Free oscillations of the earth
Abstract
Using general curvilinear coordinates, the fundamental relations of continuum mechanics have been derived. Description in terms of Lagrange's and Euler's coordinates was distinguished on principle. This mathematical and physical method was used to derive the equations of motion and boundary conditions of elastic oscillations of a body prestressed by finite static stresses. It is assumed that the free oscillations cause small deviations from equilibrium position, such that the tensor of finte deformations can be approximated by the tensor of small deformations. The expression of boundary conditions at a fluid boundary, using Lagrange's description, is relatively complicated. From the point of view of this theory, the case of free elastic gravitational oscillations, treated for a general model of the earth, is particular.
 Publication:

Travaux Geophysiques
 Pub Date:
 1987
 Bibcode:
 1987TraGe..32..117M
 Keywords:

 Free Vibration;
 Geodynamics;
 Boundary Conditions;
 Boundary Value Problems;
 Elastic Properties;
 Equations Of Motion;
 Operators (Mathematics);
 Periodic Variations;
 Secular Variations;
 Spherical Coordinates;
 Stress Tensors;
 Variational Principles;
 Vibration Mode