Abstract and numerical aspects of the problem concerning the computation of eigenfrequencies of continuous systems
Abstract
A summary is provided of the main results, both theoretical and numerical, which have been obtained since 1964 in studies concerned with the computation of the eigenfrequencies of continuous systems. Attention is given to the unitary equivalence of positive compact operators and the approximation of the eigenvalues, Green's operator for general elliptic operators and the upper approximation of their orthogonal invariants, the multiplicity of eigenvalues, the Betti numbers of a compact orientable differentiable manifold as multiplicities of eigenvalues, the eigenvalue problem for a clamped plate, and approximations and estimates for eigenvectors.
- Publication:
-
Trends in applications of pure mathematics to mechanics
- Pub Date:
- 1976
- Bibcode:
- 1976tapm.symp...63F
- Keywords:
-
- Continuum Mechanics;
- Eigenvalues;
- Eigenvectors;
- Elliptic Differential Equations;
- Operators (Mathematics);
- Approximation;
- Boundary Value Problems;
- Dirichlet Problem;
- Invariance;
- Orthogonal Functions;
- Rayleigh-Ritz Method;
- Physics (General)