Open AccessOn Variational Principles and Matrix Methods in Elastodynamics
Author(s) -
Kennett B. L. N.
Publication year - 1974
Publication title -
geophysical journal of the royal astronomical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.302
H-Index - 168
eISSN - 1365-246X
pISSN - 0016-8009
DOI - 10.1111/j.1365-246x.1974.tb04092.x
Subject(s) - variational principle , matrix (chemical analysis) , mathematical analysis , mathematics , computation , hamilton's principle , wave propagation , classical mechanics , physics , equations of motion , materials science , quantum mechanics , composite material , algorithm
Summary The equations of elastodynamics are conveniently derived from a variational principle and by considering an averaged Lagrangian for a harmonic field in a stratified elastic medium it is possible to obtain a set of coupled first order differential equations as the Hamilton's canonical equations. These equations are precisely those which form the basis of the matrix methods commonly used for handling elastic wave propagation in layered media. The variational results are extended to deal with the more complicated ‘Minor Matrix’ system of Gilbert & Backus which improves the numerical accuracy of the computations. The equivalent of Rayleigh's principle is derived for this system and used to consider the effects of perturbations on surface wave dispersion.