Lamb's problem for a linear viscoelastic medium

Technical Report · Mon Feb 01 04:00:00 EST 1988

OSTI ID:7125241

Pound, Michael J

Lamb's problem for an elastic medium is one of the fundamental theoretical problems in mathematical seismology. It has been essential to the understanding of the basic interaction of waves with surfaces, including the production of such surface effects as Rayleigh waves and head waves. All real materials, however, exhibit some dissipation, and the combined effect of dissipation and surface interactions has not been well understood, particularly in the case of transient phenomena. In this work, the distance generated in a semi-infinite linear viscoelastic medium due to an impulsive line load applied normally to the surface is investigated. Uniform asymptotic techniques based on the method of steepest descent are developed to construct the long-time solution for the half-space. It is found that the solution for long times consists primarily of a set of small amplitude ''precursor'' signals whose properties are determined largely by the initial elastic response of the medium, and a set of much larger amplitude smooth waves. It is these smooth waves, analogous to the viscoelastic ''main'' waves of one-dimensional studies, which occupy the bulk of the analysis, and some of these signals are found to exhibit some interesting and unexpected properties. The Archenbach-Chao solid (ACS) model was selected as the material model for this study primarily because of its desirable physical and mathematical properties, but the results are applicable, both qualitatively and quantitatively, to a broad class of viscoelastic materials that exhibit initial elasticity and have bounded creep function. 103 refs., 24 figs.

• Research Organization: Lawrence Livermore National Lab., CA (USA)
• DOE Contract Number: W-7405-ENG-48
• OSTI ID: 7125241
• Report Number(s): UCRL-53864; ON: DE88015408
• Country of Publication: United States
• Language: English

Related Subjects

58 GEOSCIENCES
580201* -- Geophysics-- Seismology & Tectonics-- (1980-1989)
99 GENERAL AND MISCELLANEOUS
990230 -- Mathematics & Mathematical Models-- (1987-1989)
COMPUTERIZED SIMULATION
ELASTICITY
MATHEMATICAL MODELS
MECHANICAL PROPERTIES
RAYLEIGH WAVES
SEISMIC P WAVES
SEISMIC S WAVES
SEISMIC SURFACE WAVES
SEISMIC WAVES
SEISMOLOGY
SIMULATION
SURFACE PROPERTIES
TENSILE PROPERTIES
WAVE PROPAGATION