 , x D' , a parameter. If D' is sufficiently smooth, this problem determines a sequence k of positive eigenvalues such that k ; when k ; each k is associated with an eigenfunction vk with components vkj. Set = , k = k , and *(x; ) = 3i=1 ii(x,x; ). With the aid of a Tauberian theorem one arrives at the result *(x; ) 6 12 ( a32 + b31 ) 3/2. (Author)

Document Details

Document Type
Technical Report
Publication Date
Jan 01, 1961
Accession Number
AD0258240

Entities

People

  • E.j. Pellicciaro
  • F.j. Bureau

Organizations

  • University of Liège

Tags

DTIC Thesaurus Topics

  • Boundaries
  • Eigenvalues
  • Eigenvectors
  • Elastic Properties
  • Mathematical Analysis
  • Mathematics
  • Sequences
  • Sequences (Mathematics)
  • Series (Mathematics)

Fields of Study

  • Mathematics

Readers

  • Analytical Mechanics
  • Linear Algebra